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Università degli Studi di PaviaDottorato di Ricerca in

Ingegneria Elettronica, Informatica ed Elettrica

Ciclo XXIII

Three Laser Schemes for

Optical Chaotic Cryptography

Tesi di Dottorato di

Giuseppe Aromataris

Tutore: Prof. Valerio Annovazzi Lodi

Anno Accademico 2009/2010

CONTENTS

Introduction 1

1 Electrical injection with the three laser scheme 101.1 Secure data transmission scheme . . . . . . . . . . . . . . . . . 121.2 Numerical modeling . . . . . . . . . . . . . . . . . . . . . . . . 141.3 Message transmission in baseband . . . . . . . . . . . . . . . . 17

1.3.1 Working point choice . . . . . . . . . . . . . . . . . . . 171.3.2 Working point analysis . . . . . . . . . . . . . . . . . . 20

1.4 Message transmission on a carrier . . . . . . . . . . . . . . . . 31

2 Optical injection with the three laser scheme 352.1 All-optical three laser scheme . . . . . . . . . . . . . . . . . . 372.2 Numerical modeling . . . . . . . . . . . . . . . . . . . . . . . . 402.3 Message transmission in baseband . . . . . . . . . . . . . . . . 42

2.3.1 Common working point of open and close loop . . . . . 422.3.2 Open loop analysis . . . . . . . . . . . . . . . . . . . . 472.3.3 Close loop analysis . . . . . . . . . . . . . . . . . . . . 59

2.4 Message transmission on a carrier . . . . . . . . . . . . . . . . 73

3 Analysing signal using BER 773.1 Signal impairment due to white noise . . . . . . . . . . . . . . 793.2 Signal impairment due to residual chaos . . . . . . . . . . . . 84

Conclusions 90

Ph.D. research activity 92

Bibliography 95

i

INTRODUCTION

The purpose of cryptography is to transmit information in such a waythat access to it is exclusively reserved to an authorized recipient.

Standard cryptographic techniques are based on mathematical algorithmsimplemented with software. There are two branches of such cryptographictechniques: public-key encryption and secret-key encryption.

Public-key encryption is a cryptographic approach which involves the useof asymmetric key algorithms, used to create a key pair: a secret private keyand a published public key. Each user has a pair of cryptographic keys. Theprivate key is kept secret, while the public key may be widely distributed.Messages are encrypted with the recipient’s public key and can only be de-crypted with the corresponding private key. The keys are mathematicallyrelated, and the private key cannot feasibly be derived from the public key.The discovery of algorithms that can produce private/public key pairs hasrevolutionised the practice of cryptography at the beginning of the 1970s.Public-key cryptography offers increased security and convenience, indeedprivate keys never need to be transmitted or revealed to anyone.

In contrast, secret-key encryption employs symmetric key algorithms, anda single secret key must be shared and kept private by both sender andreceiver, for both encryption and decryption. The symmetric key algorithmsare computationally much faster than the asymmetric ones. However, themain practical problem with the secret-key encryption is exchanging a secretkey. In principle any two users who wish to communicate, could agree on akey in advance, but this is problematic: if a secure communication channelhas not been established, it is difficult to come up with one, avoiding the nonauthorized listener.

These algorithms, used for both methods, are safely made public, with-out currently compromising the security of a private cryptogram. However,

1

Introduction 2

both the continuous improvement of decrypting programs and the continuousincrease of computer speed threatens the safety of these procedures.

A more practical alternative to the software encryption can be done bytechniques belonging to the class of the hardware-key encryption: the quan-tum cryptography and the optical chaotic cryptography.

Quantum cryptography exploits the properties of quantum optics in orderto exchange a secret key. If a non authorized listener draws off the commu-nication channel, transmission errors occur due to the quantum-mechanicalnature of photons. The advantage of quantum cryptography over traditionalkey exchange methods is that the exchange of information can be shown to besecure in a very strong sense. Even when assuming hypothetical eavesdrop-pers with unlimited computing power, fundamental laws of physics guaranteethat the secret key exchange will be secure. However, due to low bit-rate (inthe order of tens of KHz) and the incompatibility with some key compo-nents (e. g. optical amplifiers) of the optical communication systems, thistechnique can be used only to exchange a secret key and is not suitable formessage bitstream encryption, at least up to now.

An alternative approach to realize secure transmissions can be done bythe optical chaotic cryptography, as proposed in this thesis work. Securetransmissions are achieved by message encryption directly performed at thephysical layer, using optical chaotic carriers generated by laser diodes oper-ating in a non-linear regime. The objective of chaos hardware encryption isto encode the information signal within a chaotic carrier generated by com-ponents whose physical, structural and operating parameters form the secretkey. Once information encoding is carried out, the chaotic carrier is sent byconventional means to the receiver. Decoding is then achieved directly inreal-time through the so-called chaos-synchronization process. If necessary,this method can integrate software encryption, thus supplying an additionalsecurity level.

The relevance of this last approach has mobilized scientific institutionsbelonging to different European Member States, resulting initially in theOCCULT1 project (FP5, 2001-2004), and later in the PICASSO2 project(FP6, 2006-2009).

Within the OCCULT project, theory, modeling and preliminary experi-mental work have been made with the aim to demonstrate the feasibility oftransmission and detection systems based on optical chaos encryption.

The ultimate goal of PICASSO has been the development of photonic

1OCCULT: Optical Chaos Communication Using Laser-diode Transmitters.2PICASSO: Photonic Integrated Components Applied to Secure chaoS encoded Optical

communications systems.

Introduction 3

components and subsystems to build chaos-based optical communication sys-tems. Within the framework of this project, design, fabrication and charac-terization of monolithic as well as of hybrid photonic integrated circuits havebeen realized. Different types of chaotic transmitter and receiver pairs havebeen developed in the C band of the telecommunications window. Finally,the validity of the security assumptions has been experimentally proved, andthe compatibility with the existing infrastructure has been investigated.

Highly considerable scientific results have been obtained with these twoprojects, as recognised by the EU reviewers.

Introduction 4

Cryptography using optical chaos

Optical chaotic cryptography [1, 2] is a hardware technique for securedata transmission, which makes use of a pair of semiconductor lasers routedto chaos. A standard telecommunication laser diode operating in a chaoticregime, for example by back-reflection from a remote mirror, exhibits an ex-tremely broadened spectrum, typically in the order of many tens of GHz. Inaddition, the laser emission is both amplitude and phase modulated, show-ing a non-periodic and very complex, apparently random, behavior, which,however, can be described on the basis of a deterministic model.

In the conventional communication systems, a semiconductor laser gener-ates a coherent optical carrier on which the information is encoded using oneof the many available modulation schemes. On the contrary, in the proposedapproach of chaos based communications, one of the sources is used for thetransmission, i. e. to codify the message with chaos, the other one is usedat the receiver for extracting the message.

In the basic scheme, the information is encoded with the chaotic carrier tostrongly reduce its signal to noise ratio. For example, an efficient method isbased on the optical chaotic carrier modulation by using an external opticalmodulator electrically driven by the information bitstream [3]. Assuminga high complexity in the carrier, it is practically impossible to extract theencoded information using conventional techniques, such as linear filtering,frequency domain analysis, phase space reconstruction or chaotic waveformautocorrelation analysis.

At the receiver side of the system a second chaotic oscillator is used andthe extraction of the hidden message from chaos is based on the synchro-nization of the transmitter and receiver lasers. In the context of chaoticcommunications terminology, synchronization means that the irregular timeevolution of the transmitter output, mainly in the optical power, can be per-fectly reproduced by the receiver (see figure 1), provided that transmitterand receiver lasers are twin, i. e. chaotic oscillators with very similar in-ternal parameters; typically, the two devices must be not only of the samemodel, but also picked up in close proximity from the same wafer. Notethat minor discrepancies between the two lasers can already result in poorsynchronization, i. e. poor reproduction of the transmitted chaotic carrier.

The key issue for efficient message decoding resides in the fact that thereceiver synchronizes to the chaotic oscillations of the transmitter withoutbeing affected by the encoded message. Synchronization can be obtainedby optical injection of a fraction of the transmitter laser output into thereceiver laser, which, under suitable conditions, replicates the chaotic regimeof the transmitter but does not replicate the message. Message extraction

Introduction 5

Figure 1: Basic scheme for optical chaotic cryptography.

is then performed by making the difference between the signal coming fromthe transmitter (chaotic carrier plus data), and the chaotic signal replicatedat the receiver.

The major advantages of chaos based secure communications are:

• Real time encoding.The synchronization process relies on the ultrafast dynamics of semi-conductor lasers, on the time response of the fast photodiodes and othernonlinear elements. Then, the information encoding process does notintroduce any additional delay relative to that of the conventional op-tical communication systems.

• Enhanced security.It is very difficult for an eavesdropper to force the system, indeed thekey relies on the use of twin lasers, in the same operating conditions.The similarity refers to:

– Semiconductor laser structure.

– Emission, e. g. emitting wavelength, slope efficiency, thresholdcurrent.

– Intrinsic parameters, e. g. linewidth enhancement factor, non lin-ear gain, photon lifetime, carrier lifetime, carrier density at trans-parency.

– Feedback loop characteristics, e. g. cavity length and cavity losses,for the all-optical scheme, possible non-linearity and delay for theoptoelectronic one.

– Operating parameters, e. g. bias current, feedback strength.

The above set of hardware-related parameters constitutes the key ofthe encryption procedure.

Introduction 6

• Compatibility with the installed network infrastructure.After initial investigations on the basic principles, more recently workhas been focused towards the application of chaotic cryptography toreal networks. Digital transmission on a metropolitan network has beenperformed [4]. Analog transmission of radio and video signals on opticalfibers has been also reported [5, 6]. Several basic functional blocks havebeen already studied and experimentally demonstrated, such as thechaotic signal repeater [7], modules for point-multipoint connections[8], for two channel transmission [9], for wavelength multiplexing [10]and for wavelength conversion [11]. Moreover, if necessary, chaos basedcommunications can be complemented with software encryption, thusproviding a higher security level.

The optical chaotic cryptography using the two-laser scheme has beenextensively investigated within both the OCCULT and PICASSO projects.However its major limitations in terms of security (non reported here) are dueto the employment of an asymmetric topology, since the transmitter injectsthe receiver. In this thesis we overcome this limitation, proposing two newschemes in a symmetric topology that use three lasers. A careful comparisonof the two topologies is beyond the scope of this thesis, and it will be theobject of future work.

Introduction 7

Ph.D. research activity

My research activity takes place within the European project PICASSO.In the last three years, in which I have worked towards the Ph.D. in Electron-ics Engineering, my interests have been focused on non-linear dynamics ofoptically injected semiconductor lasers, with particular regard on the studyof optical chaos properties, and numerical analysis of new chaos based com-munication systems. These activities are briefly listed below:

• Security analysis of the two-laser scheme.

• Wavelength conversion of a chaos masked message.

• Secure chaotic transmission in free space.

• Feasibility and security of new schemes using three lasers.

• Statistical properties of a signal impaired by chaos.

However, because of density of all arguments, being interested about newtopics, in the three chapters of this thesis, i will discuss only the last twopoints, briefly summarized in the following.

Contents of chapter 1

In chapter 1, we will propose an alternative to the basic scheme for op-tical chaotic cryptography, suitable for secure data transmission in a realoptical fiber network. In detail, by programs written in Matlab, we willshow secure data transmission using synchronized twin semiconductor lasersworking in a chaotic regime. They represent the transmitter and receiver ofour cryptographic scheme. Chaotic regime and synchronization are achievedby electrical injection into their pumps of a common chaotic driving signal.Results of simulations will be reported for the configuration in which thechaotic driving current is obtained by photodetecting the emission of a thirdlaser, the driver, routed to chaos by delayed optical feedback in a short cav-ity scheme. The driver is selected with different parameters with respect tothe laser pair. Numerical analysis will show that the synchronized matchedlasers have highly correlated emissions, whereas their correlation with thedriver is low.

Message encryption will be achieved by modulation of the transmitteremission, as in a standard Chaos Modulation (CM) scheme. Message re-covery is then performed by subtracting the chaos, locally generated by the

Introduction 8

synchronized receiver laser, from the composite signal (chaos plus message)obtained by photodetecting the transmitter emission.

The performances of such method will be numerically investigated usingthe the Lang-Kobayashi equations, opportunely modified, both for a messagein baseband and on a carrier, demonstrating effective message masking andmessage recovery. Laser and photodetector noise are taken into account.

Feasibility and security will be investigated and expressed in terms of Qfactor and Bit Error Rate (BER). In detail, the feasibility is studied by con-sidering that in real conditions two matched lasers may have slight differences(0.5%) in their internal parameters. In the condition of slight mismatch onthe main internal parameters of the licensed pair, synchronization and mes-sage recovery will be demonstrated. The security, instead, will be examinedconsidering the effect, on synchronization and message recovery, of a greaterparameter mismatch (5%) between transmitter and receiver. In this condi-tion, we will show that a non authorized listener cannot intercept the messageeven acting on all external parameters of the non licensed receiver. Moreover,we will also show that an eavesdropper cannot extract the message neitherusing a twin laser with the transmitter, with the aim to realise the chaoticcryptographic basic scheme, nor by performing the difference between thecomposite signal coming from the transmitter and the signal coming fromthe driver.


In chapter 2, we will propose another interesting alternative to the basicscheme for optical chaotic cryptographic. In detail, we will numerically showsecure data transmission using twin semiconductor lasers in which a commonchaotic dynamics is achieved by optical injection into the laser pair of acommon chaotic driving signal. The driving signal is generated by a thirdlaser, the driver, subject to delayed optical feedback, in a short cavity scheme.This laser is selected with different internal parameters with respect to thetwin pair, so that the emissions of the matched lasers are synchronized andhighly correlated, whereas their correlation with the driver is low.

The transmitter emission will be modulated by the digital message, as in astandard CM scheme. Then, the message recovery is obtained by subtracting,from the transmitted chaos-masked message, the chaos locally generated bythe synchronized receiver laser. Message transmission in baseband and on acarrier will be performed.

Numerical analysis on feasibility and security of this method, by inves-tigating the effect of parameter mismatch between transmitter and receiver,will be presented in the case of open loop, where the twin lasers are not sub-

Introduction 9

ject to local feedback, and they become chaotic only due to injection fromthe third laser. Besides the open loop case, in this thesis we consider thecase of close loop, where the transmitter and receiver lasers are both subjectto delayed optical feedback, and they are chaotic even in absence of injec-tion from the driver. The performances of the open and close loop will becompared and expressed in terms of Q factor and BER. Though the openloop scheme already offers a good security level, a specific advantage of theclose loop is that the message remains masked even in case of failure of thecommon driving laser. Moreover, the close loop scheme is harder to manageby an eavesdropper, since it is more critical to implement, and it is moresensitive to parameter mismatch, as it will be shown, thus requiring a moreaccurate trimming. Also the optical phase, because of external cavities, nowplay a role. As a final security check, we will demonstrate that a non licenseduser cannot extract the message neither building an open loop receiver fed bycomposite signal coming from the transmitter, nor performing the differencebetween the last one and the signal coming from the driver.

Simulations will be performed with the Lang-Kobayashi model, keepinginto account both laser and photodetector noise.

For the close loop case, a preliminary experimental evaluation will be alsoperformed using InP integrated modules.


With respect to traditional schemes of data transmission in optical fiber,where one of the reasons of receiving an impaired message is due to whitenoise, in the schemes based on optical chaotic cryptography, the messagedeterioration is mainly due to practical difficulty of extract the message fromchaos without damaging due to residual chaos. These errors are not neg-ligible, and they are the main reason of receiving a message whose qualityis lower when compared to that of the message sent. The quality of theextracted message, for the schemes proposed in chapters 1 and 2, is numer-ically performed by Q factor evaluation, from which the BER is obtained.This procedure is much faster than applying the BER definition. In addition,it is correct in the traditional schemes of data transmission, because of gaus-sian statistics of white noise. In chapter 3, we will see that the derivation ofBER from the Q factor is justified even for systems that use optical chaoticcryptography. Indeed, we will find that residual chaos, as white noise, hasgaussian statistics.

CHAPTER 1

ELECTRICAL INJECTION WITH THE THREE LASER SCHEME

In the basic cryptographic scheme [1, 2], designed for secure data trans-mission in optical fiber, one chaotic oscillator is used for the transmission,to codify the message with chaos [3], the other one is used at the receiverside, for extracting the message. Synchronization of the two chaotic lasersis obtained by optical injection of a fraction of the transmitter laser outputinto the receiver laser, which, under suitable conditions, replicates the chaoticregime of the transmitter but does not replicate the message. The messageextraction is then performed by making the difference between the currentobtained by photodetection of the transmitter emission (chaos plus message)and the chaotic signal replicated at the receiver side. Since effective synchro-nization relies on the use of twin lasers, that is lasers with the same internalparameters, it is very difficult for an eavesdropper to extract the message.

An alternative to this basic method is based on a scheme recently pro-posed by Yamamoto et al. [12], based on an idea of Uchida et al. [13].In their setup, optical injection from a chaotic driver laser is employed forinducing chaotic regime and synchronization into a couple of twin responselasers, the transmitter and the receiver. The correlated waveforms are usedfor generation and distribution of secret communication keys.

In addition to fiberoptic networks, transmission links based on Free SpaceOptics (FSO) technology, that take advantage of modulated laser beamtraveling in open space through the atmosphere, have been envisaged anddesigned. Point-to-point connections, between two locations on the line-of-sight, are commercially available [14]. Free Space Optics Links (FSOL) repre-sent an interesting alternative to fiber optics links for small and medium-sizeprivate networks because their installation and maintenance is less expensiveand because they are license free. Point to point optical interconnections

10

Electrical injection with the three laser scheme 11

may also work by diffuse radiation, exploiting reflection and diffusion of thewalls and the ceiling of a room [15]. Another important application of freespace optics technology is represented by optical transmission links betweensatellites. Information security remains, however, a major issue in free spaceoptical networks. The absence of protected propagation increases the riskof eavesdropping and makes this kind of systems intrinsically non secure.The chaotic cryptographic basic scheme, showed in the introduction, can beproposed, in principle, also for this application. However, the different char-acteristics of the transmitted signal suggest to consider a dedicated scheme.More specifically, a major improvement, in terms of cost and practical fea-sibility, would be offered by a scheme allowing electrical, instead of optical,signal amplification.

We have proposed a possible solution in [16], presenting a cryptographicscheme, compatible with free space optics technology for line-of-sight com-munication links. Starting from the scheme proposed by Yamamoto, we havereplaced the optical injection from the driver with electrical injection. Thetransmitter and receiver are routed into a synchronized chaotic regime bymeans of injection into their pumps of a common, chaotic driving signal, andwe have used this new scheme for secure data transmission in free space. Thereduced bandwidth requirements, with respect to fiber transmission, makethis approach attractive, since low cost Monolithic Microwave IntegratedCircuits (MMIC) can be used for signal amplification.

In this thesis, we further modify this scheme considering transmissionin optical fiber, neglecting all propagation losses and using Chaos Modula-tion (CM) [3] for message transmission instead of Chaos Shift Keying (CSK)[1]-[3] used in [16]. These modifications offer a larger synchronization band-width and higher bit rate for the transmitted message. Security has been alsoinvestigated in more detail, by considering the effect, on synchronization andmessage recovery, of parameter mismatch between transmitter and receiver,demonstrating that a non authorized listener cannot intercept the messageeven acting on all external parameters of the non licensed receiver. In addi-tion, we have also shown that an eavesdropper cannot extract the messageneither using a twin laser with the transmitter, with the aim to realise thechaotic cryptographic basic scheme, nor by performing the difference betweenthe composite signal coming from the transmitter and the signal coming fromthe driver.

Simulations have been performed with the Lang-Kobayashi model [17],keeping into account both laser and photodetector noise.


1.1 Secure data transmission scheme

Figure 1.1: Three laser scheme with TX/RX electrically injected.

A suitable modification of the Yamamoto scheme is presented in figure1.1. As in the basic scheme for optical chaotic cryptography, we assume touse a pair of twin semiconductor lasers, i. e. lasers with the same internalparameters, selected in close proximity from the same wafer. These lasersrepresent the transmitter (TX) and receiver (RX) of our communication link.Security of this cryptographic configuration is supported by specific require-ments on TX and RX matching, as it will be shown in the following sections.

The driver (DRV) is selected with different internal parameters with re-spect to the transmitter and receiver lasers, and it is routed to chaos by de-layed optical feedback through the mirror MD. An optical isolator is placedjust after the DRV to prevent reflection of optical power, which can disturbits internal dynamics. The driver laser is coupled to the system through a50/50 power splitter, so that half of its power reaches the transmitter sideby the fiber channel F1, while the other one reaches the receiver side by thefiber channel F2. This common signal is photodetected by using photodiodesPD1 and PD2, then electrically amplified and applied to the pumps of TXand RX lasers, respectively. The driver laser emission represents the commonchaotic driving source for TX and RX. Under suitable conditions, this com-mon chaotic input forces the TX and RX lasers in a common chaotic regime,i. e. TX and RX generate highly correlated chaotic waveforms. However, ithas been numerically noted that the response lasers generate different wave-


forms in respect to the driver, i. e. they do not copy the DRV. This differentbehavior is due to the optical feedback from the mirrors MT and MR.

Digital data to be transmitted feed the electro-optical modulator placedafter the TX laser, as in standard CM scheme. The fiber channel F3, con-necting TX and RX sites, carries the composite signal (chaos plus message).The message can thus be recovered at the receiver side by making the dif-ference between the chaos locally generated by RX, detected by photodiodePD4, and the composite signal detected by photodiode PD3.

The proposed configuration avoids optical injection, and thus it resultsin a more stable setup and in a less critical alignment with respect to otherconfigurations. Electrical amplifiers are cheaper than optical amplifiers andtheir gain is easier to trim. Furthermore the DRV laser does not need tooperate at the same wavelength as RX and TX, and the channels F2, F3,shown in figure 1.1, may be two WDM channels on the same fiber.


1.2 Numerical modeling

The well known Lang-Kobayashi model [17] for a single-mode semicon-ductor laser subject to delayed optical feedback can be easily modified todescribe the configuration of figure 1.1. The set of equations for the driver,transmitter and receiver lasers are obtained by varying index J in the fol-lowing equations:

dEJ(t)

dt=

1

2(1 + iα)

[

GJ(t)−1

τp

]

EJ(t)+

+kJτin

EJ(t− τ)exp(−iωτ) + Fsp,J(t) + LEJ(t), (1.2.1)

dNJ(t)

dt=

ηeV[IJ +∆D,JID,J(t)]−

NJ(t)

τs−GJ(t)|EJ(t)|2 + LNJ

(t), (1.2.2)

GJ(t) =ξ[NJ(t)−N0]

1− εΓ|EJ(t)|2. (1.2.3)

For J = D, we have the equations describing the DRV dynamics, whilefor J = T and J = R we have the equations describing the TX and RXdynamics, respectively. The coefficient ∆D,J is zero for J = D, otherwise itis ∆D,J = 1. In these equations, EJ(t) is the slowly varying complex electricfield, normalized in [m−3/2], NJ(t) is the carrier density, GJ(t) is the lineargain coefficient, IJ is the pump current, and kJ is the feedback parameterfrom the external mirror. Definitions and values of the other parameters arereported in table 1.2.1.

Fsp,J is the spontaneous emission term, LEJ(t) and LNJ

(t) are the Lange-vin noise terms [18], given by

Fsp,J(t) =1

2

EJ(t)

|EJ(t)|2Rsp,J(t), (1.2.4)

LEJ(t) =

EJ(t)

|EJ(t)|

√

2Rsp,J(t)

∆t

(

1

2χe(t) + iχφ(t)

)

, (1.2.5)

LNJ(t) =

√

2NJ(t)

τs∆tχn(t)− |EJ(t)|

√

2Rsp,J(t)

∆tχe(t), (1.2.6)

where Rsp,J(t) = βNJ(t)Γ/τs is the spontaneous emission rate. The functionsχe, χφ, χn are time series randomly generated, with zero-mean value andunit-variance gaussian distribution. The term ∆t is the time resolution inthe modeling of white noise.

Since realistic comparisons with the experimental data require physicalunits, for our numerical simulations we have transformed the field EJ(t),


normalized in [m−3/2], into the true electric field EJ,True(t), expressed in[V/m], by means of

EJ,True(t) =

(

ξ~ωZ0

nζ

)1

2

EJ(t). (1.2.7)

The simbol ~ is the Planck’s constant, whereas Z0 = (1/ǫ0c) represents thevacuum impedance, with ǫ0 vacuum permittivity and c speed of light invacuum.

Whereas the pump current of the driver laser is constant, the pump cur-rents of transmitter and receiver, in the equation 1.2.2, contain also thetime-varying terms ID,T (t) and ID,R(t) that represent the electrical injectionfrom the driver into the transmitter and the receiver, respectively. Thesesignals are obtained after amplification and filtering of the output currentsIPDT (t) and IPDR(t) from photodiodes PD1 and PD2, respectively. They aregiven by

IPDJ(t) = σA

Z0

[

∣

∣ED,True(t− TDJ)∣

∣

2−⟨∣

∣ED,True(t− TDJ)∣

∣

2⟩]

+INJ(t) (1.2.8)

where J = T for the transmitter and J = R for the receiver.The term IPDJ contains the common, chaotic driving signal, ED,True. Thedc component of the photodetected currents is subtracted, since we assumethat the dc working conditions of TX and RX lasers are set by their dcpump currents, IT and IR, respectively. In the equation 1.2.8, TDJ indicatesthe propagation time between the driver and the transmitter (J = T ) andbetween the driver and the receiver (J = R). For simplicity and withoutany loss of generality, we have taken TDT = TDR = 0 in all simulations. Thesymbol | | means the module of the complex field, and < > means thetime average. INJ keeps into account the Johnson noise current of the 50 Ωtermination resistance and the shot noise current due to direct detection.

The insertion of a message M(t) (0 ≤ M ≤ 1) with the electro-opticmodulator is described by

ECM(t) = ET (t− TT,R)[

1 + γ M(t− TT,R)]

, (1.2.9)

where γ represents the modulation coefficient and TTR the propagation timebetween the transmitter and the receiver. We have taken TTR = 0 in allsimulations.

Finally, to recover the message we compute the signals ST and SR, where

SJ = σAZ−1

0|EJ,True(t)|2, (1.2.10)


Parameter Driver Twin Tx/Rx UnitLinewidth enhancement factor α = 2.8 α = 3.0Photon lifetime τp = 1.9 τp = 2.0 psCarrier lifetime τs = 1.9 τs = 2.0 nsGain coefficient ξ = 7.7 · 10−13 ξ = 8.1 · 10−13 m3 · s−1

Carrier density at transparency N0 = 1.16 · 1024 N0 = 1.10 · 1024 m−3

Threshold current Ith = 12.4 Ith = 11.0 mALaser cavity roundtrip time τin = 8.0 psSolitary laser pulsation ω = 1.2177 · 1015 rad · s−1

External cavity roundtrip time τ = 0.3 nsActive region efficiency ηe = 6.242 · 1018 C−1

Active region volume V = 8.0 · 10−17 m3

Active region emission area A = 2.0 · 10−13 m2

Non linear gain coefficient ε = 2.5 · 10−23 m3

Confinement factor Γ = 0.36Spontaneous emission factor β = 1.0 · 10−6

Active medium refractive index n = 3.0Stimulated emission cross section ζ = 1.0 · 10−20 m2

Photodiode responsivity σ = 1.0 A ·W−1

Table 1.2.1: Three laser scheme parameters.

both at TX and RX sites, by using photodiodes PD3, PD4, and take theirdifference. The message extraction is then improved by low-pass filteringat the bit-rate frequency for a message transmitted in baseband, or by amessage demodulation, followed again by low-pass filtering, for a messagetransmitted on a carrier.

In the next sections, we report numerical results obtained with this modelfor digital transmissions in baseband and on a carrier. In the simulations, inaddition to the noise of all photodetectors, the noise of the lasers, describedby the Langevin terms, has been taken into account.


1.3 Message transmission in baseband

1.3.1 Working point choice

DRV and TX/RX correlation

We have numerically studied the scheme of figure 1.1, using the laserparameters reported in table 1.2.1. The transmitter and receiver lasers areidentical, whereas the driver is taken with different internal parameters, withrespect to the twin pair. This condition is crucial for security, because itensures that the twin lasers can generate a different chaos, compared to thatof the driver, as it will be seen later.

For all our numerical investigations, for the driver, we have assumeda pump current ID equal to 22.0mA, and a fraction k2

D, of optical powercoming back from its remote mirror, equal to 4%. For this working pointthe driver emission is chaotic, with large amplitude and phase modulation.The pump currents of TX and RX lasers, instead, are free to be changedin all numerical analysis and a low back reflection value has been selected(k2

T = k2

R = 0.1%), since a large value would cause each laser to produce itsown chaos, preventing them from synchronizing to each either. Please notethat for large value of back reflection we mean a value greater than 0.5%.Indeed, other values within 0.5% are suitable for performing the numericalanalysis presented in the next sections.

It has been observed that if the transmitter and receiver are injected bythe electrical signal coming from the driver, detected by photodiode PD1and PD2, they become chaotic; furthermore, if they have the same pumpcurrent and they are subject to the same electrical injection level, they alwaysshow high correlated outputs. The driver routes them into a chaotic regime,otherwise they would not be chaotic.

In figure 1.2, we report the correlation between the transmitter and driver,as a function of the electrical injection from the driver into TX, and the TXpump current. In addition to a large region (orange area in the figure) wherethe correlation between transmitter and driver is higher than 90%, there isa region (yellow or green area in the figure), where the correlation betweenthe transmitter and the driver is lower than 80%.

Then, more than one working point can be chosen, where the correlationbetween the transmitter and the driver is low. The choice of a such workingpoint is important for guaranteeing security in message transmission, as wewill see later in the next sections. Similar results would be obtained for thecorrelation between receiver and driver.


Q factor evaluation

To investigate the possibility of using this configuration for secure datatransmission, we have refined the choice of the working point. Preliminarily,in order to perform this, we have put a message of arbitrary amplitude atthe transmitter side and then performed the message recovery at the systemoutput, by making the difference between the signal (chaos plus message)coming from the transmitter, photodetected by PD3 (see figure 1.1), andthe chaos locally generated from the receiver, photodetected by PD4. Apseudo-random NRZ digital message at 5 Gb/s, in baseband, has been usedto modulate the chaotic optical power coming from the transmitter, and thequality of the extracted message has been studied by Q factor evaluation.Simulations, in which the electrical injection from the driver into the trans-mitter and receiver, and the TX/RX pump current, are free to be changed,are reported in figure 1.3. A careful analysis of the figures 1.2 and figure 1.3,have led us to choose a working point where:

• The correlation, between DRV and TX/RX, is low.

• The Q factor of the extracted message is high.

• Small external parameter variations cause small Q factor variations.

For our following investigations and in order to stay in realistic conditions,we have selected a common pump current for the TX and RX lasers of 23mAand an electrical injection from the driver into the two response lasers of1.73mA. This last value correspond to a relative electrical injection of 14.4%.The relative electrical injection is defined as the ratio between the currentobtained by photodetection and amplification of the driver emission, and theover-threshold pump current of the response laser.


Figure 1.2: Correlation between transmitter and driver as a function of the elec-trical injection from the driver into TX and the TX pump current. Similar resultwould be obtained between RX and DRV.

Figure 1.3: Q factor of the extracted message (a pseudo-random NRZ digitalmessage at 5 Gb/s, in baseband) for ideally matched TX and RX lasers, as afunction of the electrical injection from the driver and the TX/RX pump current.


1.3.2 Working point analysis

Synchronization

For the selected working point, we have investigated the signal outputswithout message transmission. Figure 1.4 reports the RF chaotic power spec-trum obtained by photodetection (using photodiode PD1) and amplificationof the driver laser output at the TX side, after propagation. A similar spec-trum would be obtained from PD2 at the RX side.Figure 1.4 contains also the RF chaotic power spectra obtained by photode-tecting, respectively, the transmitter laser output after propagation and thereceiver laser output, both at the RX side. In this graph, for convenience,the traces relative to the driver and to the receiver have been shifted upwardsand downwards by 20 dB, respectively. The transmitter and receiver spectrawould be otherwise superposed. The trace of the difference signal betweenTX and RX is also reported, showing a chaos cancellation of about 50 dB(limited by noise) on a large frequency band.

As already specified in the section 1.2 we have taken into account theJohnson noise of the 50Ω termination resistance and the shot noise for allphotodiodes. We have also neglected all propagation losses.

Though the spectra of driver, transmitter and receiver are very similar inthe frequency domain, the different evolution between DRV, TX and RX isevident from the chaotic waveforms, plotted in the time domain (see figure1.5). Indeed, the traces of the transmitter and receiver are identical, butthey are different from the trace of the driver, suggesting a different laserdynamics for the chosen operating conditions.This difference is more evident by the correlation plots. In particular, wehave a correlation peak larger than 99% between TX and RX (see figure1.6), whereas the correlation peak between TX and DRV is lower than 60%(see figure 1.7). Similar result would be obtained for the correlation peakbetween RX and DRV. The maxima occur at time zero because we have ne-glected any delay time.The insets report the relationship between the photodetected currents in nor-malized units. It is clearly shown that TX and RX are successfully synchro-nized, but they are not synchronized with DRV, which supports the securityof the scheme. Indeed, since DRV is selected with different parameters withrespect to the twin pair, it generates a different chaos, and this prevents aneavesdropper, accessing both channel F2 and F3, from extracting the mes-sage by performing the difference between the transmitted signal and thephotodetected driver output.


Figure 1.4: Numerical RF chaotic power spectra (5 MHz resolution bandwidth) ofthe driver, transmitter and receiver lasers. For better visualization, we have shiftedupwards (+20 dB) and downwards (-20 dB) the traces relative to the driver andreceiver, respectively. The difference signal is also reported.

Figure 1.5: Simulations of chaotic waveforms for the driver, transmitter and re-ceiver lasers, as functions of time.


Figure 1.6: Cross correlation as a function of delay time for the transmitter andthe receiver. A correlation peak larger than 99% has been found. The inset showsthe relationship between the photothedected currents in normalized units.

Figure 1.7: Cross correlation as a function of delay time for the transmitter andthe driver. A correlation peak lower than 60% has been found. The inset showsthe relationship between the photothedected currents in normalized units. Sameresults are obtained for the receiver and the driver.


Message transmission

Figure 1.8: Q factor and BER as functions of the relative electrical injection ofDRV into RX, for an ideally matched pair. Each point, at a given injection, isoptimized by sweeping the RX pump current.

To investigate the possibility of using this configuration for secure datatransmission, we have numerically studied message transmission and mes-sage recovery at the system output, performing simulations following thealignment procedure that would be performed experimentally. The externalparameters of the transmitter laser have been fixed to the nominal values,whereas the working point of the receiver laser has been varied. In detail,in a range of the relative electrical injection of the receiver laser, around itsnominal value, we have performed a sweep of the RX pump current in orderto find the maximum Q factor, optimising the message extraction.

The check of the system trimmability, by varying the external parame-ters of the receiver laser, is the starting point for a more complicated andexhaustive analysis relative the system feasibility and security that will bemade later.

We have transmitted a pseudo-random NRZ digital message at 5 Gb/s, inbaseband, using a CM scheme. The figure 1.8 reports details of our numericalinvestigation, where the Q factor and the BER are plotted as functions ofthe relative electrical injection. In the figure, each circle is the result ofthe explained optimization procedure. From figure 1.8, we can conclude


that a variation of injection can be partially compensated by acting on thepump current, which helps in view of a future experimental implementation.However, it is evident that an accurate trimming is required, which alsosupports security. We have obtained Q ≈ 6, which corresponds to a BER ofabout 10−9, by using a modulation coefficient γ equal to 1.9 · 10−3. Since aBER of 10−9 provides an error every 109 bits transmitted, we have obtainedan excellent data transmission.

In the figure 1.9, we show, in the frequency domain, the plaintext message(i. e. the message detected at the system output with the DRV laser switchedoff), the transmitted signal (chaos plus message), and the message, recoveredat the system output by chaos cancellation. In the difference, some residualchaos is present at high frequency, due to limitations of the algorithm, whichextracts the signal by maximizing the Q factor. This contribution, however, isstrongly reduced by the 5 GHz baseband low-pass filter. The inset shows theeye diagram corresponding to the recovered message after low-pass filteringat 5 GHz.

In figure 1.10, we show the temporal waveforms corresponding to thetraces of figure 1.9, after low-pass filtering at 5 GHz. In the recovered messagethe bit sequence is clearly visible, while in the transmitted signal bits cannotbe identified. This last signal is what it would be seen by a non authorizedlistener accessing the channel F3 of figure 1.1, which supports the security ofthe scheme.


Figure 1.9: Numerical RF spectra (5 MHz resolution bandwidth), for CM trans-mission of a 5 Gb/s digital message in baseband. The plaintext message, thetransmitted signal (chaos plus message), and the message recovered at the systemoutput are shown. The inset shows the eye diagram corresponding to the recoveredmessage after low-pass filtering at 5 GHz (Q ≈ 6.1)

Figure 1.10: Simulated current waveforms in baseband. The plaintext message,i. e. the message transmitted with the driver laser switched off, the transmittedsignal (chaos plus message), and the message, recovered at the system output bychaos cancellation, are shown.


Feasibility and security

−0.5% +0.5% −5% +5%(αR − αT )/αT 2.4 · 10−9 2.1 · 10−9 9.8 · 10−2 1.3 · 10−1

(τp,R − τp,T )/τp,T 7.3 · 10−9 4.4 · 10−9 5.5 · 10−2 6.2 · 10−2

(τs,R − τs,T )/τs,T 1.0 · 10−9 3.7 · 10−10 2.7 · 10−4 7.4 · 10−5

(ξR − ξT )/ξT 1.1 · 10−9 6.7 · 10−10 1.1 · 10−1 9.5 · 10−2

Table 1.3.1: Effect on BER of TX/RX parameter mismatch.

The quality of the extracted message is quite good in matched condi-tions, if we optimize the working point by trimming the pump current of thereceiver and the relative electrical injection from the driver. However, it isimportant to investigate the effect on message extraction of parameter mis-match between TX and RX. Indeed, in a realistic situation even two matchedlaser have small differences. We have analysed the effect of mismatch on fiveinternal parameters: the linewidth enhancement factor α, the photon life-time τp, the carrier lifetime τs, the gain coefficient ξ and, at last, the carrierdensity at transparency N0. Moreover, we have assumed that two twin lasersare different by 0.5% on the just mentioned internal parameters.

In table 1.3.1 we report the evaluated BER, performing a one by one mis-match on the internal parameters of the receiver laser. Since, by optimizingcurrent, electrical injection and the message amplitude γ, we have obtained,on the average, BER values of 10−9, the system feasibility is numericallydemonstrated.

However, the above analysis does not support the system security, indeedit does not tell us what happens if a unauthorized listener uses a receiver laserdifferent from the transmitter laser. We have assumed that two lasers arenot twin if their internal parameters are different by 5%. Moreover, γ is fixedat the value optimizing the extraction for a mismatch in TX/RX of 0.5%.An eavesdropper cannot operate on it, which is fixed at the transmitter side.By following the previous procedure of optimization, we have performed themessage extraction evaluating its quality by Q factor and BER. Our resultsare very encouraging, indeed we have found that this scheme is very sensitiveto mismatch. The lower BER value obtained is of the order of 10−4 (see table1.3.1), that is not sufficient to perform a good message extraction. Thus, wehave numerically demonstrated that the internal parameters investigated forthe receiver laser, except the carrier density at transparency (non reportedin the table), cannot be successfully compensated by acting on the electri-


cal injection and on the receiver pump current, which supports the systemsecurity.

Now we report some results of our numerical investigation, presentedin table 1.3.1, for two parameters. We show the Q factor and the BER,evaluated for the extracted message, if the linewidth enhancement factor αfor the receiver laser is different of +0.5% and +5%, respectively, comparedto the transmitter. For the lower mismatch (see figure 1.11) we perform agood message recovery, that ensures the system feasibility, whereas for thehigher mismatch (see figure 1.12) the evaluated Q and BER are poor, whichensures the system security. Identically, a mismatch of −0.5% on the photonlifetime τp (see figure 1.13) ensures the system feasibility, whereas a mismatchof −5% (see figure 1.14) can preserve the message from unauthorized listener.

In addition, we have verified that, choosing γ so that, for a mismatchof 0.5% in the internal parameters of the receiver laser, we have a BERvalue of 10−5, the corresponding BER, for a mismatch of 5%, becomes 10−1.Then, the security of the three laser scheme can be greatly increased by usingForward Error Correction (FEC) algorithms. Within the BER threshold of10−3, such algorithms can restore BER to the value of 10−9, or lower. Then,an authorized pair of subscribers can get a high quality data recovery evensending messages of BER ≈ 10−5. On the other hand, an unauthorizedlistener, starting from a poor signal (BER ≈ 10−1), is unable to improve itby FEC. Thus, the security level is further enhanced.

In the basic cryptographic scheme, the receiver is optically injected by thetransmitter and, under proper working conditions, the injected receiver repli-cates the chaos of the transmitter, but does not replicate the message. Then,the message can be recovered by subtracting the chaos locally generated bythe receiver from the composite signal (chaos plus message) coming from thetransmitter. This approach could be used by an eavesdropper to force thesystem. However, in the three laser scheme, both the transmitter and thereceiver are electrically injected and their chaos has a different dynamics re-spect to the chaos that a laser can generate alone by back reflection. Thismakes our system more secure. Indeed, we have numerically verified thata non authorized listener accessing channel F3 cannot successfully realise atransmitter-receiver combination, even using a laser perfectly matched to thetransmitter. The obtained BER, for the extracted message, is about 10−1.

A final security check has been made. We have verified that, becauseof the low correlation (60%) between the transmitter and the driver is notpossible to extract the message by performing the difference between thecomposite signal coming from the transmitter, through the fiber channel F3,and the signal coming from the driver, through the fiber channel F1, or F2.The obtained BER is again of the order of 10−1.


We conclude observing that the maximum Q, both for a good and badmessage extraction quality, corresponds to a working point where the relax-ation frequency for the non chaotic receiver laser is very similar to relaxationfrequency for the non chaotic transmitter laser. This condition is the key tohave very similar chaotic waveforms for the TX and RX lasers, however, wehave found that it is not sufficient for guaranteeing a good chaos cancellationbetween the signal coming from the transmitter and the chaos replicatedat the receiver. A good matching between the internal parameters of thelicensed pair is necessary.


Figure 1.11: Q factor and BER as functions of the relative electrical injection ofDRV into RX for a slight mismatch (+0.5%) on the α factor. Each point, at agiven injection, is optimized by sweeping the RX pump current.

Figure 1.12: Q factor and BER as functions of the relative electrical injection ofDRV into RX for a moderate mismatch (+5%) on the α factor. Each point, at agiven injection, is optimized by sweeping the RX pump current.


Figure 1.13: Q factor and BER as functions of the relative electrical injection ofDRV into RX for a slight mismatch (−0.5%) on the photon lifetime. Each point,at a given injection, is optimized by sweeping the RX pump current.

Figure 1.14: Q factor and BER as functions of the relative electrical injection ofDRV into RX for a moderate mismatch (−5%) on the photon lifetime. Each point,at a given injection, is optimized by sweeping the RX pump current.


1.4 Message transmission on a carrier

In addition to baseband transmission, the use of a carrier modulatedby the message has been considered. Besides allowing us to use differentchannels over the same optical wavelength, this approach provides a methodto optimize performances by positioning the message at the frequency wherechaos is larger, or where synchronization is better. In fact, the use of a carrierhas been already proposed [19] for optical chaotic transmission in fiber.

For our numerical investigations, all laser parameters have been left un-changed, whereas, by following the procedure developed in the subsection1.3.1, we have found that a good working point for the transmitter and thereceiver can be done choosing for their pump currents the common value of26 mA, and a relative electrical injection from the driver of 11.5%.

The chosen message has been a pseudo-random NRZ digital signal at 4Gb/s modulating a carrier in amplitude with 100% modulation depth. Thecarrier frequency has been fixed at 5 GHz.

By following the procedure described in subsection 1.3.2, we have firststudied the synchronization of transmitter and receiver, verifying that theyare successfully synchronized whereas their synchronization with the driveris low, and later we have studied message transmission and message recoveryat the system output. We have found a correlation higher than 99% betweenthe transmitter and receiver, while the correlation between the transmitterand drivers is again lower than 60%.

In figure 1.15, the RF spectrum of the plaintext message is comparedto the spectrum of the recovered message. In the difference, some resid-ual chaos is present at low and high frequency, due to limitations of thealgorithm, which extract the message by maximizing the Q factor. Thiscontribution, however, is strongly reduced after message demodulation andlow-pass filtering at the bit-rate frequency of 4 GHz. The inset shows theeye diagram corresponding to the recovered message. It is worth noting thatin the transmitted signal the message is completely hidden by chaos and theinformation is kept secret to a non authorized listener.

Figure 1.16 reports the signals of figure 1.15 in the time domain, after de-modulation and low-pass filtering. The plaintext message, i. e. the messagetransmitted with the driver laser switched off, is shown. By comparison ofthe transmitted signal (chaos plus message) and the recovered message, bothat the system output, it comes out again that the bits are clearly visible onlyfor the authorized listener, while they are completely hidden by chaos for anon authorized listener. Moreover, the BER corresponding to the recoveredmessage is almost 10−9, while it is 10−1 by analysing the transmitted signal.Then, identically to the message transmission in baseband, the system is


expected to be secure.Further analysis has been made. The Q factor and BER parameters

have been computed as functions of current and relative electrical injection,modified with respect to the nominal working point of the RX laser, while theTX working point has been left unchanged. This has been done to evaluatethe system trimmability, that represents a reference for the studies on theeffect of mismatch. In detail, exactly as done for the baseband, with the aimto reflect the alignment procedure that would be performed experimentally, ina range of the electrical injection of DRV into RX, around its nominal value,we have performed a sweep of the RX pump current, and we have found themaximum Q factor for the recovered message. The results are shown in figure1.17, where the Q factor and the BER are plotted as functions of the relativeelectrical injection. In the figure, each circle is the result of the just explainedoptimization procedure. As well as for the baseband, from figure 1.17, it canbe concluded that a variation of injection can be partially compensated byacting on the pump current, which helps us in view of a future experimentalimplementation. In spite of that, an accurate trimming is required, whichalso supports security.

Finally, in table 1.4.1, we report numerical results regarding the systemfeasibility and security. With regard to the baseband transmission, also forthe transmission on a carrier, a slight mismatch (±0.5%) in the internal pa-rameters can be compensated by varying the electrical injection, the pumpcurrent and the modulation coefficient γ, which supports feasibility. On theaverage we have found a BER of 10−9.However, once the modulation coefficient has been fixed at the value opti-mizing the extraction for a small mismatch, a more considerable mismatch(±3%) in the internal parameters cannot be successfully compensated byacting on the external parameters, which supports security. For a mismatchof 3%, the lowest BER value that we have found is 10−4.

By comparing the effects of TX/RX parameter mismatch on BER, for amessage transmission in baseband (see table 1.3.1) and for a message trans-mission on a carrier (see table 1.4.1), it comes out that the two methodsof data transmission are comparable, in terms of feasibility and security.However, the transmitter and the receiver are more sensitive to parametermismatch if the message is transmitted on a carrier instead of in baseband.Indeed, to have comparable results with the baseband transmission, now wehave set a difference on the internal parameters of 3%, instead of 5%. Nu-merical investigations suggest that this increased sensitivity is due to themessage being positioned above the relaxation frequency of the non chaotictransmitter laser. However to verify this hypothesis, more investigations willbe made.


Figure 1.15: Numerical RF spectra (5 MHz resolution bandwidth), for CM trans-mission of 4 Gb/s digital message on a 5 GHz carrier. The plaintext message, thetransmitted signal (chaos plus message), and the message recovered at the systemoutput are shown. The inset shows the eye diagram corresponding to the recoveredmessage after demodulation and low-pass filtering (Q ≈ 6.0).

Figure 1.16: Demodulated current waveforms. The plaintext message, i. e. themessage transmitted with the driver laser switched off, the transmitted signal(chaos plus message), and the message, recovered at the system output by chaoscancellation, are shown.


Figure 1.17: Q factor and BER as functions of the relative electrical injection ofDRV into RX, for an ideally matched pair. Each point, at a given injection, isoptimized by sweeping the RX pump current.

−0.5% +0.5% −3% +3%(αR − αT )/αT 2.3 · 10−9 2.6 · 10−9 3.1 · 10−2 2.4 · 10−2

(τp,R − τp,T )/τp,T 1.6 · 10−9 2.4 · 10−9 9.0 · 10−3 6.0 · 10−3

(τs,R − τs,T )/τs,T 5.9 · 10−9 3.3 · 10−9 8.4 · 10−5 1.7 · 10−3

(ξR − ξT )/ξT 4.6 · 10−10 1.6 · 10−9 2.1 · 10−2 2.0 · 10−2


Our numerical results are very encouraging, so that we can concludethat transmission around a carrier can be also proposed for secure chaotictransmission on optical data link, which significantly widens the applicabilityrange of our cryptographic scheme.

CHAPTER 2

OPTICAL INJECTION WITH THE THREE LASER SCHEME

In this chapter we propose an interesting alternative [20, 21] to the stan-dard two-laser scheme [1, 2]. In detail, we numerically demonstrate securedata transmission using twin semiconductor lasers in which a common chaoticdynamics is achieved by optical injection into the laser pair of a commonchaotic driving signal, generated by a third laser subject to delayed opti-cal feedback, in a short cavity scheme. This laser is selected with differentinternal parameters with respect to the twin pair, so that the emissions ofthe matched lasers are synchronized and highly correlated, whereas theircorrelation with the driver is low.

The digital message modulates the emission of the transmitter, as ina standard Chaos Modulation (CM) scheme [3]. Message recovery is thenobtained by subtracting, from the transmitted chaos-masked message, thechaos, locally generated by the synchronized receiver laser.

Numerical analysis on feasibility and security of this method has beenpresented in the case of the open loop [20], when the twin lasers are notsubject to local feedback, and they are chaotic only due to injection from thethird laser.

Our scheme is based on an idea of Yamamoto et al. [12]. Though origi-nally intended for generation and distribution of secret communication keys,their scheme can be easily modified for message transmission. However, acomplete analysis of the feasibility and of the level of security of the three-laser approach has not been presented before in the literature. In this thesis,we consider the original optical injection scheme, modified for data transmis-sion on fiber networks, and analyse in detail its feasibility and security.

A similar setup, specifically designed for transmission on a Free-SpaceOptics Link (FSOL), and based on electrical injection, has been already

35

Optical injection with the three laser scheme 36

proposed in [16] and presented with some modifications and more details inchapter 1.

Besides the open loop case, in this thesis we consider the case of closeloop [21], where the transmitter and receiver lasers are subject to delayedoptical feedback, and they are chaotic even in absence of injection from thedriver. Though the open loop scheme already offers a good security level, aspecific advantage of the close loop is that, differently from the open loopscheme, the message remains masked even in case of failure of the commondriving laser. Moreover, the close loop scheme is harder to manage by aneavesdropper, since it is more critical to implement, and it is more sensitiveto parameter mismatch, as it will be shown, thus requiring a more accuratetrimming.

A similar approach has been proposed in [22], where synchronization witha long cavity scheme is investigated. However, we study the short cavityscheme, which is more convenient in view of applications, being suitable formonolithic integration. Moreover, our numerical analysis is mainly concernedwith the quality of the recovered signal, expressed in terms of Q factor andBER, rather than with synchronization. While the two topics are obviouslyconnected, the first one is more relevant when one plans to use the synchro-nized lasers for secure message transmission.

For the close loop case, a preliminary experimental evaluation has beenalso performed using InP integrated modules.

Simulations have been performed with the Lang-Kobayashi model, keep-ing into account both laser and photodetector noise. Secure transmissionhas been demonstrated by investigating the effect of parameter mismatch,between transmitter and receiver, on synchronization and message recovery.


2.1 All-optical three laser scheme

Figure 2.1: Three laser scheme with TX/RX optically injected.

The configuration proposed in this thesis, suitable for message encryption,is illustrated in figure 2.1, where we use a pair of twin semiconductor lasers,which represent, respectively, the transmitter (TX) and the receiver (RX) ofour communication link. A third semiconductor laser, the driver (DRV), isrouted to chaos by delayed optical feedback in a short cavity scheme, andpicked out with different parameters from the twin pair. All lasers work atthe same wavelength, being λ = 1550 nm.

The DRV laser is coupled to the system through a 50/50 power splitterplaced at the transmitter side, so that half of its power directly injects TX,while the other half is sent through channel A to the receiver, where it in-jects RX. To ensure balanced injection levels between TX and RX, a 3−dBunidirectional amplifier has been positioned along channel A to compensatethe loss introduced by the second coupler at the receiver side.

It has been observed that two topologies can be considered for TX andRX to ensure secure data transmissions:

• the open loop scheme

• the close loop scheme

In the open loop scheme [20] the transmitter and receiver do not suffer theoptical feedback from the remote mirrors, i. e. the mirrors MT and MR are


removed. However, as in [12], the optical output of the driver is used to injectboth TX and TX, inducing chaotic regime in these, otherwise unperturbed,devices, and pursuing synchronization.On the contrary, in the close loop scheme [21] the transmitter and receiverare routed to chaos by delayed optical feedback in a short-cavity scheme,by mirrors MT and MR. The optical output of the driver is used to injectboth TX and RX, inducing a common chaotic regime in these devices, andpursuing synchronization. With respect to the open loop, this setup is morecomplex and, thus, more difficult to align. In particular, the phase of theexternal cavities of TX and RX must be accurately trimmed, as in all close-loop chaos synchronization experiments.

As we will see in next sections, the close loop topology allows for a higherlevel of security, respect to the open loop scheme.

Digital data to be transmitted feed the electro-optic modulator placedjust after the TX laser, as in standard CM scheme [3], and the compositesignal (chaos plus message) is transmitted along channel B.

Under suitable operating conditions, the common chaotic input forcesTX and RX to synchronize to each other, i. e. to generate highly correlatedchaotic waveforms. The masked message can thus be recovered at the receiverside by subtracting the chaos locally generated by RX, and detected by pho-todiode PD2, from the composite signal, detected by photodiode PD1. SinceTX and RX are not matched with DRV, their chaotic outputs are differentfrom that generated by the DRV, as required for secure data transmission.This prevents an eavesdropper, accessing both channels (A and B), from ex-tracting the message by chaos subtraction, without the need of a matchedRX.

A similar scheme has been also proposed in [23], where, however, RX andTX are mutually coupled to DRV. For this reason, such system is not suitablefor private message transmission, but only for secret key distribution.

As already pointed out in [20], the same DRV can be shared by differentprivate interconnections. Indeed, the drawback of using a dedicated channelfor the DRV is not a major limitation, since the same DRV laser, and its fiberchannel, can be used for driving to chaos different couples of TX/RX oper-ating on different links. This is possible because the DRV has no matching(except the wavelength) with the twin lasers.

In addition to numerical simulations, preliminary experimental evalua-tion has been done to support our model [21]. In our experiments, we usedInP monolithically integrated modules (see figure 2.2) including a DFB laser,an optically transparent waveguide for the cavity, a variable optical attenua-tor/amplifier (VOA) to adjust the optical feedback level, and a phase shifter(PS) to trim the phase of the external cavity (i. e. the optical length of the


feedback path). The terminal facet of the waveguide is coated with a highlyreflective deposition, which represents the cavity mirror (HR Mirror).Such modules, described in detail in [24, 25], have been specifically fabri-cated for secure transmission experiments by the Fraunhofer Institute forTelecommunications, Heinrich Hertz Institute of Berlin (Germany) withinthe European Union project PICASSO.By using these modules, the authorized subscriber has a significant advan-tage respect to the eavesdropper, provided that the former has an easy andproprietary method to adjust his chaotic devices.

Figure 2.2: The integrated module, with all the devices included in the TX andRX boxes (see figure 2.1), is shown (PS: phase shifter, VOA: variable optical at-tenuator).


2.2 Numerical modeling

The well known Lang-Kobayashi model [17] is used to describe the setupof figure 2.1. The set of equations for the driver, transmitter and receiverlasers are obtained by varying index J in the following equations:

dEJ(t)

dt=

1

2(1 + iα)

[

GJ(t)−1

τp

]

EJ(t) + Fsp,J(t)+

+ LEJ(t) +

kJτin

EJ(t− τ)exp(−iωτ)+

+ ∆D,JkD,J

τinED(t− TD,J)exp(−iωTD,J), (2.2.1)

dNJ(t)

dt=

ηeVIJ − NJ(t)

τs−GJ(t)|EJ(t)|2 + LNJ

(t), (2.2.2)

GJ(t) =ξ[NJ(t)−N0]

1− εΓ|EJ(t)|2. (2.2.3)

For J = D, we have the equations describing the DRV dynamics, while forJ = T and J = R we have the equations describing the TX and the RXdynamics, respectively. The coefficient ∆D,J is zero for J = D, otherwise itis ∆D,J = 1. In these equations, EJ(t) is the slowly varying complex electricfield, NJ(t) is the carrier density, GJ(t) is the linear gain coefficient, IJ is thepump current, and kJ is the feedback parameter from the external mirror. ForJ assuming the values T or R, the terms kD,J and TD,J represent the injectionparameter and the propagation time from the driver into transmitter or fromthe driver into receiver, respectively. For simplicity, in the simulations wehave taken TD,T = TD,R = 0. Other parameters are the same as defined intable 1.2.1.

Fsp,J(t) is the spontaneous emission term, whereas LEJ(t) and LNJ

(t) arethe Langevin noise terms already specified in the equations (1.2.4), (1.2.5)and (1.2.6).

The insertion of a message M(t) (0 ≤ M ≤ 1) with the electro-opticmodulator is described by the equation

ECM(t) = ET (t− TT,R)[

1 + γ M(t− TT,R)]

, (2.2.4)

where γ represents the modulation coefficient and TT,R the propagation timebetween transmitter and receiver. For simplicity we have taken TT,R = 0 inall simulations.

As usual, the electric fields are normalized in [m−3/2] and the true value


of each electric field (in [V/m]) is obtained by

ETrue(t) =

(

ξ~ωZ0

nζ

)1

2

E(t), (2.2.5)

where ~ is the Planck’s constant, Z0 = (1/ǫ0c) is the vacuum impedance, ǫ0is the vacuum permittivity, and c is the speed of light.

The photodetected currents of PD1 and PD2 are obtained by computingthe signal I(t) = σAZ−1

0|ETrue(t)|2 for both TX and RX, and then, to get

the recovered message, we take their difference.In the next sections, we report numerical results obtained with this model

for digital transmissions both in baseband and on a carrier. The quality of theextracted message is increased by low-pass filtering at the bit-rate frequencyfor a message transmitted in baseband, or by message demodulation, followedagain by low-pass filtering, for a message transmitted on a carrier. In allsimulations, in addition to the Langevin noise, the photodetector noise hasbeen taken into account. This has been done by assuming, for Johnsonnoise and for shot noise, white gaussian processes of variance 4KBTB/R and2e 〈I〉B, respectively, where KB is the Boltzmann constant, T is the absolutetemperature (T = 300K), B is the bit-rate frequency, R is the load resistance(R = 50 Ω) and 〈I〉 is the mean detected current. For the simulations, timesamples for each noise source have been obtained by a standard numericalroutine.


2.3 Message transmission in baseband

2.3.1 Common working point of open and close loop

In the simulations, we have used the same laser parameters as specified intable 1.2.1. TX and RX are identical, whereas some parameters are differentfor the DRV. Throughout all our numerical investigations, for the DRV, wehave assumed the pump current ID equal to 23.4mA, whereas k2

D, i. e. thefraction of optical power coming back from the remote mirror MD, is of theorder of 4%. In this working point, the driver laser exhibits a large chaoticspectrum due to optical feedback. On the other hand, the pump currents ofTX and RX and the injection power from DRV into TX and RX lasers havebeen swept in the numerical analysis.

The correlation of TX and RX has been studied numerically as a functionof the their pump currents and of the injection power from DRV. We haverealized the open loop by setting to zero the optical power coming back fromthe remote mirrors MT and MR, whereas, for the close loop, we have chosenk2

J = 4%, where J = T,R. It is worth noting that the value of 4% forthe close loop is not the only possible choice, indeed other values could besuitable for the back reflection. The symmetry of the scheme is obtainedtaking identical pump currents and identical back reflection values for TXand RX. The correlation maxima, of the open and close loop, are reportedin figures 2.3 and 2.4, respectively. From the graphs is evident that, in viewof a comparison between open loop and close loop, more than one commonworking point, where the correlation is higher than 99%, can be found.

Also the correlation between TX and DRV has been evaluated in thesame conditions to find a suitable common working point for the open loopand close loop, where the correlation between the matched pair is high (toget a good synchronization quality) while that between TX and DRV is low(for security). Figures 2.5 and 2.6 show the computed correlation maxima.From the figures, it is evident that a range of these externally controllableparameters exists where the correlation is 70% or less. For ideally twin lasers,identical diagrams apply to the correlation between receiver and driver.

We have also studied the transmission of digital data. The quality of theextracted message has been quantified by computing the Q factor from thesimulated eye diagrams. The BER has been estimated from the Q factorunder the assumption of normal distributions both for noise and for residualchaos. This approximation avoids a direct calculation of the BER, whichwould require an extremely long computation time (especially for low BER,such as 10−9). In figures 2.7 and 2.8, we present the Q factor of the ex-tracted message for a pseudo-random NRZ digital transmission at 5Gb/s,


in baseband, for the open loop and close loop, respectively. Besides a gen-eral improvement of performances at high injection and high current, it isobserved from the figures that a proper selection of the working point can en-hance performances and minimize sensitivity to the variation of the operatingconditions.

In view of an experimental implementation, from the results shown fromfigure 2.3 to figure 2.8, we have looked for a working point, common to theopen loop and close loop, where:

• The correlation, between DRV and TX/RX, is low.

• The Q factor of the extracted message is high.

• The sensitivity of the Q factor, to small variations of pump current andinjection, is low.

We have selected for both TX and RX lasers a pump current of 41mA and anoptical injection from the DRV into the two response lasers of 1.2mW. Thisinjection corresponds to about 32% of relative optical injection (i. e. theratio of the injected DRV power with respect to the TX/RX output power)for the open loop, whereas it corresponds to about 30% of relative opticalinjection, for the close loop. It has been observed that, though the TX andRX have the same pump current and the same injection from the driver,in the close loop the relative optical injection is slightly smaller than in theopen loop. Indeed, this is due to the average power output of a chaotic laserbeing slightly higher than the power output from a steady state laser.Moreover, for the selected working conditions, the correlation between TXand RX is larger than 99%, whereas the correlation between TX and DRV,or RX and DRV, is of about 70%.


Figure 2.3: Open loop scheme: correlation between transmitter and receiver as afunction of optical injection from the driver and the TX/RX pump current.

Figure 2.4: Close loop scheme: correlation between transmitter and receiver as afunction of optical injection from the driver and the TX/RX pump current.


Figure 2.5: Open loop scheme: correlation between transmitter and driver as afunction of optical injection from the driver and the TX pump current.

Figure 2.6: Close loop scheme: correlation between transmitter and driver as afunction of optical injection from the driver and the TX pump current.


Figure 2.7: Open loop scheme: Q factor of the extracted message (a pseudo-random NRZ digital message at 5Gb/s, in baseband) for an ideally matched pair,as a function of the optical injection from the driver and the TX/RX pump current.

Figure 2.8: Close loop scheme: Q factor of the extracted message (a pseudo-random NRZ digital message at 5Gb/s, in baseband) for an ideally matched pair,as a function of the optical injection from the driver and the TX/RX pump current.


2.3.2 Open loop analysis

Synchronization

The selected working point, for the open loop scheme, has been studiedin more detail and, initially, without message transmission. Figure 2.9 showsthe RF chaotic power spectra obtained by photodetection of the driver, thetransmitter and the receiver outputs, with a 50Ω load resistance. For allphotodiodes, we have taken into account the Johnson noise and the shotnoise. We have also neglected all propagation losses. For convenience, thetraces relative to the driver and to the receiver have been shifted upwards anddownwards by 20 dB, respectively. The spectra of transmitter and receiverwould be otherwise superposed. Chaos cancellation is of approximately 50dB (limited by noise) on a large frequency band. This very high value comesfrom the assumption of identical lasers, and from using a symmetrical scheme,where TX and RX are identically injected by the DRV. Lower values are foundin the case of the standard two-laser scheme, which is not symmetrical, sincethe TX injects the RX. Slight difference of parameters (as we will see later)can significantly reduce this figure, and in experiments, where electronicsnoise and electromagnetic disturbances are present, it is difficult to obtain acancellation better than 10-15 dB on a bandwidth of few GHz.

The spectra of transmitter and receiver are identical, however they aresimilar to the driver spectrum, as it is natural to expect. Indeed TX and RXbecome chaotic due to the injection from the driver, otherwise they wouldbe not chaotic. Anyway, the different evolution between the DRV, TX andRX is evident from the chaotic waveforms plotted in the time domain (seefigure 2.10). The traces of TX and RX are identical, however, due to thedifferences in the phase of the spectral components, they are fundamentallydistinct from that of the DRV.

In figures 2.11 and 2.12, we report the correlation between TX and RXand between TX and DRV, respectively. The correlation peak between TXand RX is larger than 99%, whereas the correlation peak between TX andDRV, or RX and DRV, is lower than 70%. The maxima occur at time zerobecause we have neglected any propagation delay. From the subplots drawnin the figures, in normalized units, is evident that TX and RX are successfullysynchronized, whereas their synchronization with the driver is of poor quality,which supports the security of the scheme. Indeed, the DRV is selected withdifferent internal parameters, then it has a different internal dynamics, withrespect to the TX and the RX. This prevents an eavesdropper, accessingboth channel A e B, from extracting the message by simply performing thedifference of the photodetected signals.


Figure 2.9: Traces of the driver, transmitter and receiver in the frequency domain(5 MHz resolution bandwidth). For convenience, the traces relative to the DRVand to the RX have been shifted upwards and downwards by 20 dB, respectively.The difference signal is also drawn, showing a chaos cancellation of almost 50 dB.

Figure 2.10: Simulations of chaotic waveforms for the driver, transmitter andreceiver in the time domain.


Figure 2.11: Cross correlation, between the transmitter and the receiver, as afunction of delay time. A good correlation peak is achieved. The inset shows therelationship between the photodetected currents in normalized units.

Figure 2.12: Cross correlation, between the transmitter and the driver, as a func-tion of delay time. A poor correlation peak is achieved. The inset shows therelationship between the photodetected currents in normalized units.


Message transmission

With the aim to apply the open loop scheme to secure data transmissionin real fiber networks, we have numerically investigated message transmissionand message recovery at the system output.

The message amplitude has been adjusted (γ = 2 · 10−3) to obtain Q ≈ 6(BER ≈ 10−9) for the selected working point, then the system trimmabil-ity has been studied by fixing the external parameters (pump current andoptical injection) for the TX laser, while varying these parameters for theRX laser. In detail, for different values of the optical injection, from DRVinto RX, around its nominal value, we have performed a sweep of the RXpump current, and found the maximum Q factor for the recovered message.This reflects the alignment procedure that would be performed experimen-tally. The results are shown in figure 2.13, where the Q factor and the BERare plotted as functions of the relative injection. In the figure, each circleis the result of the explained optimization procedure. From figure 2.13, wecan conclude that a variation of injection can be partially compensated byacting on the pump current, which helps in view of a future experimentalimplementation. Moreover, since the full width at half maximum (FWHM)of the function describing the Q factor is about 1%, we deduce that an ac-curate trimming is required, which supports security. Indeed, the FWHMprovides the magnitude of the tolerable error in the alignment procedure ofthe external parameters.

It is interesting to observe that, around the nominal working point, alinear relationship holds between the relative optical injection from DRVinto RX, and the RX pump current for which we obtain the optimum Qfactor (see figure 2.14). However, from equations 2.2.1 and 2.2.2, it is notclear the reason of such behavior, then more investigations will be made.

In figure 2.15, for the selected working point we show, in the frequencydomain, the plaintext message (i. e. the message detected at the systemoutput with the DRV laser switched off), the transmitted signal (chaos plusmessage), and the message recovered at the system output by chaos cancella-tion. In the difference, some residual chaos is present at high frequency, dueto implementation of the algorithm, which extracts the signal by maximizingthe Q factor. However, this contribution is strongly reduced by the 5 GHzlow-pass filter, as it can be seen by the low signal excursion visible in theeye diagram (see inset). The Q factor is almost 6, which corresponds to anexcellent data transmission.

In figure 2.16, we report, in the time domain, the traces of figure 2.15, af-ter low-pass filtering at 5 GHz. The transmitted signal, in which the messageis hidden, is highly different from the recovered message and bits cannot be


identified. The plaintext message, i. e. the received message with the driverlaser is switched off, is also shown. We remember to the reader that in theopen loop scheme, differently from the close loop, the transmitter and thereceiver become chaotic only because of the injection from the driver. Other-wise they would be not chaotic. This can be seen as a lack of security for theopen loop scheme. Indeed, in the event of driver damage and in the absenceof an accurate monitoring of its activity, the message would be transmittedwithout any protection, making it readable for any non authorized listener.However, this lack of security will be overcome with the close loop scheme,as it will be shown later.


Figure 2.13: Q factor and BER as functions of the relative optical injection ofDRV into RX, for an ideally matched pair. Each point, at a given injection, isoptimized by sweeping the RX pump current.

Figure 2.14: Linear relationship between the optimum RX pump current and therelative optical injection.


Figure 2.15: Numerical RF spectra (5 MHz resolution bandwidth), for CM trans-mission of a 5 Gb/s digital message in baseband. The plaintext message, thetransmitted signal (chaos plus message), and the message recovered at the systemoutput are shown. The inset shows the eye diagram corresponding to the recoveredmessage after low-pass filtering at 5 GHz (Q ≈ 6).

Figure 2.16: Simulated current waveforms in baseband. The plaintext message,i. e. the message transmitted with the driver laser switched off, the transmittedsignal (chaos plus message), and the message, recovered at the system output bychaos cancellation, are shown.


Feasibility and security

−0.5% +0.5% −5% +5%(αR − αT )/αT 4.6 · 10−9 4.3 · 10−9 3.8 · 10−2 4.0 · 10−2

(τp,R − τp,T )/τp,T 4.7 · 10−9 1.6 · 10−9 5.2 · 10−2 5.3 · 10−2

(τs,R − τs,T )/τs,T 1.6 · 10−9 1.3 · 10−9 6.4 · 10−3 1.9 · 10−3

(ξR − ξT )/ξT 3.3 · 10−9 5.7 · 10−9 1.0 · 10−2 9.3 · 10−3

(N0,R −N0,T )/N0,T 3.2 · 10−9 2.3 · 10−9 2.2 · 10−9 2.1 · 10−9


Though a high quality of the recovered message can be achieved in ideal-ized conditions, it is important to investigate the effect of internal parametermismatch between TX and RX, to better evaluate both feasibility and secu-rity.

In real operating conditions twin lasers have small unavoidable differences,then to investigate the system feasibility, we have assumed a mismatch of±0.5% on the main internal parameters of the RX laser with respect tothe TX. After that, we have varied the injection from the driver into RXand the pump current of the RX in order to compensate as well as possiblethe parameter mismatch, and optimize Q factor and BER, as one would doexperimentally. As a result, it has been found that only a moderate increaseof the input message amplitude is required to get a BER of about 10−9 forthe recovered message. The required γ ranges from 2 · 10−3 for a mismatchon N0 and τs, up to 5 · 10−3 for α, while it is 3 · 10−3 and 4 · 10−3 for τp andξ, respectively. The obtained BER values are summarized in table 2.3.1.

We have then investigated the security level by evaluating the Q factorand the BER of the extracted message upon a mismatch of ±5%, on the sameinternal parameters. Again, we have tried to compensate such mismatch bymanipulating the external parameters, as a skilled eavesdropper would do.However, in this case, the message amplitude has been taken the same aswith the 0.5% mismatch, since the eavesdropper cannot act on the messageamplitude. As it can be appreciated from table 2.3.1, we have found thatthe scheme is very sensitive to a moderate mismatch of the internal parame-ters, which, with exception of the carrier density at transparency, cannot becompensated by acting on the injected optical power and on the RX pumpcurrent.

In figures 2.17 and 2.18, for example, we show graphically the numeri-cal results for one of the parameters of table 2.3.1. We plot Q factor andBER for the extracted message, when the gain coefficient ξ for RX has a


+0.5% and +5% difference, respectively, as compared to TX. In these fig-ures, all data points have been obtained by following the same procedure asfor figure 2.13. From figure 2.17, it can be concluded that a small mismatchcan be compensated, successfully recovering the message (BER ≈ 6 · 10−9),which supports the system feasibility. On the other hand (see figure 2.18),for a larger mismatch, the message quality cannot be significantly improved(BER ≈ 10−2), which confirms the system security. It is worth noting that,by increasing the signal amplitude, the tolerance on the mismatch is increasedboth for the regular addressee and for the eavesdropper. However, this trade-off between security and hardware requirements is typical of all chaos-basedcryptographic systems.

From the numerical simulations, it has been observed that the maximumQ factor corresponds to a working point where the relaxation frequenciesfor the unperturbed TX and RX lasers are very close to each other. Indetail, after optimizing the external parameters, two almost identical lasersexhibit a difference of few MHz in the relaxation frequency, whereas thatdifference can become even of 30 MHz for lasers that differ by 5% on theinternal parameters. As already pointed out in [12], the condition of equalrelaxation frequencies gives a good synchronization level, which is sufficientfor key generation. However, it has been found that this condition does notexactly correspond to the maximum Q factor. More important, if the laserscome with equal relaxation frequencies, but with a parameter mismatch ofthe order of 5%, the quality of the extracted message, optimized by varyingcurrent and optical injection, is poor (BER ≈ 10−1). For example, we presentsimulations in which two internal parameters of the RX laser (τp and τs)compensate to each other so that the transmitter and receiver laser, fed atthe same current, exhibit the same relaxation frequency. In figures 2.19and 2.20 we show results concerning the explained investigation. Whereas amismatch of +0.5% on τp can be successfully compensated with a mismatchon τs of −0.18%, simply acting on the external parameters (BER ≈ 2.2·10−9),a more high mismatch on τp (+5%) cannot be compensated by adjustingτs (−1.7%), even following the same optimization procedure. This againsupports transmission security.The mathematical relationship [26] between the relaxation frequency fR ofthe unperturbed laser, the carrier lifetime τs, the photon lifetime τp and thepump current I, is described by the equation

fR =1

2π

1√

τsτp

(

1− N0

Nth

)

√

I

Ith− 1, (2.3.1)


where Nth is the carrier density at threshold given by

Nth = N0 +1

τp ξ, (2.3.2)

and

Ith =Nth

τseV (2.3.3)

is the current of threshold. As in previous sections, N0 is the carrier densityat transparency, ξ the gain coefficient, V the active region volume and e theelectron charge, whose values are specified in table 1.2.1.

In spite of the strict matching requirements between TX and RX, aneavesdropper could try to force the system by completely disregarding chan-nel A, and building an open loop receiver fed by the composite signal ofchannel B. This different strategy considers the transmitted signal as propa-gating in a standard two-laser scheme, where the synchronization is achievedby injection of a fraction of the optical power coming from the transmitterinto the receiver, and the message is extracted by making the difference of therelative photodetected signals. However, the symmetrical design of the threelaser scheme offers better performance and high synchronization quality withrespect to the two-laser scheme, which allows us to work with a very smallsignal, still having a very low error transmission (BER ≈ 10−9). For thisreason, it is easy to find that the eavesdropper cannot successfully extractthe message by this attack, even holding a laser matched with the TX. TheBER, evaluated by numerical investigation, is of the order of 10−1.

Finally, it has been also verified that, due to the low correlation (70%)between DRV and TX, it is virtually impossible to extract the message bysubtracting the DRV chaos available in channel A from the composite signaltransmitted in channel B. Even in this case, the obtained BER is 10−1.


Figure 2.17: Q factor and BER as functions of the relative injection of DRV intoRX, for a slight mismatch (+0.5%) on the modal gain. Each point, at a giveninjection, is optimized by sweeping the RX pump current.

Figure 2.18: Q factor and BER as functions of the relative injection of DRV intoRX, for a moderate mismatch (+5%) on the modal gain. Each point, at a giveninjection, is optimized by sweeping the RX pump current.


Figure 2.19: Q factor and BER as functions of the relative injection of DRV intoRX, optimized by sweeping the RX pump current, for a slight mismatch in τp andτs. These parameters compensate to each other so that, for the nominal RX pumpcurrent, the unperturbed TX and RX exhibit the same relaxation frequency.

Figure 2.20: Q factor and BER as functions of the relative injection of DRV intoRX, optimized by sweeping the RX pump current, for a moderate mismatch in τpand τs. These parameters compensate to each other so that, for the nominal RXpump current, the unperturbed TX and RX exhibit the same relaxation frequency.


2.3.3 Close loop analysis

Message transmission with identical lasers

In view of a comparison of close and open loop, we have realised the closeloop by using the same parameters of the open loop. In all our numericalanalysis, for the DRV we have assumed again ID = 23.4mA and k2

D = 4%.In addition, we have taken k2

J = 4%, where J = T,R. Initially, to study themessage transmission, TX and RX are an identical matched pair, whereas,as in the open loop, the DRV have some different internal parameters (seetable 1.2.1).

The correlation between the transmitter and receiver has been studiednumerically as a function of the their pump currents and of the injectionpower from the driver (see figure 2.4). Also the correlation between TX andDRV has been evaluated in the same conditions and the computed correlationmaxima are shown in figure 2.6. We have also studied the transmission ofdigital data, by using a pseudo-random NRZ digital message at 5 Gb/s,in baseband. The quality of the extracted message has been quantified bycomputing the Q factor from the simulated eye diagram, and the obtainedresults, by varying the operating conditions, are presented in figure 2.8.

From the results shown in figures 2.4, 2.6, 2.8, it can be verified that theworking point, selected for TX and RX with the open loop, represents anadequate choice also for the close loop, which allows for a comparison of thetwo schemes. Then, we have held a pump current of 41 mA and an opticalinjection from the DRV into the two response lasers of 1.2 mW. In theseoperating conditions, the matched pair is subject to about 30% of relativeoptical injection (i. e. the ratio of the injected DRV power with respect tothe TX/RX output power). Moreover, the correlation between TX and RXis larger than 99%, whereas the correlation between TX and DRV, or RXand DRV, is of about 70%. The message amplitude has finally been adjusted(γ = 2.0 · 10−3) to obtain Q ≈ 6, which corresponds to a BER of about 10−9.The same value has been found for the open loop.

As specified in previous sections, one of the persuading reasons, for study-ing in detail the close loop, is that the message would still be masked bychaos to a non authorized listener even with a damaged driver, contrary tothe open loop, then enhancing transmission security. In figure 2.21 we showthe chaotic waveforms of DRV, TX and RX, in absence of optical injectionfrom the driver. TX and RX have their own chaotic dynamics. It has beenfound that, without injection from the driver, there is a correlation peakbetween TX and RX of the order of 35%. Indeed, they are twins, and it isnatural to find a similar internal dynamics, for common working conditions.


On the other hand the correlation peak of driver and transmitter (or DRVand RX) is approximately 15%. Indeed the driver is chosen with differentinternal parameters and it has a different internal dynamics with respect tothe transmitter and receiver. However, as soon as the driver injects sym-metrically TX and RX (see figure 2.22) the correlation peak of DRV andTX (or DRV and RX) becomes more or less 70%, but fortunately, the driverforce TX and RX into a common chaotic regime and their correlation peakgrows above 99%, which allows us to use the close loop scheme for securedata transmission.

Message transmission has been also studied for a complete comparisonwith the open loop. In figure 2.23, the plaintext message, the transmittedsignal (chaos plus message), and the message, recovered at the system outputby chaos cancellation, are shown in the frequency domain, for the selectedmessage amplitude. In the difference trace, the residual chaos, present at highfrequency, is strongly reduced by the 5 GHz baseband filter. By analysing theeye diagram (see figure), we find again a Q factor for the extracted messageof almost 6 which corresponds to a BER of about 10−9.

The Q factor and the BER have been computed as functions of opticalinjection and current, modified with respect to the nominal working point ofthe RX laser, while the TX working point is unchanged. This allows us toevaluate the system sensitivity to external parameters with the matched pair,preliminarily to the studies on the effect of laser mismatch that will be illus-trated in the following. In detail, for different values of the DRV/RX opticalinjection around its nominal value, we have performed a sweep of the RXpump current, and found the maximum Q factor for the recovered message.This reflects the alignment procedure that would be performed experimen-tally. The results are shown in figure 2.24, where the Q factor and BERare plotted as functions of the relative optical injection. From figure 2.24, itcan be concluded that a small variation of injection can be compensated byacting on the pump current, which helps in view of an experimental imple-mentation. However, as in the open loop, an accurate trimming is required,which helps against an eavesdropper attack.

Also for the close loop, a linear relationship holds between the relativeoptical injection and the RX pump current that realizes the optimum Q atthe given injection.

For an ideal twin pair, to quantify the relative sensitivity of the close loopwith respect to the open loop, we have calculated the FWHM for the curvesshowing the Q factor as a function of the relative optical injection (see figures2.13 and 2.24). We have found that FWHMClose loop = 0.4FWHMOpen loop.Then, the close loop is more critical to align with respect to the open loop,which supports security.


Figure 2.21: Chaotic waveforms for the DRV, TX and RX. In absence of opticalinjection from the driver, TX and RX have their own chaotic dynamics.

Figure 2.22: Chaotic waveforms for the DRV, TX and RX. TX and RX are injectedfrom the driver, which synchronizes them.


Figure 2.23: Traces in the frequency domain of the plaintext message, the trans-mitted signal (chaos plus message), and the message, recovered at the systemoutput by chaos cancellation.

Figure 2.24: Q factor and BER as functions of the relative optical injection ofDRV into RX, for an ideally matched pair. Each point, at a given injection, isoptimized by sweeping the RX pump current.


Laser parameter mismatch

The effect of internal parameter mismatch between TX and RX has alsobeen studied, to better evaluate both feasibility and security.

Since in real operating conditions twin lasers have small unavoidable dif-ferences, we have assumed that an authorized subscriber holds a receiver laserwhose internal parameters differ by ±0.5% with respect to the TX. Then, wehave varied the injection and the pump current of the RX in order to com-pensate as much as possible the parameter mismatch, and optimize Q factorand BER, as one would do experimentally. After that, only a moderate trim-ming of the input message amplitude has been required to get an excellentrecovered message (see table 2.3.2). The required value of parameter γ hasbeen 2.0 · 10−3 for a mismatch on N0 and τs, whereas it has been 5.0 · 10−3

for τp, 8.0 · 10−3 for ξ and 2.0 · 10−2 for α. It can be seen that these values(except N0 and τs) are all slightly larger than those used in the open loop.Then, since we achieve the same performance, this is indicative of a morecritical alignment of this system.

Then, we have evaluated the Q factor and the BER that could be ob-tained by an eavesdropper, assuming for its receiver a mismatch of ±5%, onthe same internal parameters. Again, we have tried to compensate such mis-match by manipulating the external parameters, as the eavesdropper woulddo. However, in this case, the message amplitude has been taken the sameas with the 0.5% mismatch, since the eavesdropper cannot act on it. As itcan be appreciated from table 2.3.2, we have found that the scheme is verysensitive to a moderate mismatch of the internal parameters, which, with theexception of the carrier density at transparency, cannot be compensated byacting on the injected optical power and on the RX pump current. As anexample, we show graphically the numerical results for the gain coefficient ξ.In figures 2.25 and 2.26, we plot Q factor and BER for the extracted mes-sage, when the gain coefficient ξ for RX has a +0.5% and +5% difference,respectively, with respect to TX. From figure 2.25, it can be concluded that asmall mismatch can be successfully compensated, ensuring message recovery(BER = 1.2 · 10−9), and this supports the system feasibility. On the otherhand (see figure 2.26), for a larger mismatch, the message quality cannot besignificantly improved (BER ≈ 10−2), which supports the system security. Itis worth noting that, to obtain BER values comparable with those obtainedwith the open loop (see figures 2.17 and 2.18), we have chosen, for the modu-lation coefficient, γ = 8.0 ·10−3, while for the open loop, γ has been 4.0 ·10−3.Although the difference is small, it emphasises that the closed loop is morecritical than the open loop. Indeed, we recall that the TX and RX lasers arechaotic even in the absence of injection from the driver.


A more complete comparison with the open loop, at least for our specificoperating point, has been performed by evaluating the accuracy requiredto optimize the system performance, i. e. to maximize the Q factor. Tothat purpose, we have considered, for parameters α, τp, τs, ξ, N0, the dia-grams of Q versus injection, both for the open and for the close loop, as-suming a 0.5% mismatch. Then, we have calculated and compared the fullwidth at half maximum (FWHM) of such diagrams. For all parameters, theclose loop has been found to be more critical to trim than the open loop.For example, for the carrier density at trasparency N0, we have found thatFWHMClose loop ≈ 0.4FWHMOpen loop. For the remaining parameters, therelative sensitivity S, where S = FWHMClose loop/FWHMOpen loop, has beencalculated and summarized in table 2.3.3.

Since this specific working point had been previously optimized for theopen loop, these results suggest that the close loop scheme is more demandingin terms of matching and trimming, and thus, that it is more challengingfor an eavesdropper. However, more extensive numerical and experimentalinvestigations should be done to fully evaluate the new scheme, and for athorough comparison with the open loop in terms of security.

−0.5% +0.5% −5% +5%(αR − αT )/αT 1.2 · 10−9 1.3 · 10−9 7.8 · 10−3 1.2 · 10−2

(τp,R − τp,T )/τp,T 3.0 · 10−9 1.8 · 10−9 1.9 · 10−2 2.2 · 10−2

(τs,R − τs,T )/τs,T 1.2 · 10−9 1.5 · 10−9 2.7 · 10−4 9.8 · 10−5

(ξR − ξT )/ξT 1.4 · 10−9 1.2 · 10−9 3.9 · 10−3 5.1 · 10−3

(N0,R −N0,T )/N0,T 1.1 · 10−9 1.9 · 10−9 3.2 · 10−9 2.3 · 10−9


−0.5% +0.5%(αR − αT )/αT 96.4% 95.1%(τp,R − τp,T )/τp,T 45.7% 44.6%(τs,R − τs,T )/τs,T 45.0% 45.0%(ξR − ξT )/ξT 51.5% 49.2%(N0,R −N0,T )/N0,T 40.4% 40.4%

Table 2.3.3: Relative sensitivity of the close loop with respect to the open loop.


Figure 2.25: Q factor and BER as functions of the relative injection of DRV intoRX, for a slight mismatch (+0.5%) on the modal gain. Each point, at a giveninjection, is optimized by sweeping the RX pump current.

Figure 2.26: Q factor and BER as functions of the relative injection of DRV intoRX, for a moderate mismatch (+5%) on the modal gain. Each point, at a giveninjection, is optimized by sweeping the RX pump current.


Phase sensitivity

It has been previously shown in literature that the optical phase of thefeedback light has a significant effect on the quality of synchronization in thestandard two-laser close loop scheme [27]. Moreover, some schemes for on-offphase shift keying have been proposed for chaos communications [28, 29].Hence the feedback phase is an important parameter.

In this thesis, we show the dependence from the feedback phase alsofor the close-loop three laser scheme. In previous simulations, cavities oftransmitter and receiver have been assumed identical. After removing thisassumption, supplementary numerical analysis has showed that an accuratephase matching is required to get a good synchronization, consistently with[22]. In particular, the effects of the feedback light phase on the correlationbetween transmitter and receiver is described. In figure 2.27, we show thecorrelation between TX and RX as a function of the relative cavity length∆L/λ, where λ is the optical wavelength of the semiconductor lasers and∆L, by taking in account the photon roundtrip time, is defined as twice thedifference between the cavity lengths of receiver and transmitter. From thefigure, it can be observed that the cross correlation changes periodically, asthe relative cavity length is varied continuously, and the correlation is maxi-mum when ∆L is equal to an integer number of wavelengths. Equivalently,the maximum correlation between the two response lasers is obtained whenthe phases of the feedback light differ by 2kπ, where k in an integer. Fromthe figure 2.27, we deduce again that the minimum correlation is achievedwhen the difference of the optical phases is π + 2kπ, where k = ±0, 1, 2, etc.It is worth noting that whereas the maximum cross correlation value is largerthan 99%, the minimum value is of the order of 60%. Then, by realising themaximum mismatch in the relative phase, the cross correlation is not com-pletely destroyed, probably due to the injected signal from the driver, whichtries to route the receiver into a common chaotic regime with the transmitter.It can be concluded that synchronization, by injection of a common chaoticsignal in semiconductor lasers with optical feedback, is sensitive with respectto the optical phase of the feedback light in the two response lasers, as in thecase of identical synchronization realized with the standard two-laser closeloop scheme [27].

A further result, in view of an experimental implementation of the dis-cussed setup, is the following. For perfectly matched lasers, a maximumdifference in the relative cavity lengths of 0.028 (∆L = 43.4 nm), whichcorresponds to a phase difference of 176mrad, it is necessary to get a cross-correlation coefficient of at least 95%. Then, an accurate trimming is re-quired and, as it has been already observed in the standard two-laser close


loop scheme, also in the close-loop three laser scheme the phase plays animportant role.

In figure 2.28, the Q factor and the BER are numerically evaluatedas functions of the relative cavity length. Since the message amplitude(γ = 2 · 10−3) is about one thousand times smaller than chaos amplitude,the curves of the Q factor and BER are very narrow. For example, theFWHM of the Q factor curve is 0.3 · 10−3, then, experimentally, it is possibleto replicate this result only qualitatively. Indeed, it is difficult to align thecavities very well, performing a mismatch nearly exactly of an integer multi-ple of the optical wavelength λ.A significant increase in FWHM of the curves of Q and BER can be achievedby increasing the message amplitude, but this procedure also helps the eaves-dropper, since the maximum security is achieved when the message is smallcompared with the chaos amplitude. However, this drawback can be over-come using twin lasers that support an efficient alignment of the externalcavities, as discussed later in the experimental part.


Figure 2.27: Numerical cross correlation between matched TX and RX as a func-tion of the relative cavity length. ∆L is twice the difference of the RX and TXcavity lengths. λ, instead, is the optical wavelength of the semiconductor lasers.

Figure 2.28: Q factor and BER as functions of the relative cavity length.


Experiments

Since the investigated scheme has been numerically proven to be sensitiveto laser parameter mismatch and to phase, it is important to evaluate itspractical feasibility, i. e. to experimentally prove synchronization, chaoscancellation and message transmission.

Experiments have been performed using two matched integrated mod-ules, the transmitter and the receiver [24, 25], specifically designed for chaotictransmissions (see figure 2.2) by the Fraunhofer Institute for Telecommunica-tions, Heinrich Hertz Institute (Berlin, Germany). They have been selectedfrom the same wafer and in close proximity, to have the same threshold, slopeof the P/I characteristic, as well as optical and RF spectra. The lasers of bothmodules work at 1548.50 nm, with a threshold of the order of 10mA. Theytypically operate between 15 and 17mA, where they produce a sufficientlylarge chaos, which is also possible to synchronize efficiently. Increasing thecurrent, they result in a more complex chaotic behaviour, which, however,is more difficult to synchronize, then performing a poor chaos cancellation.The RF chaotic spectra of both devices (with no injection from DRV) areshown in figure 2.29. They have been measured after a proper selection ofthe working point and feedback ratio (which can be changed by acting on theintegrated VOA) to match the chaotic emissions of the two modules. Thespectra of the transmitter and receiver are very similar, as it is expected fromtwin lasers in proper working conditions.

The DRV has been a Mitsubishi DFB standard telecommunication lasertrimmed in temperature to work at the same wavelength as TX and RX. Ithas a different chaotic spectrum and different electrical characteristics withrespect to the matched pair. Its threshold is 8mA and we have chosen aworking pump current of 12mA. The three devices have been used to realisethe the scheme of figure 2.1, in back to back, i. e. with a short (2 m) fiberlength.

The cavity phase is expected to play a major role in synchronization,since this fact has been already observed in the standard two-laser close loopscheme, both numerically and experimentally. For this reason, a trimmingphase shifter (PS) has been included in the integrated modules used in theexperiments. However, the requested accuracy, showed in the numerical anal-ysis, is difficult to obtain and to maintain for a long time in experiments, thenthe measured chaos cancellation is reduced with respect to the ideal case. Ina practical implementation, this drawback adds to the effect of the parametermismatch.

In figure 2.30, we show the RF chaotic spectra of DRV (shifted up by10 dB) and TX (subject to injection). As expected, from comparison of


figures 2.29 and 2.30, the TX spectrum is changed due to injection from thedriver. It follows that the TX laser does not synchronize to the DRV, sincetheir spectra are not identical; this is evident especially at low frequency.This fact can be more clearly appreciated from the spectrum of the differencebetween TX and DRV, which has been also measured, by rearranging thesetup of figure 2.1, and is also shown in figure 2.30. In the same figure, thespectrum of the difference of TX and RX is also shown, exhibiting a chaoscancellation level up to 10 dB at 1.2GHz, in optimized conditions, includingan accurate trimming of the PS bias.

To finalise our analysis, we have preliminary realised message transmis-sion. It can be observed that the distance (5− 10 dB) between the TX chaoscurve and the TX-RX cancellation curve (see figure 2.30), is sufficient to ac-commodate a signal for a transmission in baseband. Then, a pseudo-randomNRZ message at 1 Gb/s has been transmitted by chaos modulation.In figure 2.31 we present the eye diagram of the the extracted signal with-out chaos cancellation (BER ≈ 10−1). This is the signal recovered by a nonauthorized listener accessing channel B (see the scheme in figure 2.1); themessage cannot be recognised, which supports security.Then, we have performed the message extraction by chaos cancellation. Eventhough the aperture of the eye in figure 2.32 is not excellent (BER ≈ 5·10−4),FEC can be used to reduce the BER to value of 10−9 or lower.

From figure 2.30, we observe again that a transmission on a carrier at1.2GHz, where chaos is stronger, can be realized [19]. Manchester coding[30] may also be considered to transfer the message spectrum under the peakof the chaos amplitude.

As final remark, since it is very difficult to extract the parameters ofthe Lang-Kobayashi model from real devices, and to measure their matchinglevel, a quantitative comparison between the numerical analysis and the ex-periments cannot be done. However, the experimental measurements qual-itatively agree with the simulations, even though the absolute values aredifferent.


Figure 2.29: Experimental RF chaotic spectra of two matched devices (TX, RX),without injection from the driver and in optimized conditions.

Figure 2.30: Experimental spectra of DRV (shifted upwards by 10 dB), and ofTX, under injection from DRV. The spectra of the difference between TX and RXand between TX and DRV, are also shown.


Figure 2.31: Eye diagram of the extracted signal without chaos cancellation(BER ≈ 10−1). This is the signal recovered by a non authorized listener accessingchannel B in the scheme of figure 2.1.

Figure 2.32: Eye diagram of the message extracted by chaos cancellation. TheBER, which corresponds to the eye aperture, is approximately 5 · 10−4.


2.4 Message transmission on a carrier

To extend the range of applicability of our scheme and in view of anextensive application to real fiber networks, besides the baseband transmis-sion, the transmission on a carrier has been considered. The use of a carrierhas been already proposed in scientific literature [19] for chaos based com-munications. Indeed, to optimize system performance, it can be convenientto place the message where the chaos amplitude is stronger or where thesynchronization is better.

By following the procedure described in subsection 2.3.1, we have chosenproper working conditions for the twin pair consisting of transmitter andreceiver, whereas the internal and external parameters of the driver laserhave been left unchanged. In view of a comparison between open and closeloop, the pump currents of TX and RX have been fixed to 51 mA for bothschemes, whereas the injection from the driver has been placed to 2.4 mW,which corresponds to a relative optical injection of about 46%.

For both open and close loop, in the chosen working point, DRV and TX,or DRV and RX, realise a poor correlation (70%) whereas the correlationbetween transmitter and receiver is over 99%. Then, the system is suitablefor message transmission and a pseudo-random NRZ digital signal at 4 Gb/s,modulating a carrier in amplitude with 100% modulation depth, has beenconsidered. The carrier frequency has been fixed at 5 GHz.

We do not want to retrace step by step the procedure performed in theprevious sections, so we focus directly on the system performance. We havestudied the sensitivity to external parameters for a perfectly matched pairand, after that, we have simulated real lasers, i. e. lasers with internalparameters different by 0.5%. The attack by an unauthorized listener, whichuse a receiver laser with internal parameters different by 5%, has been alsotaken in consideration in order to estimate transmission security on a carrier.

In a range of values of the relative optical injection around the nominalworking point of the RX laser, the RX pump current has been swept in orderto optimize the Q factor and the BER of the extracted message, while theTX working point has been left unchanged. For a perfectly matched pair, infigures 2.33 and 2.34, we report the Q factor and the BER as functions ofthe relative optical injection, both for the open and close loop, respectively.As seen in the preceding numerical investigations, a small change in theinjection can be successfully compensated by adjusting the pump current,which is promising in view of experimental realization. At the same time,it is required an accurate alignment, supporting security. The obtained Q isabout 6 (equivalently, BER ≈ 10−9), however from the figures it stands outthat the Q factor curve of the close loop is narrower compared to that of open


loop. Indeed, FWHMClose loop ≈ 0.2FWHMOpen loop, which stresses that theclose loop is more demanding in terms of implementation and alignment,compared to the open loop.

The system feasibility and security have been numerically investigated.In tables 2.4.1 and 2.4.2 we report the obtained results. As well as for thetransmission in baseband, also for the transmission on a carrier, a smallmismatch in the internal parameters can be compensated by acting on theexternal parameters and on the modulation coefficient γ, which supportsthe feasibility. At the same time, as soon as the transmission is optimizedfor a small mismatch in the TX/RX lasers, a mismatch of 5% cannot becompensated by acting again on the external parameters, then supportingthe security of the scheme.

The relative sensitivity S, where S = FWHMClose loop/FWHMOpen loop,has been finally estimated. It is sufficient to look at the table 2.4.3 to realizethat for a message transmitted on a carrier, as for a message transmitted inbaseband, the close loop has greater demands in terms of trimming, beingthe Q factor functions of the close loop narrower than the Q factor functionsof the open loop.

In conclusion, in view of a practical implementation of our scheme forsecure data transmission in real fiber networks, the transmission on a car-rier, as well as the transmission in baseband, has been considered and boththe open and close loop schemes perform well, according to simulations andpreliminary experiments. The close loop ensures that the message remainscovered by chaos also in the event of damage of the driver and in additionit results more challenging in terms of implementation, guaranteeing greaterlevel of security respect to the open loop.


Figure 2.33: Open loop: Q factor and BER as functions of the relative opticalinjection of DRV into RX, for an ideally matched pair. Each point, at a giveninjection, is optimized by sweeping the RX pump current.

Figure 2.34: Close loop: Q factor and BER as functions of the relative opticalinjection of DRV into RX, for an ideally matched pair. Each point, at a giveninjection, is optimized by sweeping the RX pump current.


−0.5% +0.5% −5% +5%(αR − αT )/αT 4.0 · 10−9 7.5 · 10−9 1.2 · 10−3 1.7 · 10−3

(τp,R − τp,T )/τp,T 5.0 · 10−9 5.3 · 10−9 2.4 · 10−3 7.1 · 10−3

(τs,R − τs,T )/τs,T 6.8 · 10−9 6.9 · 10−9 6.6 · 10−4 7.0 · 10−4

(ξR − ξT )/ξT 4.9 · 10−9 6.9 · 10−9 4.8 · 10−5 7.3 · 10−5

(N0,R −N0,T )/N0,T 4.8 · 10−9 7.8 · 10−9 7.8 · 10−9 9.0 · 10−9

Table 2.4.1: Open loop: effect on BER of TX/RX parameter mismatch.

−0.5% +0.5% −5% +5%(αR − αT )/αT 7.2 · 10−10 1.0 · 10−9 9.5 · 10−3 3.4 · 10−2

(τp,R − τp,T )/τp,T 8.1 · 10−10 3.0 · 10−9 2.9 · 10−2 6.3 · 10−2

(τs,R − τs,T )/τs,T 2.4 · 10−9 2.4 · 10−9 2.4 · 10−4 7.4 · 10−5

(ξR − ξT )/ξT 4.2 · 10−9 5.1 · 10−9 2.6 · 10−2 5.4 · 10−2

(N0,R −N0,T )/N0,T 4.7 · 10−9 3.5 · 10−9 3.5 · 10−9 4.9 · 10−9

Table 2.4.2: Close loop: effect on BER of TX/RX parameter mismatch.

−0.5% +0.5%(αR − αT )/αT 27.5% 27.6%(τp,R − τp,T )/τp,T 13.3% 11.2%(τs,R − τs,T )/τs,T 93.3% 95.9%(ξR − ξT )/ξT 10.7% 8.9%(N0,R −N0,T )/N0,T 25.6% 25.6%

Table 2.4.3: Relative sensitivity of the close loop with respect to the open loop.

CHAPTER 3

ANALYSING SIGNAL USING BER

In real optical networks, because of inevitable imperfections, the conveyedmessages are subject to different damages. Then, the quality evaluation of amessage by error analysis is important, and its examination can be useful inthe evaluation, or troubleshooting, of digital transmission systems.

A digital message, i. e. data composed by a single sequence of zerosand ones, consists of a train of squared digital pulses. NRZ codification isthe most commonly used. The black trace in figure 3.1 represents a NRZdigital message at 5 Gb/s. This is one of the signals used in the previouschapters, where secure data transmission schemes have been investigated andthe technical skill to mask the message to an undesired listener is based onthe use of chaotic lasers.

Squared pulses contain considerable amount of energy at multiples of therepetition rate (harmonics), and the amount of energy in the harmonics, rel-ative to the fundamental, is related to rise and fall time and pulse duration.Fast rise and fall times (square transitions) and narrow pulse durations giverise to a great harmonic energy. A great harmonic energy in the data sig-nal produces corresponding modulation sidebands that extend well beyondthe intended bandwidth of the allocated communication channel. In orderto reduce interference, it is not permitted to have channels with unlimitedbandwidth. Then, to reduce these unwanted sidebands, it is preferable tofilter the data signal at the bit rate frequency (first harmonic). From figure3.1 (see blue trace), it can be appreciated that, even though the filteringoperation reduces the harmonic energy, the integrity of the transmitted datais preserved.

Signal impairments can occur in many places, from the pre-filtering in thetransmitter, along the propagation path (e. g. dispersion, optical amplifier

77

Analysing signal using BER 78

noise, and distortion from non linear effects), from the receiver front-endand baseband signal processing. Besides these message damaging, whitenoise is a characteristic of all optical devices and electronic circuits, andit can be produced by several different effects. For example, thermal andshot noise are unavoidable and due to the laws of nature, whereas othertypes of noise depend mostly on manufacturing quality and semiconductordefects. A message, clean at the transmitter side, can appear distorted atthe receiver output, because of the above mentioned suffered transmissionproblems. Suitable filtering can partially eliminate the damage caused bythe message transmission and processing, however, errors are introduced andtheir measurement is required for an evaluation of the whole transmissionnetwork.

In addition to the above mentioned transmission problems, data trans-mission schemes proposed in previous chapters, where, in order to ensuresecurity, the message to be transmitted is masked with chaos, introduceadditional errors. In detail, the introduced errors are due to the practi-cal difficulty of extracting the message from chaos without impairments dueto residual chaos. Errors in the signal transmission can be experimentallyquantified with a BER tester. Unfortunately, the direct BER evaluation isnumerically very time expensive and we cannot afford to perform. In spite ofthis, if the message impairment is due to white noise, another parameter, theQ factor, from which the BER can obtained, can be easily estimated bothnumerically and experimentally. In the following, we will see that the BERcan be obtained from the Q factor, also if the message impairment is due toresidual chaos.


Figure 3.1: The black trace represents a train of squared digital pulses codifiedNRZ at 5 Gb/s. The blue trace is the above squared message filtered at the bitrate frequency of 5 GHz.

3.1 Signal impairment due to white noise

Because it is numerically difficult to take into account all causes of mes-sage damaging, for our numerical investigations we consider only the deterio-ration due to filtering and white noise. A message suffering such impairmentis represented by the blue trace in figure 3.2. The squared message is reportedto allow a visual comparison between the whole and damaged message.

A common indicator of performance in digital transmission systems is theeye diagram. It is done by shifting all the bits of a train of digital pulseson the same frame. For example, the result of this operation, applied to thedamaged message of figure 3.2, is shown in figure 3.3. From the b region infigure 3.3, it is evident that the white noise leads to a broadening of the logicallevels zero and one. The a region, instead, is due to filtering, and becauseof the perturbation introduced by white noise, a non negligible amount ofvariation, where the zero crossing occurs, is present. The eye aperture, alongboth the x and y axis, provides, at a glance, evaluation of system performanceand offers insight into the nature of channel imperfections. Careful analysisof its appearance can give the user a first order approximation of signal tonoise ratio, clock timing jitter and skew. Besides the qualitative evaluationof the transmitted message, a quantitative parameter, known as Q factor, is


Figure 3.2: The blue trace describes the filtered message impaired by white noise.The squared message is reported to allow a visual comparison between the twosignals.

defined. By taking into account only the eye aperture along the y axis (seefigure 3.3), we have

Q =l

σ0 + σ1

, (3.1.1)

where l is the mean eye aperture, whereas σ0 and σ1 are the standard de-viations of the logical levels zero and one, respectively. From the Q factordefinition is clear that a high Q factor corresponds to a high quality of thereceived message. In particular, it takes into account that in optical fibersystems the standard deviation of the logical levels is different for the re-ceived logical zero and one. Further comments on the Q factor will be donein the following.

In practice, there are different criteria of measuring the rate of erroroccurrences in a digital data stream [31]. One common approach is to dividethe number Ne of errors occurring over a certain time interval by the totalnumber Nt of zeros and ones transmitted during the same interval. The BitError Rate, commonly abbreviated BER, is thus defined as:

BER =Ne

Nt

. (3.1.2)


Figure 3.3: The eye diagram is a common indicator of performance in digitaltransmission systems. l is the mean eye aperture, σ0 and σ1 are the standarddeviations of the logical levels zero and one, respectively.

The BER is expressed by a number, such as 10−9, which states that, on theaverage, one error occurs for every billion pulses sent. Typical error rates foroptical fiber telecommunication systems range from 10−9 to 10−12. This errorrate depends on the ratio of signal power to noise power at the receiver. Thesystem error rate requirements and the receiver noise levels thus set a lowerlimit on the optical signal power level that is required at the photodetector.

To compute the bit error rate from the eye diagram, we have to know theprobability distribution [32] of the signal at the equalizer output. Knowingthe signal probability distribution at this point is important because it isthere that the decision is made as to whether a zero or one is sent.

The probability function describing a squared message is discrete, andthe total probability occurrence of logical zero and one is 100%. However,a message suffering impairments due to filtering and white noise must to bedescribed by a continuous probability function, which inevitably results in acomplicated shape. For example, the probability density as a function of thephotodetected current, which describes the damaged message in the figure3.2 (see blue trace), is represented by the blue spots in figure 3.4. To facilitatethe analysis of the obtained result, coherently with the division in regions ofthe eye diagram (see figure 3.3), we have also divided figure 3.4 into the aand b regions. Again, the blue spots in the a region are principally due to


Figure 3.4: Probability density for received logical zero and one signal pulses, asa function of the photodetected signal. The impairment of the logical levels is dueto white noise.

message filtering. Indeed, due to filtering, there is a significant probability, atthe receiver, of detecting a signal value close to zero mA. On the other hand,as expected, because of gaussian probability distribution of white noise, theshape of the logical zero or one (blue spots in the b region) has a gaussianappearance. Note that the different shape of the two gaussian distributionsin figure 3.4, numerically, is due to the use of a message of reduced length,in which the logical level zero is more common that the logical level one. Onthe contrary, in a real optical system, this may happen because the noisepower for a logical zero is usually not the same as that for a logical one.For example, this may occur because of signal alterations from transmissionimpairments, noise contributions due to amplification chain, different opticalpower for the logical zero and one signal pulses.

With the aim to calculate the error probability, a tradeoff between com-putational simplicity and accuracy of the results has been made. The sim-plest way takes into account only the distribution of the logical levels, thenneglecting the alteration introduced by filtering. This operation does notproduce a significant error. What is important, it is the average distance ofthe logical levels and their standard deviations. Note that, neglecting the aregion, in figure 3.4, is equivalent to neglect the a region marked out in theeye diagram (see figure 3.3). In addition, this simplification does not affect


the Q factor definition, which takes into account only the eye aperture alongthe y axis. If this method is assumed, when the sequence of optical pulsesis known, the equalizer output current can be described by a combinationof two gaussian random variables. The red curve in figure 3.4 represents thebest combination of two gaussian distributions interpolating the blue spots inthe b region. Note that, whereas the correlation of the functions (blue spotsand red curve) in the b region is above 99%, the total correlation, obtainedincluding the a region, is almost 97%.

Under the assumption of gaussian distribution for the noise of the logicallevels, a relationship [33] exists between the BER and the Q factor:

BER =1

2·[

1− erf

(

Q√2

)]

, (3.1.3)

where

erf(x) =2√π

∫ x

0

e−y2dy (3.1.4)

is the error function, which is tabulated in various mathematical handbooks.The Q factor is widely used to specify receiver performance, since it is

related to the signal to noise ratio required to achieve a specific bit errorrate. Furthermore, experimentally, the Q factor is easily estimated using asampling oscilloscope, thus avoiding the employment of an expensive BERtester. Figure 3.5 shows how the BER varies with the Q factor. A commonlyquoted Q value is 6, since it corresponds to a BER of almost 10−9.


Figure 3.5: Plot of the BER as a function of the Q factor.

3.2 Signal impairment due to residual chaos

In the previous chapters, we have proposed two new schemes for securedata transmission and the quality of the extracted message has been eval-uated by analysing the errors due, in part, to filtering and photodetectornoise, and principally to residual chaos. These errors are not negligible, andthey are the main reason of receiving a message whose quality is lower whencompared with that of the message sent. The BER has been obtained by theQ factor, however nothing has been said about the statistical properties ofresidual chaos.

In the scheme proposed in chapter 1, chaotic dynamics and synchroniza-tion of transmitter and receiver have been achieved by electrical injection intheir pumps of a common chaotic driving signal, generated by a third chaoticlaser, the driver. The scheme proposed in chapter 2 is similar to that of chap-ter 1, indeed we have used again a driver, a transmitter and a receiver, butnow the transmitter and receiver are forced into a common chaotic regimeby optical injection from the driver, and not by electrical injection. For bothschemes, the baseband message transmission has been realized by chaos mod-ulation and a NRZ digital signal at 5 Gb/s has been used. The dark tracein figure 3.6 represents the employed message before filtering.

In both schemes, the message has been filtered at the bit rate frequencyof 5 GHz, and then transmitted masked by chaos. The blue trace in figure


3.6 represents the typical message, extracted at the receiver side by makingthe difference between the transmitted signal and the chaos replicated atthe receiver. Because of system complexity there is a practical difficulty torealise a complete chaos cancellation. Message impairing is evident, indeed,its quality is reduced principally due to residual chaos.

The probability density of the extracted message, as a function of thephotodetected current (see blue trace in figure 3.6), has been numericallystudied, and it is represented by the blue spots in figure 3.7. The analysis ofthe obtained result is similar to that reported in section 3.1 of this chapter,where the message impairment is mainly due to white noise.

As in section 3.1, the blue spots in the a region are principally due tomessage filtering. Indeed, due to filtering, there is a significant probability todetect, at the equalizer output, a current value close to zero mA. However, atradeoff between simplicity and accuracy of the results asks again to neglectthe amount of signal distortion close to zero crossing (see the a region infigure 3.7). So, the attention is again on the distribution of the logical levelszero and one.

Though the distortion of the logical level zero or one (blue spots in the bregion of figure 3.7) is principally due to residual chaos, gaussian appearanceis again present. Indeed, the red trace in figure 3.7 is the best combination oftwo gaussian distributions interpolating the blue spots in the b region. Then,the logical level zero or one can be described by a gaussian distribution, and,as it has been done in section 3.1, the BER can still be obtained from the Qfactor. Thus, the relation 3.1.3 remains valid.

To confirm the obtained results, in figure 3.8 (see blue spots), we showthe probability distribution of residual chaos. This has been numericallyobtained by performing the difference between the recovered and the sentmessage. Since the red trace in figure 3.8 is the best gaussian fitting ofthe blue spots, we conclude, as expected, that residual chaos has a gaussianstatistics. This is consistent with the analysis of other working points takeninto account for the schemes proposed in the previous chapters.

Note that, although we have used the same short logical sequence, em-ployed previously in the case of message corrupted by white noise, where thelogical level zero is most common that the logical level one, now the heightand width of the distributions are comparable (see figure 3.7). Moreover, wehave noted that performing new simulations, in which the initial conditionsare changed, we obtain again a slightly different form for the distribution ofthe logical levels. This may be due to the unpredictable nature of chaoticphenomena. In spite of this, such behavior has never been observed if themessage is corrupted by white noise, although we have used different timeseries of white noise randomly generated.


Figure 3.6: The dark trace represents the squared message employed in theschemes presented in chapters 1 and 2. The blue trace describes the filtered messageimpaired by chaos.

We have still observed that, whereas the correlation of the functions,described by the blue spots and red curve in the b region, is above 99%, thetotal correlation, obtained including the a region, is almost 96%.

In conclusion, the error analysis on a message can be performed usingBER, without applying its definition, even though the impairment on themessage is produced by residual chaos. Indeed, since residual chaos has agaussian statistics, the BER can be obtained by the Q factor. The Q factor iseasily estimated by the eye diagram. This is done, numerically, by shifting allthe bits on the same frame, experimentally, by using a sampling oscilloscope.

Final remark

The result reported above is not obvious. Consider that chaos is describedby nonlinear differential equations, which, moreover, are extremely sensitiveto initial conditions. In addition, one may think that the distribution of achaotic waveform is itself gaussian, but this is not always true. In spite ofthis, it has been numerically noted that the difference between the signals ofa chaotic transmitter and a synchronized receiver laser has always a gaussianstatistics. This seems to be linked to the cancellation quality. Indeed, it hasbeen noted that, if the spectrum of the difference is flat, i. e. all frequency


components have the same power, the shape of the resulting distributionis gaussian. However, careful experiments must be done to confirm thisnumerical result.

Furthermore, we have observed, first numerically and then experimen-tally, by analysing of waveforms obtained in the laboratory, that the distri-bution of a chaotic waveform also depends on the frequency cut-off of thelow-pass filter. For example, from figure 3.9 a to figure 3.9 d, we show theprobability density obtained by analysing a simulated chaotic waveform byvarying the frequency of filtering from 1 GHz to 4 GHz with step of 1 GHz,respectively. Even though the obtained distributions are not perfectly gaus-sian, the correlation between each of them and the gaussian best fitting isabove 90%. Experimentally, the situation is not very different. Real chaoticwaveforms have been acquired in the laboratory with a real time oscilloscope.In detail, they have been generated by using the HHI1 InP monolithically in-tegrated module described in figure 2.2. From figure 3.10 a to figure 3.10d, we show the probability distribution obtained by varying the frequency offiltering from 1 GHz to 4 GHz with step of 1 GHz, respectively. It is evidentthat the behavior of the probability distributions shows a great variabilityfor both simulated and chaotic waveforms. In addition, we observe that eachtrace presented in figures 3.9 and 3.10 is well interpolated by a linear com-bination of two gaussian distributions (red trace). The reason of this is stillnot understood and deserves further study.

1Laser produced by the Fraunhofer Institute for Telecommunications, Heinrich HertzInstitute (Berlin, Germany), within the European project PICASSO.


Figure 3.7: Probability density for received logical zero and one signal pulses, asa function of the photodetected signal. The distortion of the logical levels is dueto residual chaos.

Figure 3.8: Probability distribution of residual chaos (blue spots). This is numer-ically obtained by performing the difference between the recovered and the sentmessage. The red trace is the best gaussian fitting of the blue spots.


Figure 3.9: Probability distribution analysis for a simulated chaotic waveform.From figure a to d, the waveform has been filtered from 1 GHz to 4 GHz with stepof 1 GHz, respectively.

Figure 3.10: Probability distribution analysis for a real chaotic waveform. Fromfigure a to d, the waveform has been filtered from 1 GHz to 4 GHz with step of 1GHz, respectively.

CONCLUSIONS

In the first two chapters, we have proposed two different schemes suitablefor secure data transmission in optical fiber networks. All the schemes makeuse of three semiconductor lasers, identified as driver, transmitter and re-ceiver. The key of the encryption procedure relies on the use of a transmitterand receiver that are a twin pair, i. e. lasers with the same internal param-eters, chosen in close proximity on the same wafer. The driver, instead, isselected with different internal parameters with respect to the twin pair. Inthe scheme proposed in chapter 1, chaotic dynamics and synchronization oftransmitter and receiver are achieved by electrical injection in their pumpsof a common chaotic driving signal, generated by the third laser, i. e. thedriver. The scheme proposed in chapter 2 is similar to that of chapter 1,but now transmitter and receiver are forced into a common chaotic regimeby optical injection from the driver, and not by electrical injection. For bothschemes, the message encryption has been achieved by direct modulationof the transmitter chaotic emission. We have first considered the basebandtransmission of a NRZ digital signal at 5 Gb/s, and then the transmission ofa 4 Gb/s NRZ digital message modulating a 5 GHz carrier. In both cases,the message has been extracted at the receiver side by making the differencebetween the transmitted signal and the chaos replicated by the receiver.

For both schemes, message masking and message recovery have beendemonstrated preliminary in ideal conditions, i. e. with transmitter andreceiver as a perfectly twin pair, then, we have analysed and demonstratedthe system feasibility, by assuming that in real conditions two matched lasershave differences of 0.5% in their main internal parameters. Also the secu-rity of both schemes has been investigated and demonstrated. Indeed, wehave supposed that a non authorized listener try to force the system usinga receiver laser whose internal parameters differ by 5%, with respect to the

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Conclusions 91

pair of authorized subscribers. For both schemes, we have also verified that,because of different chaotic dynamics, it is virtually impossible to extract themessage by performing the difference between the composite signal comingfrom the transmitter and the signal coming from the driver. We have alsoanalysed the different strategy, in which the transmitted signal is consideredas propagating in a two-laser scheme. Again, the eavesdropper fails with thisattack.

For both schemes, we have observed that, in the working point wheretransmitter and receiver realise their better correlation, the relaxation fre-quencies of the unperturbed lasers are very similar to each other. This isthe key to have very similar waveforms, but it is not sufficient to realise agood message extraction. A good matching of the internal parameters oftransmitter and receiver is necessary, and this is the key point of the system.

In conclusion, even though the three laser scheme with electrical injec-tion is especially suitable for transmission in free space, both schemes are wellsuited to secure data transmission in real fiber networks. Although experi-ments demonstrating the feasibility of the three laser scheme with electricalinjection must be completed, for the three laser scheme with optical injec-tion, preliminary experiments have been successfully realised. The three laserscheme with electrical injection results in a more stable setup and in a lesscritical alignment with respect to the all-optical configuration. Electricalamplifiers are cheaper than optical amplifiers and their gain is easier to trim.In addition, the DRV laser does not need to operate at the same wavelengthas the transmitter and receiver. However, the all-optical three laser schemehas the advantage that the message remains hidden to an undesired listener,even in case of driver failure.

Finally, in this thesis we have obtained the non obvious result that resid-ual chaos, which is the main cause of message impairment in systems basedon optical chaotic cryptography, has gaussian statistics.

PH.D. RESEARCH ACTIVITY

Publications

• V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, M. Hama-cher, S. Merlo, V. Vercesi, Close-Loop Three-Laser Scheme forChaos-Encrypted Message Transmission, Optical and Quantum Elec-tronics, DOI 10.1007/s11082-010-9435-6.

• V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, S. Merlo,Private Message Transmission by Common Driving of Two ChaoticLasers, IEEE Journal of Quantum Electronics, vol. 46, no. 2, February2010.

• V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, S. Merlo,Secure Chaotic Transmission on a Free-Space Optics Data Link, IEEEJournal of Quantum Electronics, vol. 44, no. 11, November 2008.

• V. Annovazzi-Lodi, C. Antonelli, G. Aromataris, M. Bene-detti, M. Guglielmucci, A. Mecozzi, S. Merlo, M. Santag-iustina, L. Ursini, Chaos Encrypted Optical Communication System,Fiber and Integrated Optics, Issue 4, pages 308-316, July 2008.

• V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, I. Cris-tiani, S. Merlo, P. Minzioni, All-Optical Wavelength Conversionof a Chaos Masked Signal, IEEE Photonics Tecnology Letters, vol. 19,no. 22, pp. 1783-1785, November 2007.

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International conferences

• V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, S. Merlo,V. Vercesi and M. Hamacher, Multisection integrated modules forchaos applications, European Semiconductor Laser Workshop 2010, 24-25 September 2010.

• V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, S. Merloand V. Vercesi, Secure Transmission with Chaotic Lasers Synchro-nized by Electrical Injection, Proceedings of OECC 2009, 14th Opto-electronics and Communications Conference, Hong Kong Conventionand Exhibition Centre, 13-17 July 2009.

• V. Annovazzi-Lodi, G. Aromataris (speaker), M. Benedetti,S. Merlo and V. Vercesi, Chaotic Transmission System in FreeSpace, CATS workshop, 2-3 June 2009, Chania, Greece.

National conferences

• V. Annovazzi-Lodi, G. Aromataris (speaker), M. Benedetti,S. Merlo and V. Vercesi, Secure Data Transmission Using TwoSemiconductor Lasers Routed to Chaos and Synchronized by ElectricalInjection, FOTONICA 2010, Pisa, Italy.

• V. Annovazzi Lodi, G. Aromataris, M. Benedetti, M. Hama-cher, S. Merlo, V. Vercesi, Three-laser close-loop scheme fortransmission of messages encrypted with optical chaos, FOTONICA2010, Pisa, Italy.

PICASSO European project meeting

• G. Aromataris (speaker), V. Annovazzi-Lodi, M. Benedetti,S. Merlo and V. Vercesi, Secure Message Transmission by Com-mon Driving of Two Chaotic Lasers, 4 June 2009, Chania, Greece.

• G. Aromataris (speaker), V. Annovazzi-Lodi, M. Benedetti,S. Merlo and V. Vercesi, Received Message Quality by ParameterMismatch on the two laser-scheme, 18-21 March 2009, Berlin, Germany.

• G. Aromataris (speaker), V. Annovazzi-Lodi, M. Benedetti,S. Merlo and V. Vercesi, Three Laser Secure Scheme For All-Optical Data Transmission, 18-21 March 2009, Berlin, Germany.


• G. Aromataris (speaker), V. Annovazzi-Lodi, M. Benedettiand S. Merlo, Effect Of Parameter Mismatch On Received MessageQuality, 25-28 June 2008, Dublin, Ireland.

Other project meeting participations:

• Pavia, Italy, 21-22 February 2008.

• Palma de Mallorca, Spain, 04-06 October 2007.

Ph.D schools

• Introduction to Inverse Problems in Electromagnetism,Università degli Studi di Pavia (Italy), 14 November - 05 December2008.

• Summer School of Advanced Computing, CASPUR, IV edition,01-12 September 2008, Roma, Italy.

• Nanoscale & Ultra Past Photonics, Cost 288 training school,18-23 May 2008 Cetraro, Italy.

Other activities

• Participation to:

– Giornata di studio sulla Crittografia nelle reti ot-tiche, 16 February 2009, Pavia, Italy.

– 25 specialised seminars relative to the Ph.D. course.

• In the academic year 2008/2009, Giuseppe Aromataris has been co-supervisor of the thesis work (three year degree in Electronics Engi-neering) of Gabriele Porro (supervisor: Prof. Valerio Annovazzi-Lodi).Thesis title: Analisi numerica di uno schema a tre laser per crittografiaottica caotica in spazio libero.

BIBLIOGRAPHY

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[4] A. Argyris et al., Chaos-based communications at high bit rates usingcommercial fiber-optic links, Nature vol. 438, pp. 343-346, 2005.

[5] V. Annovazzi-Lodi, M. Benedetti, S. Merlo, M. Norgia, B.Provinzano, Optical chaos masking of video signals, IEEE Phot. Tech.Lett. vol. 17, pp. 1995-1197, 2005.

[6] V. Annovazzi-Lodi, M. Benedetti, S. Merlo, T. Perez, P. Co-let, C.R. Mirasso, Message encryption by phase modulation of achaotic optical carrier, IEEE Photonics Technology Letters, vol. 19, no.2, pp. 76-78, 2007.

[7] M. W. Lee, K. A. Shore, Demonstration of a chaotic optical messagerelay using DFB laser diode, IEEE Phot. Tech. Lett., vol. 18, pp. 169-171, 2006.

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