suppression of nonlinear xpm phenomenon by selection of...

Research ArticleSuppression of Nonlinear XPM Phenomenon by Selection ofAppropriate Transmit Power Levels in the DWDM System

Tomaacuteš Ivaniga 1 and Petr Ivaniga 2

1Department of Electronics and Multimedia Communications University of Technology Kosice Kosice Slovakia2Department of Information Networks Faculty of Management Science and Informatics University of Zilina Zilina Slovakia

Correspondence should be addressed to Tomas Ivaniga tomasivanigatukesk

Received 16 March 2019 Revised 25 April 2019 Accepted 14 May 2019 Published 2 June 2019

Guest Editor Tibor Berceli

Copyright copy 2019 Tomas Ivaniga and Petr Ivaniga This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

In the 21st century it is not possible to implement fully optical communication systems without software tools to test the system forall unwanted phenomena occurring during real-time operationWith ever-increasing transmission rate and low latency nonlinearphenomena are associated with higher power levels and smaller spacing between channels began to appear in OFs (optical fibers)This paper aims to implement a four-channel DWDM (Dense Wavelength Division Multiplex) system on which the nonlinearXPM (cross-phase modulation) phenomenon will be investigated At the output of the system we will eliminate the phenomenon(partially suppressed) by the appropriate choice of transmitting power levels (power levels operating at 193025 THz to 193175 THz)when the OF is dispersed In optical transfer data systems a system is functioning if the measured BER parameter is not bigger than10minus12

1 Introduction

One of the parameters for assessing the quality of life inour modern age is also access to information and infor-mation resources in general their veracity timeliness andpunctuality Current development trends in the area ofcommunication technologies in addition to the nonlinearincreasing requirements for transmission speed and theincrease in the volume of transmitted data also highlight thequality requirements of high-speed infrastructure [1ndash3] Thissteady increase in requirements moves from the developmentof telecommunication services and is due to the rapidlyevolving use of information technology of various broadbandmultimedia services The optimal use of telecommunicationsservices by users is conditional on themaximum possible uti-lization of the OF transmission bandwidth More efficient useof fiber optic transmission bandwidth is currently enabled byWDM (Wavelength Division Multiplexing) technology withongoing upgrades to achieve higher speed and transmissionquality

One of the systems working on the WDM platform isthe DWDM transport transmission system which will be

discussed in more detail in the next subchapter Thanks toDWDM systems it is possible to attain the transfer speed of1T Considering the ever-increasing amount of transmitteddata the demand for data transmission speeds increasesapproximately 15 times a year along with the increasingdemand for transmission quality [4] The second chapter isdevoted to WDM and their standards CWDM and DWDMNext chapter is focused on nonlinear phenomenon XPM andits possible applications In the last chapter is created a 4-channel DWDM system in programme OptSim where XPMis shown

2 WDM Technology

The continually increasing bandwidth requirements haveprompted telecom operators to look for new technologiesthat would allow them to work at high bandwidths [4] Thesolution provides a WDM wavelength division multiplexwhich employs multiple optical waves transmitting with oneOF for data transmission each of which is at a differentwavelength

HindawiInternational Journal of OpticsVolume 2019 Article ID 9357949 8 pageshttpsdoiorg10115520199357949

2 International Journal of Optics

Transmitter AITU Ch1

4-ChDWDM

Mux

Data In

Transmitter BITU Ch2

Transmitter CITU Ch3

Transmitter DITU Ch4

EDFA 25 dbGain

Data In

Data In

Data In

Receiver A

4-ChDWDMDemux

Data Out

Receiver B

Receiver C

Receiver D

Data Out

Data Out

Data Out

100 km Fiber

100 km Fiber

1

1

2

2

3

3

4

4

1+2+3+4

1+2+3+4

Figure 1 Suggestion for 4-channel DWDM system

The implementation of WDM devices into existing opti-cal networks is very simple and easy as it is only necessaryfor the technology to innovate or complete the transmissionsystems while the OFs remain physically unchangeable [5ndash8] For this reason WDM transmission systems are currentlythe most used and come with the best advantages WDMnetworks have several significant advantages compared toconventional optical networks

(i) Make better use of the transmission capacity of opticalnetworks

(ii) One OF can transmit signals with different transmis-sion rates and different modulation and signal types

(iii) Simultaneous transmission of analog and digital sig-nals at different wavelengths

(iv) If we need to increase the transfer capacity there is noneed to increase the transfer rate on one channel butadd another wavelength

(v) The demand for the speed of electronic supportcircuits (optoelectronic transducers modulation cir-cuits etc) decreases

As WDM disadvantages we can mention

(i) Additional attenuation of WDM multiplexers anddemultiplexers

(ii) Use of quality and stable light sources for differentwavelengths

(iii) The need for top quality filters

(iv) The technological difficulty and hence a higher pricelevel for each component

21 DWDM Technology By implementing DWDM technol-ogy in optical transport networks we will be able to transmitdata at a speed of even several Tbitsminus1 which are transmittedover a thousand-kilometer distance These features make thistechnology highly competitive for international telecommu-nications transmission providers despite its financial costDWDM systems utilize bandwidth mainly around the basicwidth of 1550nm and the channels used range from 1525 to1610 nm with a pitch of 02 nm to even 01 nm by default [6]Currently 16- 24- 40- 80- 128- and 256-channel systems arecommercially used The 40-channel system uses a 100GHzchannel range and 50GHz for an 80-channel system Thisseparation determines the width of the spectral wavelengthof each channel ie as the channels are close to each other[8] The number of channels used also depends on the OFused on the optical path but for standard SM (single mode)OF we can transport data over a distance of more than 80 kmwithout using an amplifier If we have to transmit data overlong distances signal amplifiers placed in cascade style areused every approximately 80-100 km [7ndash9] By competingamong the companies that are trying to break the recordin achieving the highest speed bridging distance and usingmultiple channels on a single OF the DWDM technology ismoving fast This trend is likely to continue until the physicallimits for this technology reached its boundaries Figure 1shows the basic DWDM system topology More than 1000-channel systems can theoretically be usedMost recently 1024wavelength single-strand transmission devices have beendemonstrated where the transmission capacity is 100 Gbitsminus1per length This value goes over beyond todayrsquos needs but itmay not be soon enough when data is transmitted and theprogress keeps up as the forecast shows

Initially only the point-to-point network topology wasused in DWDM technology but nowadays different types

International Journal of Optics 3

such as a circle star or polygonal topology are beingcombined This is important for service providers who needto cover a vast territory with optical networks and flexiblyrespond to the possibility of extending the network to anew territory Depending on the topology and OF lengthsignal amplifiers are placed The need for an amplifier canbe estimated from a distance between the transmitter andthe receiver and the parameters of the transmission systemsuch as the number of wavelengths channel width channelspacing modulation technique transmission rate and OFtype

DWDM systems apply to many types of networks onall network layers such as those used from intercontinentalsystems that connect entire continents to intercity networkswhere technology is only deployed on several networknodes They apply to various types of operations such asSONETSDH ATM IP TDM and the like where eachwavelength can transmit another type of service The resultis practical systems designed to transfer different types ofservices In DWDM networks the ITU G709 protocol isused which encapsulates the transmitted data and providesfunctions for operating managing maintaining and deploy-ing services to the system [10] It also provides controlprotection and repair of data in various forms Correctionmechanisms significantly reduce transmission error rates andallow multiple distances without signal regeneration

Key advantages of DWDM are(i) High data transfer efficiency by a single OF(ii) Theoretical range up to 100 km without the need for

a signal amplifier(iii) Compatibility with other technologies(iv) Easy extensibility with additional data channels(v) Optical-level backup to minimize downtime(vi) Easy expansion for additional DWDMCWDM sites(vii) The possibility of creating different logical topologies(viii) Management using a Simple Network Management

Protocol supervisory channel(ix) Multiple uses of existing OFs

22 CWDMDWDM The fusion of wave multiplexes WDMis implemented mostly to increase the total capacity ofthe transfer system This increase of WDM capacity canbe reached in several ways not necessarily exclusive ofone another The first option is to add more channels tothe system though that would result in the increase ofthe whole work spectrum which can already be exhaustedbecause the majority of the components operate only withina limited spectrum The second method is the decrease ofgaping between channels eg 100GHz 50GHz 25GHz to125GHz [11 12] The last solution would be to increase thedata speed of individual channels The coexistence of systemsis understood as the incorporation of systems with higherdata transfer speeds of its channels (eg 40 Gbitsminus1) intothe existing systems with lower data transfer speeds of theirchannels (eg 10 Gbitsminus1)

In the technical terminology such systems could befound under ldquoThe hybrid transfer systems 10G40Grdquo or ldquomix10G40Grdquo According to the recommendation ITU-T G6961the majority of fully optical communication systems workwith a transfer speed of 10 Gbitsminus1 using NRZ (Nonreturnto Zero) with gaping of 50GHz or 100GHz [11] Becauseconsiderable finances have been devoted to the constructionof systems with a transfer speed of 10 Gbitsminus1 uprootingthe entire system for something newer would be very costlyTherefore it is logical that the next step for operatorsregarding how to increase transfer speeds would be to usethe already existing infrastructure It goes without saying thatthe new system would also be expected to be retroactivelycompatible Due to the stated reasons the 40 Gbitsminus1 and 100Gbitsminus1 systems have a number of limitations requiring someattention They are able to exist within the old infrastructure(OFs of type SMF) without changes to the dispersion mapresistance to nonlinear effects and PMD (Polarization ModeDispersion) the signalrsquos transition through OADM (OpticalAdd-Drop Multiplexor) their mutual influencing between10 Gbitsminus1 and 40 Gbitsminus1100 Gbitsminus1 and the option ofmaintaining the 50GHz gaping Increasing the transfer speedfrom 10 Gbitsminus1 to 40 Gbitsminus1 and more brings severalproblemsmaking the typical solution of the classic amplitudemodulation OOK-NRZ (On-Off Keying Nonreturn to Zero)unusable for this level This is why the systems with greatertransfer speed utilize the duobinary modulations (DPSK andDQPSK) and phase modulation PSK (Phase Shift Keying) Atthe mentioned transit the BER is increased 16 times causedby the chromatic dispersion squaring the speed multipleThe value of chromatic dispersion at the speed of 10 Gbitsminus1is tolerated by NRZ to 1000 psnmkm whereas for thespeed of 40 Gbitsminus1 it is only 60 psnmkm [11 13] Thatimplies that with the increase of transfer speed dispersioncompensation is necessary if not indispensable The otherrestriction is the requirement forOSNRwhich has to be largerby 6 dB (10 dB) for the 40 Gbitsminus1 (100 Gbitsminus1) receiverif the original BER is to be maintained Also the resistanceagainst PMD decreases with the multiplication of speed tothe limiting points of 3 ps for 40 Gbitsminus1 and 1 ps for 100Gbitsminus1 [11] It is created due to the production imperfectionsof OF and it causes a delay between polarisation componentsIts compensation is not a stochastic process compared tothe chromatic dispersion OF from before 1994 are unusablefor high-speed and high-capacity transfers because of theirhigh values of PMD It has been proven that the restrictiondue to PMD and chromatic dispersion is negligible if usinga coherent reception with digital signal processing [14ndash16]Also the influence of 10 Gbitsminus1 or 40 Gbitsminus1100 Gbitsminus1needs to be mentioned

If the system with a transfer speed of 10 Gbitsminus1 OOK-NRZ is merged into a system with a speed of 40 Gbitsminus1using PSK the 40Gbitsminus1 the systemwill interferewithXPMwhich originates fromamplitudemodulationThe interactionbetween transfer systems with 10 Gbitsminus1 and 40 Gbitsminus1can be influenced by a simple change of transfer power orby a correct placing of channels With appropriate planningfor dispersion compensation and by the introduction of


RDPS (Residual Dispersion Per Span) these reductions arepossible XPM and FWM (Four-WaveMixing)This is closelyconnected with choosing the correct type of OF ITU-T G652shows a greater chromatic dispersion than ITU-T G655 orITU-T G653 so it is better to suppress the occurrence ofnonlinear effects at the output It has been experimentallydiscovered that the phase-modulated signals with a highersymbolic speed (eg DPSK) have the tendency to be lessinfluenced by XPM than the signals with a lower symbolicspeed (eg DQPSK) [17]The other alternative to coexistenceis the fusion of CWDM and DWDM systems (in technicalterminology marked as ldquoCWDMDWDMrdquo)

3 Nonlinear Phenomena Focusing on XPM

Nonlinear phenomena in OFs are generated by changing therefractive index of the medium with optical intensity andinelastic scattering The dependence of the output from therefractive index is responsible for the Kerr effect Dependingon the type of input signal Kerrrsquos effect is manifested inthree different phenomena such as the SPM (Self-Phasemodulation) FWM (Four- Wave Mixing) and XPM Thebasic description of SPM and its applications has beenexplained in [7] The origin elimination and descriptionand mathematical description of FWM have been described[15] At high power levels inelastic scattering can causestimulated phenomena such as SBS (Stimulated BrillouinScattering) and SRS (Stimulated Raman Scattering) [18 19]The diffusion intensity of light increases exponentially ifthe incident power exceeds a certain threshold The differ-ence between Brillouin and Raman scattering is that SBSgenerates (acoustic) phonons that are coherent and causemacroscopic acoustic waves in the OF while SRS generatesphonons that are incoherent and donot generatemacroscopicwaves Apart from SPM and XPM all nonlinear phenom-ena generate profits in specific channels at the expenseof performance depletion from other channels SPM andXPM only affect the signal phase and can cause spectralexpansion leading to increased dispersion The followingtopic will be explained in the basic description of the XPMphenomenon

Refractive index intensity leads to a nonlinear phe-nomenon called XPM If two or more optical pulses prop-agate simultaneously a cross-phase modulation is createdaccompanied by the actual phase modulation of the SPM Itis caused because the nonlinear refractive index of the opticalpulse depends on not only the intensity of this beam butalso the intensity of other propagating pulses XPM convertspower fluctuations at a particular wavelength into phasefluctuations in other propagating channels [13 20ndash22] XPMcan result in a disproportionate extension of the spectralline and distortion of the pulse shape The effective refrac-tive index 119899119890119891119891 of the nonlinear medium can be expressedby the input power P and the effective base region Aeffas

119899119890119891119891 = 119899119897 + 119899119899119897 119875119860119890119891119891 (1)

where 119899119897 is linear refractive index and 119899119899119897 is nonlinearrefractive index For fused silica OF 119899119897 is approximately 146and 119899119899119897 is approximately 32x10minus20m2W [23]

Nonlinear phenomena are dependent on the ratio of lightoutput to a cross-sectional area of the OF

119896119890119891119891 = 119896119897 + 119896119899119897119875 (2)

where 119896119897 is the linear portion of the spread constant and knlis the nonlinear propagation constant [11 23 24] The phaseshift caused by the nonlinear constant is after passing thedistance L inside the OF stated as

120601119899119897 = int1198710

(119896119890119891119891 minus 119896119897) 119889119911 (3)

Consequently the nonlinear phase shift is expressed by therelation

120601119899119897 = 119896119899119897119875119894119899119871119890119891119891 (4)

If several optical pulses coincide the nonlinear phase shiftof the first channel depends on not only the strength of thischannel but also the signal strength of the other channels[23 24] For two channels the nonlinear phase shift is statedas

1206011119899119897 = 119896119890119891119891119871119890119891119891 (1198751 + 21198752) (5)

For the N-channel system the shift for the ith channel isexpressed by the relation

120601119894119899119897 = 119896119899119897119871119890119891119891(119875119894 + 2 119873sum119899 =119894

119875119899) (6)

The second term in the above equation is a nonlinearsensitivity form and suggests that XPM is twice as efficient asSPM at the same energy [23] The first part of the equationis the SPM contribution and the second part is the XPMcontribution [18 24 25] XPM is only valid if the influencingsignals overlap in time XPM limits system performance inthe sameway as SPM ie frequency ldquochirpingrdquo and chromaticdispersion

However XPM can interfere with system performancemore than SPM XPM has a significant impact on the systemespecially with a large number of channels

31Threshold Values Control and XPMApplication Aphaseshift can only occur if two pulses overlap in time Dueto this overlap the phase shift is heavily dependent andsubsequent ldquochirpingrdquo is increased Hence the extension ofthe pulse is also increased limiting the performance of thelight wave propagating systems The effect of XPM can bereduced by increasing the separation between channels Forincreased wavelength spacing the pulses overlap for sucha short time that the XPM effect is virtually negligibleIn DWDM systems XPM converts power fluctuations inindividual wavelength channels to phase fluctuations in othersimultaneously propagating channels [18 26 27]This causes


awidening of the pulse which can be significantly suppressedin WDM systems using standard nondispersive single modeOFs One of the advantages of this kind of OF is its effectivecore area which usually has a value of 80 120583m2 This largeeffective area is useful in reducing nonlinear effects becauseknl is inversely proportional to Aeff

XPM as well as SPM are dependent on OF interactionsThe great length of interaction causes to some extent thecreation of this effect By maintaining a small interactiontime it can reduce this kind of nonlinearity

32 Threshold Values Control and XPM Application Thephase shift in the optical pulse caused by the XPM effectcan be used for optical switching Many interferometricmethods have been used to take advantage of phase shiftingfor ultrafast optical switching An interferometer designedin such a way that a weak signal pulse is distributed evenlyover two portions recording an identical phase shift in eachportion is transmitted through constructive interference [26]A built-in pulse of any wavelength led into one of the partschanges the signal phase through XPM in this section

If the induced phase shift is too large (close to 120587) itcreates destructive interference and thus the signal pulse isnot transmitted The intense excitation pulse can thereforeswitch the signal pulse

33 XPM Application with Impulses Pressing Like SPMcausing frequency ldquochirprdquo as well as XPM frequency ldquochirprdquocan be used to press (compress) pulse For SPM techniquesthe input pulse needs to be intense and energetic but theXPM can compress even weak input pulses because thepropagating intense excitation pulse produces a frequencyldquochirprdquo The pulsating impulse influences the XPM ldquochirprdquoand critically depends on the initial relative delay of theexcitation signal [17 19 28 29] Given the use of the XPMpulse compression it is necessary to strictly control theexcitation pulse parameters namely its width peak powerwavelength and initial relative signal pulse delay

34 Influence of XPM to Complete an Optical CommunicationSystem A set ofM differential equations can describemutualconnection or the interaction between M WDM channelsIf only the effects of SPM and XPM are considered theseequations are given

120597119880119895120597119911 = minus119894119910119895(10038161003816100381610038161003816119880119895100381610038161003816100381610038162 + 2 119872sum119898 =119895

100381610038161003816100381611988011989810038161003816100381610038162) 119880119895 (7)

where j = 1 to M U is a slowly varying amplitude 120574j is anonlinear parameter and z denotes the propagation distancetraveled [23 25] In the case of a continuous wave thenonlinear phase shift of j is due to the combination of SPMand XPM given by the relation

120601119895 = 120574119895119871119890119891119891 = [[119875119895 + 2 119872sum

119898 =119895

119875119898]] (8)

in which 119875119895 is the input power of the wave Equation (8)shows that the impact of XPM is much more important thanthe impact of SPM in multichannel communication systemsHowever OF dispersion generally decreases this effect Theeffect of cross-phase modulation varies in amplitude andphase-modulated systems If the power in each channelis the same for all bits the main limitation results fromindependent phase fluctuations which directly leads to adeterioration of the signal-to-noise ratio [13 23] Such phasefluctuations can be caused by the XPM phenomenon bychanges in intensity which occur when semiconductor lasersare directly phase modulated [30 31] Within amplitudemodulated direct detection systems XPM does not affectthe performance of the dispersion neglect system Since thechanges in the phase caused by the XPM phenomenon arerelated to frequency changes the dispersion determines theadditional time extension or compression of the spectrallyextended pulses affecting system performance

4 Realization of a 4-Channel System toEliminate XPM

OptSim is a programme that facilitates the modeling andsimulation of optical communication systems It containsmore than 400 algorithms representing a wide variety ofoptical and optoelectronic components used in practice Thetypical end-users of OptSim are companies engaged in thedevelopment and implementation of network infrastructuresto access a remote networkOptSim allows simulating varioustypes ofmultiplexes onprofessional level for exampleWDMDWDM TDM and CATV or all-optical LAN With OptSimwe can propose and experimentally verify optical networksbefore their real deployment [5 18]

A four-channel DWDM system was created to eliminatethe XPM phenomenon The simulations aimed to suppressthe XPM phenomenon by varying the dispersion in theOV and uneven distribution of optical power in adjacentchannels The optical mesh with an OF EDFA amplifier anddispersion compensator was implemented in the followingconfiguration the output power of the EDFA booster is set at9 dBm (7943mW) and the OF behind the amplifier at 100 kmwith losses of 033 dBkmminus1 Neither SBS nor PMD are takeninto account in this topology

An EDFA IN-Line amplifier is located behind the OFwhich has a gain of 20 dB with NF = 45 (Figure 1) Thelength of the Erbium-doped OF was 14m and it was chosenaccording to Figure 2 showing the best amplification wasattained by precisely this length of OF

An OF follows this with a length of 100 km with a specificattenuation of 033 dBkmminus1 and in the final stage there isa compensator and an amplifier [28] For our simulation 4loops were created with a different increment The individualreceiving units are designed to filter only the desired signalThe first simulation was done with the intention of changingthe transmission power of the spectrum from 193025 THzto 193175 THz with an increment of 005 THz (nonuniformtransmission power -10 dBm -30 dBm -10 dBm -30 dBm) Inthis simulation we created an optical loop where we changed


Length of erbium doped fibre [m]

Gai

n [d

B]

10

15

20

25

30

35

40

45

Pump power 20 mW4Approximation by polynominal y = 00008x

3 2- 0028 8x + 00780x + 51342x - 28843

4Approximation by polynominal y = 00013x3 2- 0050 8x + 0446x + 32503x - 02876


Pump power 80 mW

Pump power 50 mW

4 6 8 10 12 14 16 18 20

Figure 2 Length of Erbium-doped OF to EDFA gain

30

10

minus10

minus30

-10 dBm-10 dBm

-30 dBm-30 dBm

D = 4 psnmkm

D = 1 psnmkm

D = 0 psnmkm

1926 193 1934

Frequency [Thz]

Figure 3 Final signal spectrum for simulation no 1

the dispersion with an increment of 1 from 0 psnm kmto 4 psnm km at different power transmissions (Figure 3)The resulting BER and Q factor values at 193075 THz are inTable 1

Figure 3 presents a green curve showing a dispersionvalue of 0 psnm km a blue curve showing a spectrum ata dispersion of 1 psnm km and a red curve showing a 4psnm km spectrum From the resulting values in Table 1

Table 1 Final results of BER simulations no1 at 193075 THz

Iteration Variance[psnmkm]

BER Q-factor

1 4 278sdot10minus27 1088972 3 181sdot10minus20 9451663 2 249sdot10minus11 6772864 1 0000541 3369115 0 0022251 2

Table 2 Final BER results with simulation no 2 193075 THz

Iteration Variance[psnmkm] BER Q-factor

1 4 110sdot10minus40 1362352 3 201sdot10minus28 1129433 2 575sdot10minus16 8018674 1 115sdot10minus17 5123065 0 0022501 2

D = 0 psnmkm

D = 1 psnmkm

D = 4 psnmkm

-10 dBm

-20 dBm

-30 dBm

-40 dBm

1926 193 1934

Frequency [Thz]

30

10

minus10

minus30


we can confirm that with the decrease in dispersion the valueof BER increases An optical channel at 193075 THz willbe accepted for dispersion values 4 3 and 2 Due to thedifferent input power values we can partially suppress theXPM phenomenon at its output The second simulation wasapplied to the same scheme but we changed the transmittingpower of all four channels (nonuniform transmit power -10dBm -20 dBm -30 dBm and -40 dBm) In Figure 4 we cansee how the change in broadcasting power affects XPM

The resulting BER and Q factor values at 193075 THzat -10 dBm -20 dBm -30 dBm and -40 dBm are given inTable 2 From the simulation results (Tables 1 and 2) wecan conclude that the nonlinear phenomenon XPM couldbe partially suppressed by appropriate choice of transmitting


power and dispersions The line is accepted for dispersionvalues 4 3 2 and 1

5 Conclusion

The aim of this paper was a basic description of the nonlinearXPM phenomenon occurring in xWDM systems Two simu-lation topologies of a 4-channel DWDM system with 50GHzoutputwere designed to eliminate (suppress) XPMThepaperpointed to the improvement of BER at a particularwavelengthwith the appropriate choice of broadcasting power in neigh-boring channels (uneven distribution of power levels) Bycomparing Tables 1 and 2 we can state that the improvementof BER is achieved by a suitable choice of transmitting powersin neighboring channels Simulation also pointed out that thepresence of the OF dispersion affects line error and how it isrelated to the nonlinear XPM phenomenon

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] B Batagelj V Janyani and S Tomazic ldquoResearch challenges inoptical communications towards 2020 and beyondrdquo InformacijeMidem vol 44 no 3 pp 177ndash184 2014

[2] M Vidmar ldquoOptical-fiber communications components andsystemsrdquo Informacije Midem vol 31 no 4 pp 246ndash251 2001

[3] J Smiesko and J Uramova ldquoAccess node dimensioning forIPTV traffic using effective bandwidthrdquo Komunikacie vol 14no 2 pp 11ndash16 2012

[4] T Ivaniga P Ivaniga J Turan and L Ovsenik ldquoAnalysis ofpossibilities of increasing the spanned distance using EDFA andDRA in DWDM systemrdquo Communications - Scientific Letters ofthe University of Zilina vol 19 no 3 pp 88ndash95 2017

[5] B Archana and S Krithika ldquoImplementation of BB84 quantumkey distribution using OptSimrdquo in Proceedings of the 2015 2ndInternational Conference on Electronics and CommunicationSystems (ICECS) pp 457ndash460 Coimbatore India Feburary2015

[6] Lrsquo Mikus ldquoEvaluations of the error rate in backbone networksrdquoElektrorevue vol 12 no 2 pp 1ndash10 2010

[7] H Nain U Jadon and V Mishra ldquoEvaluation and analysis ofnon-linear effect in WDM optical networkrdquo in Proceedings ofthe 2016 IEEE International Conference on Recent Trends in Elec-tronics Information amp Communication Technology (RTEICT)pp 36ndash39 Bangalore India May 2016

[8] O Kovac P Lukacs and I Gladisova ldquoTextures classificationbased on DWTrdquo in Proceedings of the 2018 28th InternationalConference Radioelektronika (RADIOELEKTRONIKA) pp 1ndash5Prague Czechia April 2018

[9] P Ivaniga and T Ivaniga ldquoThe design of EDFA with forwardpumping at the distance line in DWDMrdquo Journal of EngineeringScience and Technology vol 14 no 2 pp 531ndash540 2019

[10] S Gorshe ldquoA tutorial on ITU-T G709 optical transport net-worksrdquo 2010

[11] Z Bosternak and R Roka ldquoBandwidth scheduling methodsfor the upstream traffic in passive optical networksrdquo PrzeglądElektrotechniczny vol 94 no 4 pp 9ndash12 2018

[12] S Bansal S Singh and S Gupta ldquoPerformance analysis ofa gain clamped 16 times 40 GbS WDM optical communicationsystemrdquo in Proceedings of the 2008 International Conference onSignal Processing Communications and Networking pp 396ndash400 Chennai India January 2008

[13] T Huszanık J Turan and E Ovsenık ldquoComparative analysis ofoptical IQ modulation in four-channel DWDM system in thepresence of fiber nonlinearitiesrdquo in Proceedings of the 2018 19thInternational Carpathian Control Conference (ICCC) pp 468ndash473 Szilvasvarad Hungary May 2018

[14] M Srivastava andV Kapoor ldquoAnalysis and compensation of selfphase modulation in wavelength division multiplexing systemrdquoin Proceedings of the 2014 Students Conference on Engineeringand Systems (SCES) pp 1ndash4 Allahabad India May 2014

[15] T Huszanık J Turan and L Ovsenık ldquoImpact of the opticalfiber nonlinear phenomenon on the 16-channel DWDM OC-768 long-haul linkrdquo Elektrotechniski Vestnik vol 85 no 5 pp255ndash262 2018

[16] Y M Karfaa M Ismail F M Abbou S Shaari and S PMajumder ldquoChannel spacing effects onXPMcrosstalk inWDMnetworks for various fiber typesrdquo in Proceedings of the 2ndMalaysia Conference on Photonics (MCP) pp 1ndash5 PutrajayaMalaysia August 2008

[17] N Badraoui T Berceli and S Singh ldquoDistortion cancellationfor solitons carrying high speed information inWDM systemsrdquoin Proceedings of the 2017 19th International Conference onTransparent Optical Networks (ICTON) pp 1ndash4 Girona SpainJuly 2017

[18] J Ruzbarsky J Turan and L Ovsenik ldquoStimulated brillouinscattering in DWDM all optical communication systemsrdquo inProceedings of the 26th International Conference Radioelektron-ika (RADIOELEKTRONIKA rsquo16) pp 395ndash398 April 2016

[19] ITU-TG652 ldquoCharacteristics of a single-mode optical fibre andcablerdquo ITU-T November 2009

[20] H Rongqing K R Demarest and C T Allen ldquoCross-phasemodulation in multispan WDM optical fiber systemsrdquo Journalof Lightwave Technology vol 17 no 6 pp 1018ndash1026 1999

[21] B S Marks C R Menyuk A L Campillo and F BucholtzldquoInterchannel crosstalk reduction in an analog fiber link usingdispersion managementrdquo IEEE Photonics Technology Lettersvol 20 no 4 pp 267ndash269 2008

[22] J Ruzbarsky J Turan and L Ovsenik ldquoEffects act on trans-mitted signal in a fully optical fiber WDM systemsrdquo in Pro-ceedings of the IEEE 13th International Scientific Conference onInformatics (INFORMATICS rsquo15) pp 217ndash221 Poprad SlovakiaNovember 2015

[23] G P Agrawal Applications of Nonlinear Fiber Optics 2nd edi-tion 2008

[24] N Kikuchi and S Sasaki ldquoAnalytical evaluation technique ofself-phase-modulation effect on the performance of cascadedoptical amplifier systemsrdquo Journal of Lightwave Technology vol13 no 5 pp 868ndash878 1995


[25] A R Chraplyvy ldquoLimitations on lightwave communicationsimposed by optical-fiber nonlinearitiesrdquo Journal of LightwaveTechnology vol 8 no 10 pp 1548ndash1557 1990

[26] I Lyubomirsky Q Tiequn J Roman M Nayfeh M Y FrankelandMG Taylor ldquoInterplay of fiber nonlinearity and optical fil-tering in ultradense WDMrdquo IEEE Photonics Technology Lettersvol 15 no 1 pp 147ndash149 2003

[27] P Liptai B Dolnık M Pavlık J Zbojovsky and M SpesldquoCheck measurements of magnetic flux density Equipmentdesign and the determination of the confidence interval for EFA300 measuring devicesrdquoMeasurement vol 111 pp 51ndash59 2017

[28] K Bachrata and H Bachraty ldquoComputer as a tool for changingattitudes towards mathematicsrdquo in Proceedings of the 2012IEEE 10th International Conference on Emerging eLearningTechnologies and Applications (ICETA) pp 21ndash25 Star Lesn Slovakia November 2012

[29] J Papan P Segec M Drozdova L Mikus M Moravcıkand J Hrabovsky ldquoThe IPFRR mechanism inspired by BIERalgorithmrdquo in Proceedings of the 2016 International Conferenceon Emerging eLearning Technologies and Applications (ICETA)pp 257ndash262 Vysoke Tatry Slovakia November 2016

[30] T Kovacikova P Segec and M Kubina ldquoIMS in the NextGeneration Networkrdquo in Proceedings of the 11th WSEAS Inter-national Conference on Communications pp 45ndash50 AgiosNikolaos Crete Island Greece July 2007

[31] D Zrakova M Kubina and G Koman ldquoInfluence of infor-mation-communication system to reputation management of acompanyrdquo Procedia Engineering vol 192 pp 1000ndash1005 2017

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Transmitter AITU Ch1

4-ChDWDM

Mux

Data In

Transmitter BITU Ch2

Transmitter CITU Ch3

Transmitter DITU Ch4

EDFA 25 dbGain

Data In

Data In

Data In

Receiver A

4-ChDWDMDemux

Data Out

Receiver B

Receiver C

Receiver D

Data Out

Data Out

Data Out

100 km Fiber

100 km Fiber

1

1

2

2

3

3

4

4

1+2+3+4

1+2+3+4

Figure 1 Suggestion for 4-channel DWDM system

The implementation of WDM devices into existing opti-cal networks is very simple and easy as it is only necessaryfor the technology to innovate or complete the transmissionsystems while the OFs remain physically unchangeable [5ndash8] For this reason WDM transmission systems are currentlythe most used and come with the best advantages WDMnetworks have several significant advantages compared toconventional optical networks

(i) Make better use of the transmission capacity of opticalnetworks

(ii) One OF can transmit signals with different transmis-sion rates and different modulation and signal types

(iii) Simultaneous transmission of analog and digital sig-nals at different wavelengths

(iv) If we need to increase the transfer capacity there is noneed to increase the transfer rate on one channel butadd another wavelength

(v) The demand for the speed of electronic supportcircuits (optoelectronic transducers modulation cir-cuits etc) decreases

As WDM disadvantages we can mention

(i) Additional attenuation of WDM multiplexers anddemultiplexers

(ii) Use of quality and stable light sources for differentwavelengths

(iii) The need for top quality filters

(iv) The technological difficulty and hence a higher pricelevel for each component

21 DWDM Technology By implementing DWDM technol-ogy in optical transport networks we will be able to transmitdata at a speed of even several Tbitsminus1 which are transmittedover a thousand-kilometer distance These features make thistechnology highly competitive for international telecommu-nications transmission providers despite its financial costDWDM systems utilize bandwidth mainly around the basicwidth of 1550nm and the channels used range from 1525 to1610 nm with a pitch of 02 nm to even 01 nm by default [6]Currently 16- 24- 40- 80- 128- and 256-channel systems arecommercially used The 40-channel system uses a 100GHzchannel range and 50GHz for an 80-channel system Thisseparation determines the width of the spectral wavelengthof each channel ie as the channels are close to each other[8] The number of channels used also depends on the OFused on the optical path but for standard SM (single mode)OF we can transport data over a distance of more than 80 kmwithout using an amplifier If we have to transmit data overlong distances signal amplifiers placed in cascade style areused every approximately 80-100 km [7ndash9] By competingamong the companies that are trying to break the recordin achieving the highest speed bridging distance and usingmultiple channels on a single OF the DWDM technology ismoving fast This trend is likely to continue until the physicallimits for this technology reached its boundaries Figure 1shows the basic DWDM system topology More than 1000-channel systems can theoretically be usedMost recently 1024wavelength single-strand transmission devices have beendemonstrated where the transmission capacity is 100 Gbitsminus1per length This value goes over beyond todayrsquos needs but itmay not be soon enough when data is transmitted and theprogress keeps up as the forecast shows

Initially only the point-to-point network topology wasused in DWDM technology but nowadays different types















119899119890119891119891 = 119899119897 + 119899119899119897 119875119860119890119891119891 (1)



119896119890119891119891 = 119896119897 + 119896119899119897119875 (2)


120601119899119897 = int1198710

(119896119890119891119891 minus 119896119897) 119889119911 (3)


120601119899119897 = 119896119899119897119875119894119899119871119890119891119891 (4)


1206011119899119897 = 119896119890119891119891119871119890119891119891 (1198751 + 21198752) (5)


120601119894119899119897 = 119896119899119897119871119890119891119891(119875119894 + 2 119873sum119899 =119894

119875119899) (6)











120597119880119895120597119911 = minus119894119910119895(10038161003816100381610038161003816119880119895100381610038161003816100381610038162 + 2 119872sum119898 =119895

100381610038161003816100381611988011989810038161003816100381610038162) 119880119895 (7)


120601119895 = 120574119895119871119890119891119891 = [[119875119895 + 2 119872sum

119898 =119895

119875119898]] (8)









Gai

n [d

B]

10

15

20

25

30

35

40

45


3 2- 0028 8x + 00780x + 51342x - 28843



Pump power 80 mW

Pump power 50 mW

4 6 8 10 12 14 16 18 20


30

10

minus10

minus30

-10 dBm-10 dBm

-30 dBm-30 dBm

D = 4 psnmkm

D = 1 psnmkm

D = 0 psnmkm

1926 193 1934

Frequency [Thz]






BER Q-factor





D = 0 psnmkm

D = 1 psnmkm

D = 4 psnmkm

-10 dBm

-20 dBm

-30 dBm

-40 dBm

1926 193 1934

Frequency [Thz]

30

10

minus10

minus30






5 Conclusion


Data Availability




References




































Shock and Vibration





Volume 2018














Geophysics



Volume 2018




Volume 2018






Journal of

Chemistry




RotatingMachinery



















119899119890119891119891 = 119899119897 + 119899119899119897 119875119860119890119891119891 (1)



119896119890119891119891 = 119896119897 + 119896119899119897119875 (2)


120601119899119897 = int1198710

(119896119890119891119891 minus 119896119897) 119889119911 (3)


120601119899119897 = 119896119899119897119875119894119899119871119890119891119891 (4)


1206011119899119897 = 119896119890119891119891119871119890119891119891 (1198751 + 21198752) (5)


120601119894119899119897 = 119896119899119897119871119890119891119891(119875119894 + 2 119873sum119899 =119894

119875119899) (6)











120597119880119895120597119911 = minus119894119910119895(10038161003816100381610038161003816119880119895100381610038161003816100381610038162 + 2 119872sum119898 =119895

100381610038161003816100381611988011989810038161003816100381610038162) 119880119895 (7)


120601119895 = 120574119895119871119890119891119891 = [[119875119895 + 2 119872sum

119898 =119895

119875119898]] (8)









Gai

n [d

B]

10

15

20

25

30

35

40

45


3 2- 0028 8x + 00780x + 51342x - 28843



Pump power 80 mW

Pump power 50 mW

4 6 8 10 12 14 16 18 20


30

10

minus10

minus30

-10 dBm-10 dBm

-30 dBm-30 dBm

D = 4 psnmkm

D = 1 psnmkm

D = 0 psnmkm

1926 193 1934

Frequency [Thz]






BER Q-factor





D = 0 psnmkm

D = 1 psnmkm

D = 4 psnmkm

-10 dBm

-20 dBm

-30 dBm

-40 dBm

1926 193 1934

Frequency [Thz]

30

10

minus10

minus30






5 Conclusion


Data Availability




References




































Shock and Vibration





Volume 2018














Geophysics



Volume 2018




Volume 2018






Journal of

Chemistry




RotatingMachinery












120597119880119895120597119911 = minus119894119910119895(10038161003816100381610038161003816119880119895100381610038161003816100381610038162 + 2 119872sum119898 =119895

100381610038161003816100381611988011989810038161003816100381610038162) 119880119895 (7)


120601119895 = 120574119895119871119890119891119891 = [[119875119895 + 2 119872sum

119898 =119895

119875119898]] (8)









Gai

n [d

B]

10

15

20

25

30

35

40

45


3 2- 0028 8x + 00780x + 51342x - 28843



Pump power 80 mW

Pump power 50 mW

4 6 8 10 12 14 16 18 20


30

10

minus10

minus30

-10 dBm-10 dBm

-30 dBm-30 dBm

D = 4 psnmkm

D = 1 psnmkm

D = 0 psnmkm

1926 193 1934

Frequency [Thz]






BER Q-factor





D = 0 psnmkm

D = 1 psnmkm

D = 4 psnmkm

-10 dBm

-20 dBm

-30 dBm

-40 dBm

1926 193 1934

Frequency [Thz]

30

10

minus10

minus30






5 Conclusion


Data Availability




References




































Shock and Vibration





Volume 2018














Geophysics



Volume 2018




Volume 2018






Journal of

Chemistry




RotatingMachinery







Gai

n [d

B]

10

15

20

25

30

35

40

45


3 2- 0028 8x + 00780x + 51342x - 28843



Pump power 80 mW

Pump power 50 mW

4 6 8 10 12 14 16 18 20


30

10

minus10

minus30

-10 dBm-10 dBm

-30 dBm-30 dBm

D = 4 psnmkm

D = 1 psnmkm

D = 0 psnmkm

1926 193 1934

Frequency [Thz]






BER Q-factor





D = 0 psnmkm

D = 1 psnmkm

D = 4 psnmkm

-10 dBm

-20 dBm

-30 dBm

-40 dBm

1926 193 1934

Frequency [Thz]

30

10

minus10

minus30






5 Conclusion


Data Availability




References




































Shock and Vibration





Volume 2018














Geophysics



Volume 2018




Volume 2018






Journal of

Chemistry




RotatingMachinery







5 Conclusion


Data Availability




References




































Shock and Vibration





Volume 2018














Geophysics



Volume 2018




Volume 2018






Journal of

Chemistry




RotatingMachinery
















Shock and Vibration





Volume 2018














Geophysics



Volume 2018




Volume 2018






Journal of

Chemistry




RotatingMachinery





suppression of nonlinear xpm phenomenon by selection of...

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