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1584 J. Opt. Soc. Am. B/Vol. 24, No. 7 /July 2007 Yosia et al.

All-optical transistor operation based on thebistability principle in nonlinear distributed

feedback GaInAsP-InP waveguide:a transient perspective

Yosia,1,2,* Yoichi Akano,1 Kazuhiko Tamura,1 Tetsuya Mizumoto,1 and Shum Ping2

1Department of Electrical and Electronic Engineering, Mizumoto Laboratory, Tokyo Institute of Technology,2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan

2Department of Electrical and Electronic Engineering, Network Technology Research Centre, Nanyang TechnologicalUniversity, Research Technoplaza, 50 Nanyang Drive, 4th Floor, XFrontiers Block, Singapore 637553

*Corresponding author: yosi0001@ntu.edu.sg

Received January 10, 2007; revised March 24, 2007; accepted March 25, 2007;posted April 2, 2007 (Doc. ID 78766); published June 15, 2007

We demonstrated all-optical transistor operation based on the bistability principle in nonlinear distributedfeedback GaInAsP–InP waveguide. By increasing the pump power above a certain limit, the probe transmis-sion that operates in the bistable regime can turn from switching to transistor mode. The unstable state isshown to play a crucial role in distinguishing the probe transmission artifacts between switching and transis-tor mode. © 2007 Optical Society of America

OCIS codes: 190.1450, 230.1150, 230.1480, 070.1170.

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. INTRODUCTIONn the vision to realize the future all-optical technologyhat will revolutionize the information and telecommuni-ation industry, there is a need to do signal processing inptical domain without electronics. Nonlinear periodictructures such as fiber Bragg gratings, photonic crystalsPhCs) distributed feedback (DFB) GaInAsP-InP wave-uide, and pseudoatilene toluene sulfonate crystal withragg gratings are capable of producing a plethora of non-

inear phenomena [1–12]. One of the most useful nonlin-ar phenomena in periodic structures for signal process-ng purposes is optical bistability. The wave propagationnside a nonlinear periodic structure with weak refractivendex modulation can be well described by the set of non-inear coupled-mode equations (NLCMEs). For uniformrating, NLCMEs can be solved analytically and the so-ution is given by Jacobi elliptic functions as first de-cribed by Winful [1]. Thus the shape of the bistabilityurve can be well described by this function.

Based on the optical bistability principle, various all-ptical signal processing capabilities have been demon-trated theoretically and experimentally. Jeong et al.10,11] showed polarization-independent all-opticalwitching in the nonlinear GaInAsP–InP high-mesaaveguide with a vertically etched Bragg reflector experi-entally and investigated the dependence of threshold

witching power on the control-light wavelength in a non-inear DFB GaInAsP waveguide. In 2003, Yanik et al. [13]heoretically showed all-optical transistor in the PhCross-waveguide geometry. In 2005, Shinya et al. [14]emonstrated all-optical memory in nonlinear PhC ex-

0740-3224/07/071584-5/$15.00 © 2

erimentally and performed numerical simulations onll-optical sequential circuit that can synchronize inputon-return-to-zero optical data with its clock to regener-te input data with return-to-zero format. Last, Yosiat al. [15] speculated on all-optical switching, inverting,nd limiting operation in nonlinear fiber Bragg grating byross-phase modulation (XPM) between strong probe andtrong pump by numerical simulations.

Building on the research accomplishment above, in thisaper, we report the experimental demonstrations of anll-optical transistor operation based on the bistabilityrinciple in the nonlinear DFB GaInAsP-InP waveguide.ince the physical characteristics of the device, such asoupling coefficient �, linear absorption coefficients �, ef-ective cross-sectional area, effective linear refractive in-ex, and nonlinear optical properties, as well as thehysical dimension of the waveguide have been investi-ated in detail and reported in [10–12,16], our focus wille on its transmission characteristics.The paper is organized as follows. The theoreticalodel of nonlinear wave propagation in periodic struc-

ures under strong probe and strong pump governed byLCMEs is given in Section 2. By increasing the pumpower above a certain limit, the probe transmission thatperates in switching mode is turned into transistor modes presented in Section 3. In Section 4, the experimentalesults are justified by solving NLCMEs numerically tonvestigate the probe transmissions transient artifactsrom the transient perspective. The unstable state ishown to play a crucial role in distinguishing the proberansmission artifacts between the switching and transis-

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Yosia et al. Vol. 24, No. 7 /July 2007 /J. Opt. Soc. Am. B 1585

or mode. Finally, the existence of an unstable state iserified in the experiments by taking the snapshots ofrobe transmissions as reported in Section 5.

. THEORETICAL MODEL OF NONLINEARRAGG GRATINGSonlinear coupled mode equations govern the nonlinearave propagation inside the periodic structures underaraxial approximations and weak grating modulationssumptions [1]. When strong probe and strong pumpropagate inside the grating, the set of NLCMEs can beritten as

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ig. 1. Transmission spectrum of DFB waveguide in linear re-ime (solid curve) and probe spectrum (dashed curve).

Fig. 3. Schemati

The above set of NLCMEs is valid when the probeavelength is located around the bandgap while theump wavelength is located far from the bandgap, hencet is unperturbed by the grating. Unless otherwise stated,ll notations in this paper follow closely the conventionssed in [15].

. EXPERIMENTAL RESULTS OF ALL-PTICAL TRANSISTOR OPERATION

he linear transmission spectrum of the DFB waveguidend probe spectrum are shown in Fig. 1. The probe wave-ength � is set around the bandgap edge at 1566.2 nmhile its power is set in the bistable regime. The Braggavelength �B of DFB waveguide is 1565.9 nm.While the probe wavelength is located at the bandgap

dge, the pump wavelength is set at 1550 nm, hence it isnperturbed by the grating. The pump power is varied to

nvestigate various probe transmission operating modes.he probe is set at 135 ns long, while the shorter pump iset at 50 ns long and overlapped around the middle of therobe as shown in Fig. 2.Both probe and pump outputs were visualized by opti-

al oscilloscope in the time-averaging mode to suppresshe noise. The schematic of experimental setup is shownn Fig. 3.

ig. 2. Normalized input probe (solid curve) at 1566.2 nm andump wavelength (dotted curve) at 1550 nm.

perimental setup.

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1586 J. Opt. Soc. Am. B/Vol. 24, No. 7 /July 2007 Yosia et al.

Three pump power regimes can be distinguishedlearly where the time average of probe transmission ar-ifacts behave differently as shown in Fig. 4. In the lowump regime, the probe transmission is in the switchingode (a). In the medium pump regime, the time average

f probe transmission after the pump is turned off�100 ns� always varies between the low and high stateb). Last, in the high pump regime, the probe transmis-ion is in the transistor mode (c). The term of all-opticalransistor operation shown in Fig. 4(c) is derived based onhe fact that the relatively low pump power when it is onan produce high probe transmission as it operates in theigh state of bistable regime. However, when the pump isff, the probe transmission is low as it operates in the low

ig. 4. Experimental results on time average probe transmis-ions in the (a) switching, (b) unstable, and (c) transistor modehen the pump is in low, medium, and high regime, respectively.

tate of bistable regime. The best gain �G� of the transis-or operation, which is calculated as the ratio betweenrobe transmission and the pump output is estimated toe �6 dB. However, when the pump is off, some of therobe transmission remains as it operates in the low statef bistable regime. This is regarded as the noise in theransistor operation. The best signal-to-noise ratio, whichs roughly equal to the extinction ratio of bistable switch-ng, is estimated at 12.7 dB. The rise time was measuredt 3 ns, thus limiting the bandwidth of our device forransistor operation roughly at 333 MHz.

We would like to highlight that the trace shown in Fig.is not purely for probe transmission. However, it is the

um of the probe transmission and the pump output.omparing the trace in Figs. 4(a)–4(c) when the pump is

urned on, one can note that the trace in Fig. 4(a) is theowest ��720 �W), in Fig. 4(b) is the highest ��750 �W�,hile in Fig. 4(c) is in between the two ��730 �W�. As theump power is increased from low, medium, to high re-ime, the probe transmission is reduced in the presence ofump. The stronger pump will result in more reductionsf probe transmission as the bistability curve shift to theower intensity regime and thus producing lower trans-

ission for the same input probe intensity as explained in13]. We speculate that the reduction of probe transmis-ion is lower than the increment of pump from Figs. 4(a)o 4(b) so that the trace is higher in Fig. 4(b). However,he reduction of probe transmission is higher than the in-rement of pump from Figs. 4(b) to Fig. 4(c) so that therace is lower in Fig. 4(c).

. TRANSIENT PERSPECTIVE OF ALL-PTICAL TRANSISTOR FROM NUMERICALIMULATIONSo understand the three probe transmission operatingodes shown in Fig. 4, some numerical simulations by

he implicit fourth-order Runge–Kutta method [17] toolve the set of NLCMEs (1)–(3) given in Section 2 undertrong probe and strong pump assumptions is shown inig. 5. When the pump power is in the low regime, therobe transmission exhibits switching operation. How-ver, as the pump power is increased, it turns the proberansmission from the switching to transistor operation.

From the transient perspective, the pump can bereated as the temporary perturbation to the bistable sys-em as it is shorter than the probe. When the pump isurned off (indicated by the circle in Fig. 5), the probe haso decide whether to stay at the low or high state in theistable regime. If the probe is above the unstable statefter the pump is turned off, it will settle at the high stateswitching mode); otherwise it will settle at the low statetransistor mode). By weak XPM with low pump power,he probe transmission dip is consequently shallow to bebove the unstable state when the pump is turned off ashown by the dashed curve in Fig. 5. As the bistabilityurve goes back to its initial state when the pump is to-ally off, there are more photons in the probe transmis-ion than the unstable state of initial bistability curve. Asiscussed in [4], the addition of photons into the unstabletate will result in the additions of more photons. Hence,he probe transmission finally settles at the high state.

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Yosia et al. Vol. 24, No. 7 /July 2007 /J. Opt. Soc. Am. B 1587

n the contrary, the probe transmission dip is corre-pondingly deep due to the strong XPM with high pumpower when the pump is turned off as shown by the solidurve in Fig. 5. Hence the probe transmission is pushedelow the unstable state. Since the probe transmissionoes back to its initial bistable curve after the pump isompletely off, there are lesser photons than the unstabletate of the initial bistable curve. Similarly, as explainedn [4], the reduction of photons from the unstable branchill result in the reductions of more photons to finally

ettle the probe transmission at the low state. Figure 5hows the critical case where the pump power is set at theaximum value of low regime and minimum value of

igh regime for the dashed and solid curves, respectively,o that the unstable state line can be drawn clearly to dis-inguish the two probe transmission transient artifacts.

While theoretically there are only two pump power re-imes (low and high) to differentiate the probe transmis-ions transient artifacts, three pump power regimes (low,edium, and high) are distinguished clearly in the ex-

eriments as pointed out in Section 3. The different pumpower classification between the theory and experiment isue to the influence of the noise in the experiment as ex-lained below.In the experiment, low pump regime is defined when

he probe transmission is well above the unstable statefter the pump is turned off. The noise therefore seldomrings the final probe transmission to settle at the lowtate. Through the time averaging process, the proberansmission shows stable switching operation as shownn Fig. 4(a). We would like to highlight the discrepancyetween the simulation artifact and experimental resultn the switching mode. In Fig. 5, the probe transmissiontate when the pump is on �t�50–100 ns� is lower thanfter the pump is turned off �t�100 ns�. This is becausehe bistability curve is shifted to the lower intensity re-ime in the presence of the pump as explained in [13]. As

ig. 5. Transient perspective of all-optical transistor operationsransmission artifacts between the switching and transistor mod

he bistability curve is shifted to the left, the transmissiv-ty and consequently the output drops for the same inputower. However, the experimental result shown in Fig.(a) contradicts the simulation artifact, i.e., the trace inhe middle state (when the pump is on) is higher thanhat in the final state (when the pump is turned off). Theeason is because the trace in the experiment consists ofhe sum between the probe transmission and the pumputput as pointed out earlier in Section 3.

In medium pump regime, the time average of proberansmissions always varies in between but settles nei-her in low nor high state after the pump is turned off ashown in Fig. 4(b). This is because the noise mainly gen-rated by an erbium-doped fiber amplifier often causeshe probe transmissions to settle at the “wrong” state.ence, the time averaging of probe transmissions just

ives roughly the value between the low and high states.e call this regime the noise-prone regime.Last, in high pump regime, the probe transmission is

ell below the unstable state once the pump is turned off.he noise therefore seldom brings the final probe trans-ission to the high state. Through the time averaging

rocess, the probe transmission shows consistent all-ptical transistor operations as shown in Fig. 4(c).

. VERIFICATION OF UNSTABLE STATE INHE EXPERIMENTSs the unstable state is shown to play a crucial role in dis-

inguishing probe transmissions artifacts by numericalimulations in Section 4, its existence can be verified inhe experiment by setting the probe transmission in thenstable mode (noise-prone regime) as described in Sec-ion 3 [Fig. 4(b)]. However, the snapshots by interleavedampling (instantaneous measurements) were taken in-tead of time averaging so that at one point of time the

merical simulations. The unstable state distinguishes the probe

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1588 J. Opt. Soc. Am. B/Vol. 24, No. 7 /July 2007 Yosia et al.

robe transmission is in the switching operation but atther point of time it is in the transistor operation ashown in Fig. 6.

As the probe transmission operates in the unstableode, its transient artifact after turning off the pump (at

�100 ns) is around the lowest point during switching op-ration while it is around its highest point during transis-or operation. Therefore, the unstable state line can berawn clearly to distinguish the two transient artifacts byooming in Fig. 6 at the time when the pump is justurned off (indicated by the ellipse) as shown in Fig. 7.

. CONCLUSIONShe experimental demonstration of an all-optical transis-or operation based on the bistability principle in DFBaAsInP-InP waveguide is reported. Three pump power

egimes in the experiments are defined as the proberansmission operates in the switching, unstable, andransistor modes for the low, medium, and high pumpower regimes, respectively. The unstable state is showns a boundary to distinguish the probe transmission tran-ient artifacts between the switching and transistor op-

ig. 6. Snapshots of probe transmissions in the switching (solidurve) and transistor (dotted curve) operations by setting theump power in medium regime.

ig. 7. Unstable state (dashed line) is drawn from the experi-ent as the boundary to distinguish between the switching (solid

urve) and transistor (dotted curve) operations.

rations by numerical simulations as well as by takinghe snapshots of probe transmission when it is operatingn the unstable mode.

CKNOWLEDGMENTShis research is partially supported by Mizumoto Labora-

ory, Tokyo Institute of Technology, Japan and Agency forcience, Technology, and Research �A*STAR�, Singapore.

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