Optical Flip-Flop Using Bistable Vertical-Cavity Semiconductor ...

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 21, NOVEMBER 1, 2009 4703

Optical Flip-Flop Using Bistable Vertical-CavitySemiconductor Optical Amplifiers With

Anti-Resonant Reflecting Optical WaveguideW. L. Zhang and S. F. Yu, Senior Member, IEEE

Abstract—Flip-flop operations of anti-resonant reflecting- op-tical-waveguide (ARROW) vertical-cavity semiconductor opticalamplifiers (VCSOAs) under the influence of undesired high-orderinjection modes are investigated theoretically. Three types offlip-flop operations, namely: 1) flip-flop triggered by opticalinjection, 2) inverse flip-flop triggered by optical injection, and3) flip-flop triggered by injection current, are to be considered inthe studies. It is found that with the presence of ARROW, all threetypes of optical flip-flop are insensitive to high-order injectionmodes, and stable single-mode flip-flop can be maintained in theoperation.

Index Terms—Anti-resonant reflecting optical waveguide, op-tical bistability, optical flip-flop, optical switching, vertical-cavitysemiconductor optical amplifier.

I. INTRODUCTION

B ISTABLE vertical-cavity semiconductor optical-ampli-fiers (VCSOAs), of which operating characteristics have

been intensively studied in the past few years, are one of thekey components in future all-optical processing, optical controland optical computation due to their low switching power,fast response time, and single-longitudinal mode operation[1]–[4]. Recently, studies have extended to the realization ofoptical flip-flop by using bistable VCSOAs. In order to achieveflip-flop operations, VCSOAs should be able to be controlledresponsibly by an external injection signal (i.e., the holdingbeam). The set and reset external injection signals can bedefined to trigger the VCSOAs to follow one of the two stableoutput states. Based on this concept, flip-flop operations ofVCSOAs were analyzed. In addition, the corresponding set andreset signals were obtained by using cross-phase modulation(XPM) and cross-gain modulation (XGM) respectively [5],[6]. A cascadable optical flip-flop was also constructed by twocross-coupled electrically pumped VCSOAs [7].

In the previous studies of optical flip-flop based on bistableVCSOAs, single-transverse-mode operation was only consid-ered. This implies that the holding beam was restricted to be

Manuscript received March 20, 2009; revised May 20, 2009. First publishedJune 19, 2009; current version published September 10, 2009. This work wassupported by the Singapore Ministry of Education Academic Research FundTier 1, Grant no RGM 40/06.

The authors are with the School of Electrical and Electronic Engi-neering, Nanyang Technological University, 639798 Singapore (e-mail:[email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JLT.2009.2025664

coupled to the fundamental mode of VCSOAs. However, it isalso possible that some undesired high-order injection modes ofthe holding beam can be coupled to the high-order modes of VC-SOAs [8]. As a result, the bistable characteristics of VCSOAswill be affected and the flip-flop operations may be destroyed.Especially, the interests to investigate larger-area VCSOAs (fortheir lower resistance, lower thermal impedance, lower currentdensity and higher output power [9], [10]) make this problemincreasingly crucial. Hence, it is necessary to find alternativeapproach, besides the use of single-mode VCSOAs with smallarea, to stabilize the flip-flop operations of VCSOAs.

It has been verified that the use of anti-resonant reflecting op-tical waveguide (ARROW) can suppress the emission of high-order modes in vertical-cavity devices [8]–[11]. Hence, it isalso believed that the presence of ARROW structure can sus-tain stable single-mode flip-flop operations in VCSOAs. In thispaper, the possibilities to realize optical flip-flop in VCSOAswith insensitivity to the undesired high-order injection modesby using ARROW structure are studied theoretically. This paperis organized as follows. In Section II, a simple theoretical modelis developed to analyze the dynamic response of ARROW VC-SOAs. In Section III, 3 types of flip-flop operations, namely:type I—flip-flop (i.e., based on counterclockwise bistability)triggered by external optical injection, type II—reverse flip-flop(i.e., based on clockwise bistability) triggered by external op-tical injection, and type III—flip-flop (i.e., based on counter-clockwise bistability) triggered by injection current, are inves-tigated. Furthermore, the influence of undesired high-order in-jection modes on the flip-flop operation of ARROW VCSOAsis discussed. The results are also compared with those obtainedfrom the conventional index-guided (CIG) VCSOAs. Conclu-sions are given in Section IV.

II. THEORETICAL MODEL OF BISTABLE ARROW VCSOAS

A. Devices Structure

Schematic of an ARROW VCSOA operating at reflectionmode is shown in Fig. 1. External optical injection and biasingcurrent are applied through a transparent circular metal contactcovering the core region of the device. The low-index coreregion is surrounded by the ARROW including the first, thesecond, and the outer cladding layers. The design of ARROWmeets the anti-resonant condition of the fundamental mode.However, high-order modes will experience large radiationlosses due to their deviation from the anti-resonant wavelength.The bias current is confined within the core region by ion-im-

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Fig. 1. Schematic of the ARROW VCSOA operating in reflection mode.

planted cladding region. However, the injection current may bepoorly confined inside the active layer so that some portion ofinjection current will diffuse toward the cladding region.

B. Theoretical Model of the Arrow VCSOAs

Static and dynamic characteristics of an ARROW VCSOAcan be investigated by expanding a self-consistent model pro-posed in our previous studies [11], [12]. It was shown that thecalculated lasing characteristics of ARROW VCSELs by theproposed model matched with the experimental observation re-ported in [9] and [13].

We start our analysis with the nonuniform distribution of car-rier concentration, , inside the active layer of the VCSOA. Weonly considered two lowest-order leaky modes (i.e., and

) with the lowest radiation losses into calculation. This isbecause high-order modes experience very high radiation lossesin the ARROW [8]. Thus, the carrier rate equation can be writtenas [8], [11]

(1)

where is the group velocity, is the carrier life time, isthe carrier diffusion coefficient, is the electron charge, is thethickness of active layer, is the photon density of

inside the active layer, and is the azimuth-averagedfield distribution of [11]. The injection current density, ,can be written as

(2)

where is the injection current density within the core region,and is the effective diffusion length of the injection current.In (1), the material gain, , is defined as

(3)

where is the gain coefficient, is the carrier densityat transparency, is the saturation photon density, and

is the total photon density inside the cavity.In addition, the single-pass gain of , , is defined as

(4)

where is the longitudinal confinement factor, is the ef-fective cavity length, and are the total internal cavityloss and radiation loss experienced by , respectively. Theaverage material gain, , in (4) is expressed as

(5)

With the definition of single-pass gain, , the expressionsof ARROW VCSOA’s internal gain, , and reflection gain,

, can be given as [14], [15] see (6)–(7), shown at the bottomof the page, where and are the reflectivity of the topand bottom mirror respectively. The rate equation of single-passphase change, , can be written as

(8)

where is the linewidth enhancement factor, is the wave-length of the injection field, and is the initial resonant wave-length of .

(6)

(7)

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TABLE IPROPERTIES IN THE SIMULATION

C. Calculation Method

The typical values of the device parameters used in the sim-ulation are listed in Table I. Some of these parameters are se-lected from the published literature [1]–[3], [8], [11], [15], andsome other parameters are deduced by comparing the calculatedresults (i.e., counterclockwise/clockwise bistabilities and turn-on/off dynamics) obtained from the model with the available ex-perimental results [5], [16].

In addition, the dimension of the ARROW (i.e., width of thefirst and second cladding layers, and ) is optimized usingthe method present in our previous works [8], so as to maximize(minimize) the radiation loss of . Hence, the opti-mized combination of and are found to be 2.04 and 5.01

, respectively, with and .The term, , in (1) and (8) can be calculated from

(9)

where is the Planck’s constant, is the

radius of the VCSOA, is the frequency of the

input field, and is the injection power coupled to .

Thus, the output power of , , can be

deduced by solving (1) and (7)–(9) self-consistently if andare given in the calculation.

In the following calculation, only the amount of externalinjection field coupled to is defined as the holdingbeam so that the power of holding beam, , is equated to

. However, the external injection field can also coupleto high-order modes simultaneously. Hence, a power ratio,

, is defined to evaluate the amount of unde-sired external optical injection coupled to . Furthermore,only the output power of , , is treated as the effectiveoutput of the optical flip-flop. It is also worth mentioningthat the ARROW is designed to support with wave-length, , set to 1550 nm. One can derive the wavelength

of for other operation conditions through the relation,, where “ ” represents the

real part, is the effective refractive index correspond toand is the effective refractive index of (see [11] forthe detailed calculation of effective refractive index).

III. NUMERICAL RESULTS

VCSOAs can exhibit counterclockwise, butterfly, and clock-wise bistabilities under the influence of external optical injec-tion [1], [2], and [16]. Counterclockwise and clockwise bista-bilities can be used to realize type I and II flip-flop operationsrespectively under the control of external optical injection. Thisis because either turn-on or -off state, which emergence is de-pendent on the input history of VCSOAs, can be triggered.Counterclockwise bistable VCSOAs under the trigger of ex-ternal injection current will also be used to achieve type III op-tical flip-flop. In this section, these three types of flip-flop oper-ations for ARROW VCSOAs with the influence of high-orderinjection modes will be studied. The results are also comparedwith those obtained from bistable CIG VCSOAs.

A. Flip-Flop Triggered by External Optical Injection (Type-IOptical Flip-Flop)

Fig. 2 shows the output power of , , as a functionof the holding beam power, , injected into the ARROWVCSOA. It is observed that the VCSOA exhibits counter-clockwise bistability for all the range of . In the calculation,

is used and the threshold current, , is found to be4830 A/cm . It is assumed that the injection current, , is setto and the wavelength detuning is 0.11 nm. Forthe case (i.e., external optical injection is only coupled to

), the values of for turn-on and -off of the hystereticloop are found to be 0.0325 and 0.023 mW, respectively. When

increases (i.e., more undesired power is coupled to ),the turn-on and -off thresholds move to smaller values ofand the width of the hysteretic loop decreases. This is becausethe undesired injection coupled to depletes the carrierconcentration so that the effective refractive index of activelayer is increased. As a result, the cavity resonant wavelengthis shifted toward the injection wavelength. This is equivalent todecrease the wavelength detuning, , as well as increasethe single-pass phase change, , and thereby the hystereticloop moves to smaller [14].

In Fig. 2, it is noted that the influence of undesired injectionis not significant. For example, can still exhibit similarbistable characteristics and the bistable regions are overlappedeven the value of is three times to that of (i.e.,

). This implies that bistability of the fundamental mode is notsensitive to high-order injection mode.

We also calculated the reflection gain of the two LMs as afunction of the injection wavelength, which is given in an in-sert of Fig. 2. has a gain peak (gain valley) of19 dB dB at its resonant wavelength. Hence, a large gaindifference between and can be obtained duringoperation. This large gain different between andof the ARROW VCSOA is also beneficial to achieve 1) stablesingle-mode flip-flop and 2) insensitivity to high-order injectionmode.



Fig. 2. Output power of �� , � , of the ARROW VCSOA versusthe holding beam input power, � . In the calculation, � � ��,� � �� A/cm , � � �� and � � � � �� nmare used. The inset is the reflection gain of �� , � , versus the injectionwavelength, � , where � � and � � � mW.

Fig. 3. Dynamic response of for the ARROW VCSOA during a type-Iflip-flop operation. In the calculation, � � �� mW, � � ��,� � �� A/cm , � � �� and � � � � �� nm areused. In the set (reset) transient, a value of 0.02 �� mW with duration of2 ns is added to � to switch the output power.

To demonstrate the type I flip-flop operation, Fig. 3 shows thedynamics response of the VCSOA when set and reset signalsare applied. The holding beam with a baseline power of 0.03mW (i.e., dotted in Fig. 2) is injected into the VCSOA. Theset (reset) signal with duration of 2 ns, which can be adoptedoutside or inside the VCSOA through either XGM or XPM [5],[6], increases (decreases) the power of the holding beam (Here,the holding beam power is treated as the power injected into

. For the calculation purpose, we allowed the variation ofholding beam power. In reality, its value is a constant and itseffectiveness is modulated by XGM or XPM).

For (i.e., single-mode injection), the value of fallswithin the bistable region. At the beginning of the switching,the VCSOA’s output locates at the lower bistable state (symbol“ ” in Fig. 2). During the set transient, additional power isadded to the holding beam by the set signal and increasesbeyond the turn-on threshold. As a result, the VCSOA’s output

Fig. 4. Output power of �� , � , of the conventional index-guidedVCSOA versus the holding beam injection power, � . In the calculation,� � ��A/cm , and other descriptions are the same as that for Fig. 2. Theinset is the reflection gain of �� , � , versus the injection wavelength,� , where � � and � � � mW.

switches to the upper bistable state (symbol “ ” in Fig. 2). TheVCSOA remains at this stable state until further trigger from thereset signal. The reset signal decreases below the turn-offthreshold and resets VCSOA’s output to its initial value, thatis the lower bistable state. Thus, single-mode type-I flip-flop isrealized. For the cases 0.5, 1, and 3 (i.e., multimode in-jection), there is unwanted injection coupled to the high-ordermode. However, the bistability is not affected distinctly (seeFig. 2) and is still within the bistable region, so flip-flop canstill be excited. This verifies that type-I optical flip-flop basedon ARROW VCSOAs is insensitive to the undesired high-orderinjection mode. Spikes are also observed from the output powerwhen a set signal is applied. The trigger of spikes during theturn-on state of the VCSOAs is due to the relaxation oscillationof photon density coupled to carrier concentration inside the ac-tive region of the VCSOAs. Hence, the switching speed of VC-SOAs will be limited by the finite relaxation time of the spikes.So moderate amplitude of the set/reset signal should be used(i.e., set signal with large amplitude will often triggers largespike) in the operation. A further discussion on the switchingspeed of VCSOAs will be presented in part D of this section.

For comparison, Fig. 4 repeats the plot of Fig. 2 for the CIGVCSOA (i.e., the values of , and are all set to 3.25, butother parameters are kept unchanged in the calculation). In thissimulation, the values of , and for the CIG VCSOAare found to be 1550, 1549.07, and 4710 A/cm , respectively.

For , the hysteretic loop is similar to that of the ARROWVCSOA. However, for , hysteretic loops shifted to the lowvalue of with the increase of . This indicates that the bista-bility of the fundamental mode is very sensitive to the high-orderinjection mode. The inset of Fig. 4 shows that the CIG VCSOAcan support amplifications of both the fundamental andthe high-order modes . Hence, unwanted injection cou-pled to the high-order mode will also be amplified effi-ciently. As a result, carrier depletion enhances greatly comparedto that for , leading to the shift of bistable loops.



Fig. 5. Dynamic response of � for the conventional index-guided VCSOAduring a type-I flip-flop operation. In the calculation, � � �� A/cm , andother descriptions are the same as that for Fig. 3.

Fig. 5 demonstrates type-I flip-flop operation based on theCIG VCSOA, where different values of are considered. Theholding beam, set and reset signals are the same as those usedin Fig. 3. For the case , falls within the bistable regionand VCSOA’s output initially locates at the lower bistablestate (symbol “ ” in Fig. 4). When the set signal applies,increases beyond the turn-on threshold and VCSOA’s outputswitches to the upper stable state. This state is kept until thereset signal is applied. The reset signal decreases belowthe turn-off threshold and switches the output back to the lowerbistable state. Thus, single-mode type-I flip-flop operationbased on the CIG VCSOA is realized. For the case ,the holding beam power is no longer within the bistable region.The output power of CIG VCSOA remains at a single valueregardless of the adoption of the set and reset signals. Similarresults are obtained from the cases of and 3. So wecan concluded that type-I flip-flop based on the CIG VCSOAis easily to be affected by the unwanted high-order injectionmode.

By now, we have shown that VCSOAs with and without theARROW structure exhibit different tolerance to unwanted high-order injection mode. With the presence of ARROW, the ampli-fication of high-order mode is suppressed. Carrier depletion aswell as phase change [14] induce by the high-order mode is lim-ited. Thus, single-mode flip-flop operation is slightly affected bythe injection power coupled to the high-order mode and the pres-ence of ARROW structure is beneficial to stable single-modeflip-flop. While the case is reverse for VCSOA without ARROWstructure.

B. Inverse Flip-Flop Triggered by Optical Injection Power(Type-II Optical Flip-Flop)

Besides counterclockwise bistabilities, the clockwise bista-bilities can also be use to realize optical flip-flop, namely, type-IIoptical flip-flop. It must be noted that the turn-on and -off statesof the clockwise bistabilities are triggered by the set and resetsignals in a reverse manner to that of the counterclockwise bista-bilities, hence, the type-II optical flip-flop is also referred to re-verse optical flip-flop.

Fig. 6. Output power of �� , � , of the ARROW VCSOA versus theholding beam injection power, � . In the calculation, � � ��, � ��A/cm , � � �� , and �� nm are used.

Fig. 7. Dynamic response of for the ARROW VCSOA during a type-IIflip-flop operation. In the calculation � � �� mW, � � ��,� � � A/cm , � � �� and �� nm areused. In the set (reset) transient, a value of 0.25 �� mW with duration of2 ns is added to � to switch the output power.

Fig. 6 plots the output power of , , as a functionof for the ARROW VCSOA. In this simulation, a larger topmirror reflectivity, , and a larger wavelength de-tuning, nm, are considered. The calcu-lated threshold current, , is 3330 A cm . For all the 4 valuesof , shows clockwise bistability. Furthermore, most partsof the 4 bistable regions are overlapped. Hence, the clockwisebistability (type-II flip-flop operation) obtained in the ARROWVCSOA is also insensitive to the high-order injection mode.

Fig. 7 exhibits the transient response of the ARROW VCSOAduring a type-II flip-flop operation. The baseline power ofis 0.37 mW (see also the dotted line in Fig. 6) and is ini-tially located at the upper bistable state (symbol “ ” in Fig.6). When the set signal is applied, increases beyond theturn-off threshold so that switches to the lower bistablestate (symbol “ ” in Fig. 6) and maintains at this stable stateuntil triggered by the reset signal. The reset signal reducesbelow the turn-on threshold, and the output power returns to itsinitial state (i.e., the upper stable state). Obviously, this flip-flop



Fig. 8. Output power of �� , � , of the conventional index-guidedVCSOA versus the holding beam injection power, � . In the calcu-lation, � � ��, � � �� A/cm , � � �� , and� � � � �� nm are used.

Fig. 9. Dynamic response of for the conventional index-guided VCSOA duringa type-II flip-flop operation. In the calculation, � � ��mW, � � ��,� � �� A/cm , � � �� and � � � � �� nm areused. In the set (reset) transient, a value of 0.3 ��mW with duration of 2 nsis added to � to switch the output power.

operation is in reverse to that observed in Fig. 3. Hence, it isverified that the type-II flip-flop operation base on ARROWVCSOA is stable and can tolerate relative strong high-order in-jection modes.

For comparison, the clockwise bistability of the CIG VCSOAis given in Fig. 8. It is observed that the operation of VCSOA isvery sensitive to high-order injection mode (i.e., a small amountof high-order-mode injection can move the bistable region awayfrom the holding beam) leading to the unsuccessful of flip-flopoperation. The transient response of CIG VCSOA given in Fig. 9shows that the flip-flop operation is completely destroyed when

increases to 0.5. Hence, in order to achieve reverse flip-flopfrom CIG VCSOAs, the injection power should be strictly tosingle-mode.

C. Flip-Flop Triggered by Injection Current (Type-III OpticalFlip-Flop)

In the above discussions, the holding beam is used to triggerflip-flop operation. On the other hand, the injection current, ,

Fig. 10. Output power of �� , � , of the ARROW VCSOA versus injec-tion current, � . In the calculation, � � �� mW, � � ��, � �� A/cm and � � � � �� nm are used.

can also be used to trigger flip-flop operation in VCSOAs andthis is referred to as type-III flip-flop operation. For type-I and-II flip-flop, the holding beam power, , is initially set withinthe bistable region, and the output of the device is either set orreset by the variation of PH induced by the set and reset sig-nals. While for type-III flip-flop, the value of PH (as well asthe amount of power coupled to high-order modes) is consid-ered unchanged, and the output is either set or reset through thetrigger of . In other words, the output power of VCSOAs canalso show bistability as a function of for a certain amount ofexternal optical injection.

Fig. 10 gives the output power of , , as a functionof the injection current, , for the ARROW VCSOA, wherethe holding beam, , is kept at 0.0343 mW. It is observed that

shows counterclockwise bistability as a function of .When increases (i.e., more input power coupled to ), thebistable region moves to smaller value of and the width ofbistable loops is reduced. However, owning to the suppressionof by the presence of ARROW, the bistable loops are notchanged significantly (i.e., they are mostly overlapped with eachother except for the case ).

The transient response of the ARROW VCSOA duringa type-III flip-flop operation is presented in Fig. 11. In thissimulation, is set at a baseline value of . Thisvalue corresponds to the dotted line in Fig. 10, and is withinthe bistable regions for , 0.5, and 1. The set (reset) signalis adopted by increasing (decreasing) beyond (below)the turn-on (turn-off) threshold of the hysteretic loop, so asto switch the output state. We can conclude that the type-IIIflip-flop operation using ARROW VCSOA can tolerate mod-erate undesired high-order injection modes (i.e., .

Plots of Figs. 12 and 13 repeat the calculation given inFigs. 10 and 11, respectively, for the CIG VCSOAs. In Fig. 12,it is observed that when high-order injection modes are con-sidered , the counterclockwise bistability of asa function of disappears, and varies almost linearlywith . As a result, flip-flop operation is only observed inFig. 13 for the case . This again verified that the presenceof ARROW, which increases the radiation loss of high-order



TABLE IISWITCHING TIME FOR THE TURN-ON AND TURN-OFF TRANSIENTS

Fig. 11. Dynamic response of for the ARROW VCSOA during a type-IIIflip-flop operation. In the calculation, � � ��mW, � � �� A/cm , � � �� and �� nm are used. Inthe set (reset) transient, a value of 100 �� A/cm with duration of 4 ns isadded to � to switch the output power.

Fig. 12. Output power of � , � , of the conventional index-guidedVCSOA versus injection current, � . In the calculation � � �� mW,� � ��, � � ��A/cm and �� nm are used.

modes, can guarantee stable single-mode flip-flop operationeven with the consideration of undesired high-order injectionmodes.

Also, it is worth mentioning that the injection current cantrigger clockwise bistable VCSOAs to achieve reverse flip-flop

Fig. 13. Dynamic response of� for the conventional index-guided VCSOAduring a type-III flip-flop operation. In the calculation, � � �� mW,� � ��, � � �� A/cm , � � �� and �� nm are used. In the set (reset) transient, a value of 100 ��A/cm withduration of 4 ns is added to � to switch the output power.

operation. The results are similar to that given in Section B andare not repeated here.

D. Switching Speed of the Flip-Flop

To evaluated the switching speed of the VCSOAs under theflip-flop operation, a set (reset) jitter, , is defined as theduration between the end of set (reset) signal and the time whenthe fluctuation of output power is less than 5% of its final steady-state. Table II shows the calculated value of and for type-Iflip-flop. In the calculation, the duration, , and the amplitude,

, of the set (reset) signal are considered as the variables.It is found that relative small values of and (smaller than0.5 ns, bolded figures in Table II) can be obtained from theenergy of the triggering pulses, , of about 0.04–0.05 fJ.This indicated that there is a trade-off between the duration andamplitude of the set/reset signal. However, other energies (i.e.,other combination of and ) of the triggered pulses inducelarge set and reset jitters. Similar conclusion can be obtainedfrom type-II and type-III flip-flop operations, and the calcula-tions are not repeated. It is also noted that the width of thebistable region and the value of can affect the switchingspeed of the VCSOAs. Hence, more detailed studies on the



switching speed of VCSOAs will be carried out in our futureworks.

IV. CONCLUSION

The flip-flop operations of the bistable VCSOAs can be trig-gered by either the holding beam or the bias current (i.e., as theset and reset signals) to switch between the two stable states ofthe output power. Three types of flip-flop operations can be real-ized by bistable VCSOAs. Type-I and -II optical flip-flop repre-sent VCSOAs to be functioned at counterclockwise and clock-wise bistabilities respectively. It is required that the bistableVCSOAs to be operated at small optical injection powers andsmall wavelength detunings in order to achieve type-I flip-flopoperation. For type-II flip-flop operation, the bistable VCSOAsshould be operated at relative large optical injection powers andlarge wavelength detunings. On the other hand, type-III flip-flopoperation requires that the set and reset signal to be controlledby injection current. This is because VCSOAs can also exhibitbistable operation under the trigger of injection current if a cer-tain holding beam is applied. However, it has been shown thatstable flip-flop operation is not guaranteed if either the VCSOAscan support amplification of high-order modes or the externaloptical injection has component of high-order modes.

Hence, we proposed the use of ARROW in VCSOAs toachieve stable single-mode flip-flop operation. It is found thatall three types of optical flip-flop using ARROW VCSOAs cantolerate undesired high-order injection modes with powers up to2 to 3 times of the injection power of the holding beam. This isbecause the high-order modes experience large radiation lossesand their amplifications are strongly suppressed due to thepresence of ARROW. Hence, it is verified that ARROW makesthe VCSOA insensitive to undesired high-order injection modesand, thus, sustains stable single-mode flip-flop operations.

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W. L. Zhang was born in Hen’nan, China, in 1980.He received the B.Eng. degree and the Ph.D. degreein communication engineering from Southwest Jiao-tong University, Si’chuan, China, in 2003 and 2008,respectively.

He is currently a Research Fellow in the Schoolof Electrical and Electronic Engineering, NanyangTechnological University, Singapore. His mainresearch interests include optical communication,nonlinear dynamics, design and analysis of semicon-ductor lasers, and amplifiers.

S. F. Yu (M’03–SM’03) received the Ph.D. degree inoptoelectronics engineering from Cambridge Univer-sity, Robinson College, U.K., in 1993.

Currently, he is an Associate Professor andprogram director of the M.Sc. (MicroE) program atthe School of Electrical and Electronic Engineering,Nanyang Technological University, Singapore. Hismain research interests include the fundamentalstudy, design and optimization of semiconductorlasers including distributed feedback lasers andvertical-cavity surface-emitting lasers.


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