354 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 46, NO. 3, MARCH 2010

Tb/s Optical Logic Gates Based on Quantum-DotSemiconductor Optical Amplifiers

Ali Rostami, Hamed Baghban Asghari Nejad, Reza Maram Qartavol, and Hassan Rasooli Saghai

Abstract—The performance of an ultrafast all-optical logic gatebased on quantum-dot semiconductor optical amplifier (QD-SOA)has been theoretically analyzed in this paper. We introduce a novelapproach to accelerate the gain recovery process with a controlpulse (CP) using the cross-gain modulation (XGM) effect. It isshown that the optical XOR gate in a Mach–Zehnder interferom-eter-based structure is feasible at Tb/s speeds with proper qualityfactor. The operation capability at 2.5 Tb/s with a -factor of 4.9and 2 Tb/s with a -factor of 8.8 is reported for the first time. Thiscapability indicates great potential for ultrafast all-optical signalprocessing and switching.

Index Terms—All-optical processing, control pulse, quantum-dot (QD) amplifier, Tb/s optical gate.

I. INTRODUCTION

H IGH-BIT-RATE semiconductor optical amplifier-baseddevices are essential in today’s optoelectronic systems

since they can perform many functions ranging from linear ap-plications such as linear amplification to ultrafast signal pro-cessing [1], [2]. Optical communication systems with a capacityof gigabits per second are commercially available and the ca-pacity has been pushed above 10 Tb/s in research laboratories.As an optical switch or logic gate, semiconductor optical am-plifier (SOA) has been utilized extensively in variety of config-urations such as the symmetric Mach–Zehnder (SMZ) interfer-ometer, the ultrafast nonlinear interferometer (UNI), and the ter-ahertz optical asymmetric demultiplexer (TOAD) [3]–[5]. Thespeed of all-optical switches based on SOA is determined bythe carrier dynamics of the SOA. Various schemes of all-op-tical logic gates like XOR operation using the nonlinearity ofSOAs have been reported [6]–[9]. However these demonstra-tions are usually limited to 100 Gb/s by patterning effect dueto the long carrier life time in the SOA active region. Thus,the predicted superiority of quantum dot SOAs because of their

Manuscript received June 05, 2009; revised August 10, 2009. Current versionpublished January 29, 2010. This work was supported in part by the ITRC underGrant 12368\500.

A. Rostami is with with the Photonic and Nanocrystal Research Laboratory(PNRL), Faculty of Electrical and Computer Engineering, University of Tabriz,Tabriz 51664, Iran, and also with the School of Engineering Emerging Technolo-gies, University of Tabriz, Tabriz 51664, Iran (e-mail: rostami@tabrizu.ac.ir).

H. B. A. Nejad and R. M. Qartavol are with the Photonic and NanocrystalResearch Laboratory (PNRL), Faculty of Electrical and Computer Engineering,University of Tabriz, Tabriz 51664, Iran.

H. R. Saghai is with the School of Engineering Emerging Technologies, Uni-versity of Tabriz, Tabriz 51664, Iran.

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

Digital Object Identifier 10.1109/JQE.2009.2033253

physical properties come into work. Quantum-dot (QD)-SOAsare supposed to have several advantages such as: negligible pat-tern effect due to compensation of the spectral holes by the car-rier relaxation from excited state (ES), negligible cross talk be-tween different wavelength channels due to spatial isolation ofdots and prevention the carrier transfer among dots, and utiliza-tion of the cross gain modulation effect of two different wave-length channels in switching applications. The response timeof gain saturation is 100 fs-1 ps which is enough for a gigabitto sub-terabit optical transmission system [2]. The main advan-tage of QD-SOAs, as compared to the bulk and quantum-wellSOAs (QW-SOAs), is based on the existence of the gap betweenthe QD levels and wetting layer (WL), and on the lower crosssection of carrier-photon interaction which results, in partic-ular, in shorter carrier relaxation times and lower gain saturation[10], [11]. The observed relaxation times in QD-SOAs, rangefrom hundred of femtoseconds to tens of picoseconds which aresignificantly shorter than its value in QW-SOAs [12] and bulkSOAs [13]. However the main challenge in QD-based SOAs isstill related to carrier relaxation from WL into ground or ESof QD because of the phonon bottleneck phenomenon peculiarto discrete energy levels [14], [15]. Considering the benefits ofQD-based optical devices, all-optical logic gates based on QDsseem to be vital elements in ultrahigh speed networks as they canperform many critical functionalities. In [16] the capability of250 Gb/s operation of QD-SOA-based logic gates has been pre-dicted and in [1] it has been discussed and theoretically provedthat high quality pattern-free operation of XOR logic gate andalso an all-optical processor is limited to 200 Gb/s at 50 mA biascurrent which is limited by electron relaxation time from WLto ES. Thus, an upper limit has been concluded for SOA-basedlogic gates and systems. In this paper, we develop a theoret-ical approach for compensation of the carrier relaxation timeinto ES. In our model, we have considered two energy levels inboth conduction and valence bands. It will be shown that ap-plying a CP with energy of (as depicted in Fig. 2) willhighly accelerate the recovery process of QD-SOA and will leadto high-bit-rate operation of QD-SOA-MZI structure in the pres-ence of the CP. The arrival time of the CP will be discussed inthe next sections and finally, the capability of 2.5 Tb/s XORoperation in a SOA-MZI based XOR logic gate will be investi-gated. The structure of this paper is as follows. In Section II theoperation principles of QD-SOA-MZI XOR gate are presentedand discussed. Section III is dedicated to operation theory of theQD-SOA and the rate equation model for the proposed idea. Theachieved simulation results are presented in Section IV. Finally,Section V gives a brief summary of our work.

0018-9197/$26.00 © 2010 IEEE

ROSTAMI et al.: TB/S OPTICAL LOGIC GATES BASED ON QUANTUM-DOT SEMICONDUCTOR OPTICAL AMPLIFIERS 355

Fig. 1. Configuration of all-optical XOR gate using QD-SOA with CP.

II. QD SOA-MZI-BASED XOR GATE

The optical XOR gate in our study consists of a symmetricalMZI with one QD-SOA located in the same relative positionof each arm as shown in Fig. 1 ([1] and [16]). For the Booleanoperation , the input logic signals, A and B at wave-length , enter the arms of MZI via two multiplexers, respec-tively. A probe signal at wavelength enters to the structureand splits into two equal parts in coupler C1. The wavelengthseparation between and should be less than the homoge-neous broadening of the single QD gain to ensure effective crossgain modulation. If the input signals A and B are identical, theQD-SOA-MZI is balanced and no signal emerges from XORoutput. In contrast, if one of the input signals is zero while theother is one; a differential phase shift is introduced due to thecross-phase modulation (XPM) in the QD-SOA and the probesignal switches to the output consequently. The CPs at wave-length enter to each QD-SOA according the input signalpatterns (A, B) via the multiplexers. The time delay betweencontrol pulses and input signals, which affects the QD-SOA per-formance and hence the XOR gate operation, will be discussedin Section IV.

The XOR output intensity can be expressed as [16]

(1)

where , are the integral of QD-SOA gains and, are nonlinear phase shifts. and are the ra-

tios of couplers C1 and C2 which are equally set to 0.5 for sim-plicity.

III. THEORY OF OPERATION

The output power, gain and phase characteristics of theQD-SOA can be obtained by solving the rate equations ofthe structure. To describe the control-pulse-assisted QD-SOAmodel, the two band model of Fig. 2 is considered where thetransition of conduction band ground state (CBGS) to valenceband ground state (VBGS) is assumed to be the main stimulatedtransition by input signal and the transition of valence band ES(VBES) to conduction band ES (CBES) is assumed to populatethe CBES via absorption of CP.

Fig. 2. Band diagram of the QD structure with related energy levels.

The photon rate equations for input signal, probe and CP aregiven as

(2)

(3)

where is time transformed by with the groupvelocity of the light pulse, , and arethe photon densities of input signal, probe and CP, respec-tively, is modal gain, is the material absorptioncoefficient, is modal absorption coefficient of CP and

is the distance in longitudinal direction i.e., andstand for input and output facets of the QD-SOA. In

terms of photon density, ,where is the effective cross section of QD-SOA and

declares the photon energy. The gain expression is givenbywhere is maximum modal gain[17] and is the electron (hole) occupation probabilityin the ground state (GS). The term is the ef-fective population inversion in GSs. The expressions ofand are given in [18]. For simplicity, isassumed [19], [20]. Equations (3) may primitively be written as

or in the other words,

and finally it can be described in the form presented in(3). The modal absorption coefficient of the CP may bedescribed as where

is the maximum modal absorptioncoefficient and is the electron (hole) occupation prob-ability in the ES. QD-SOA dynamics relate to CP propagationequation through term which describes theES carrier dynamic, i.e., andstand for optical gain and absorption (in the proposed model),respectively ( is presumed). Due to the largereffective mass of holes compared to electrons, and the resultingsmaller level spacing, holes are expected to relax faster thanelectrons and therefore, electrons are assumed to limit thecarrier dynamics [21]. Thus, the rate equations for the WL, ESand GS can be written as ([1], [19], and [24])

(4)

356 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 46, NO. 3, MARCH 2010

(5)

(6)

where is electron charge and is the injection current density.Also is the electron relaxation time from the WL to the ES,

is the electron escape time from the ES to the WL, isthe spontaneous radiative lifetime in WL, is the electron re-laxation time from the ES to the GS, is the electron escapetime from the GS to the ES, is the spontaneous radiativelifetime in the QD. is the surface density of QDs where itstypical value is 5 cm , is the electron density inthe WL, is the effective thickness of active layer, is theSOA material permittivity and is the velocity of light in freespace. The last term in (5) and two last terms in (6) demonstratethe absorption of CP and stimulated emission in CBGS, re-spectively. For simplicity, we presume an ideal facet reflectivityand neglect the amplified spontaneous emission. The time-de-pendence of the integral QD-SOA gain and pulse phase-shiftcan be expressed as and

, respectively, where is the linewidth en-hancement factor. It has been discussed in several articles thatlinewidth enhancement factor (LEF) may vary in a large intervalfrom the experimentally measured value of 0.1 up to giant valuesof 60 in QDs [22], [23].

IV. SIMULATION RESULTS AND DISCUSSION

In order to study the performance of the proposed QD-SOA,we have solved (2)–(6) numerically, using typical values ofInAs-InGaAs QD amplifiers. As a common model, carriers arecaptured into the CBES from the WL which serves as a carrierreservoir for the QD and after a stimulated depletion fromCBGS, the CBES carriers are replaced by fast carrier transferfrom the WL, in this manner limits the gain dynamics asit mentioned before. To investigate the effect of CP on gaincharacteristics of the QD-SOA, we have considered the energyseparation between the CBES and CBGS and also VBES andVBGS to be about to avoid the overlappingproblem at higher bit rates. The wavelengths of signal, probeand CP are considered to be: m, mand m. For the following structure parameters[19], [21], [24], [25]: cm , cm ,

cm , , ps, ns,ns, ns, ps, ps,m, m, m (the width of

QD-SOA), (the confinement factor), the state oc-cupation probabilities of electrons in the presence and withoutCP for one of the QD-SOAs located on MZI arms, at 1 Tb/s

Fig. 3. Electron state occupation probabilities of GS, f(t), and ES, h(t), in thepresence and without CP. The dashed lines correspond to input bit sequence at1 Tb/s. The bias current is 50 mA, input signal, CP and probe signal powers are:��� �W, ��� �W and � �W, respectively.

Fig. 4. Electron state occupation probabilities of GS, f(t), and ES, h(t), in thepresence and without CP. The dashed lines correspond to input bit sequence at2 Tb/s. The bias current is 50 mA, input signal, CP and probe signal powers are:��� �W, ��� �W and � �W, respectively.

and 2 Tb/s input bit sequences, 50 mA bias current, Winput signal, W CP and W probe signal are displayedin Figs. 3 and 4, respectively.

At both bit rates of 1 Tb/s and 2 Tb/s the oscillation of ESand GS completely follows the input signal variation howeverat 2 Tb/s bit sequence, the population variation can’t reach to thefinal population value but still varies with relatively high ampli-tude. The high population of GS 0.75 and ES 0.35is due to fast electron transition between ES and GS and ab-sorption of the CP which compensates the relaxed population ofES to GS. The maximum value for state population probabilityof ES, h, versus increasing the CP power and in enough largevalues of CP power will tend to 0.5. This fact can be justified byconsidering the last term of (5). Whenever the h value tends to0.5, the expression (1–2 h) tends to zero and in this case, the ef-fect of last term in (5) (absorption of CP) on increasing the pop-ulation of ES vanishes. Thus, temporal decrease of h motivatesthe term (1–2 h) to become positive and effective absorption of

ROSTAMI et al.: TB/S OPTICAL LOGIC GATES BASED ON QUANTUM-DOT SEMICONDUCTOR OPTICAL AMPLIFIERS 357

Fig. 5. Gain dynamics of QD-SOA following an input pulse with 1 ps FWHMand ��� �W pulse power in presence and without considering the CP for twodifferent input and CP temporal positions. The dotted line corresponds to thecase that the CP isn’t applied.

Fig. 6. The effect of input and CP timing on state occupation probabilities.

CP will happened. It should be mentioned that the process ofcontrolling the h value below 0.5 is related to XGM phenom-enon. In fact, the influence of the CP on gain recovery processis similar to a fast current source which is applied when the gaindynamics reaches to its minimum value.

In Fig. 5 two possible temporal positions of input signal andCP with 1 ps FWHM and also the related gain variations areillustrated. It can be concluded that applying the CP when thegain variation tends to zero (i.e., when the input pulse reaches toits maximum amplitude), will obtain the optimum gain recoverytime. In this case, absorption of the CP will populate the CBESand hence the recovery process will accelerate. Otherwise, asit can be seen in Fig. 6, a variation in ES population appearswhich leads to longer recovery time (dashed curve in Fig. 5).However, the recovery process is still much faster compared tothe case that no CP is applied in the same input power and in-jected current (dotted curve in Fig. 5).

Fig. 7. The effect of bias current on electron state occupation probabilities ofGS, f(t), and ES, h(t), in the presence of the CP. The input bit sequence is 1Tb/s. The bias current is 50 mA, input signal, CP and probe signal powers are:��� �W, ��� �W and � �W, respectively.

Fig. 8. XOR operation of QD-SOA-MZI structure for 1 Tb/s input bit sequenceand 50 mA injected current. The input signal, CP and probe signal powers are:��� �W, � mW and � �W, respectively.

The bias current in QD-SOAs is known to be an effective pa-rameter to decrease the recovery time [16]. High injection cur-rent decreases the ES refilling time and therefore leads to fasterrecovery process. In Fig. 7 the influence of 20 mA and 50 mAbias currents on the state population dynamics is illustrated (inthe presence of CP). Generally, the dynamic gain range is depen-dant to bias current. So, higher bias current is necessary in orderto have acceptable gain and phase variations. The bold curve inFig. 7 (20 mA bias current), describes the case that the CP risesthe state occupation probability over the final steady state valueand therefore increase the dynamic gain range. However whenthe input sequence remains zero for several bit periods, the dy-namic range of the first coming pulses is limited due to low biascurrent.

The results for the XOR logic operation with CW probe signalat 1, 2 and 2.5 Tb/s input sequences are displayed in Figs. 8–10,

358 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 46, NO. 3, MARCH 2010

Fig. 9. XOR operation of QD-SOA-MZI structure for 2 Tb/s input bit sequenceand 50 mA injected current. The input signal, CP and probe signal powers are:��� �W, � mW and � �W, respectively.

Fig. 10. XOR operation of QD-SOA-MZI structure for 2.5 Tb/s input bit se-quence and 50 mA injected current. The input signal, CP and probe signalpowers are: ��� �W, � mW and � �W, respectively.

respectively. The results describe that the pattern effect is neg-ligible at 1 Tb/s but in Figs. 9 and 10 it is seen that the form ofXOR signal is distorted.

In order to obtain the eye diagram, we use a pseudo-random RZ sequence input. The corresponding eye diagramsof the XOR gate output signal are shown in Fig. 11. A quan-tity known as Q is widely utilized to analyze and predict thesignal quality for pseudo-random signals [26] and is defined as

where and are the averagepower of output signals “1” and “0,” and are standard de-viation of all “1” and “0,” respectively. As it described before, ina QD-SOA, bias current and electron relaxation time from WLto ES determine the SOA performance and hence high currentsand faster relaxation times improve the Q factor. But beside thefact that too high current is prohibited for practical applications,the Q factor saturates above a specific bias current as reported in

Fig. 11. Eye diagrams of the XOR output signals. In each case the pulsewidthis 1/5th of the bit period. The input bit sequences are at (a) 1 Tb/s, (2) 2 Tb/sand (c) 2.5 Tb/s.

[16]. Also the Q value is sensitive to the input pulsewidth and in-creasing the pulsewidth decreases the Q factor because of over-lapping of two neighboring pulses. The Q factor is also depen-dant on parameter. Multilayer QD structures are consideredas a technique to increase the modal gain due to increasing theparameter and therefore reducing the threshold current. As it canbe seen in Fig. 11, because of ultrafast gain recovery in the pres-ence of CP, at the bit rate of 1 Tb/s, the pattern effect is almostabsent and the eye pattern is clearly open with Q of 28.4.Alsofor the bit rate of 2 Tb/s and 2.5 Tb/s the -factor drops to 8.8and 4.9, respectively, and the eye is gradually closing due to pat-tern effect.

Achieving to high speed signal processing, as it mentionedbefore, depends strongly on WL to ES and ES to GS relax-ation times. However, is not a limiting factor in conventionalQD-SOA’s operation 200 (according to the reported re-sults for ([1], [19], [27]–[29]) which are 160 fs becauseof longer WL to ES relaxation time. However, this parametercan be important in achieving high-speed operation in the pro-posed approach as a higher limit. Increasing the relaxationtime and consequently ,decreases the quality factor of XOR output, as shown in Fig. 12.

is the Boltzmann constant, T is the absolute temperature andis the energy separation between the ES and GS.

V. CONCLUSION

In this article, for the first time, we introduced a novel theo-retical approach to compensate the slow carrier relaxation timefrom WL to ES (using XGM effect) which is the main limit toachieve to higher speeds in QD-SOAs. It concluded that the pro-posed approach accelerates the recovery process of the SOA.Applying a 2 mW CP to the two-energy-level-QD at certain

ROSTAMI et al.: TB/S OPTICAL LOGIC GATES BASED ON QUANTUM-DOT SEMICONDUCTOR OPTICAL AMPLIFIERS 359

Fig. 12. Quality factor of XOR gate as a function of ES to GS relaxation timefor input bit sequences at 1 Tb/s (dashed) and 2 Tb/s (solid).

times enables the QD-SOA-MZI-based XOR gate to operateunder 1, 2, and 2.5 Tb/s input bit sequences with Q factors of28.4, 8.8, and 4.9, respectively. Also the eye patterns relatedto XOR operation presented. This capability of control-pulse-assisted-QD-SOA is promising for ultra-high-speed all-opticallogic gates, all-optical switching and processing.

ACKNOWLEDGMENT

The authors would also like to thank the editor of the journaland anonymous referees for the important comments that helpedus to improve the content of this paper.

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360 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 46, NO. 3, MARCH 2010

Ali Rostami received the Ph.D. degrees in photonic/electronic engineering from University of Amirk-abir, Tehran, Iran, in 1998.

He was in sabbatical leave in the University ofToronto, Toronto, ON, Canada, (2004–2005) at thePhotonic Group. He is currently full Professor ofElectronic Engineering and Photonics Science at theUniversity of Tabriz, Tabriz, Iran. His teaching andresearch interests include optical integrated circuitsand optoelectronic devices. He is a member of theOptical Society of America. He is the author and

coauthor of more than 220 scientific international journal and conferencepapers and 4 text books. Also, he collaborates with some international journalsas reviewer boards (more than 10 journals) and works as editorial committee oftwo Iranian journals.

Dr. Rostami has served on several other committees and panels in govern-ment, industry, and technical conferences.

Hamed Baghban Asghari Nejad received the B.S.and M.S. degrees in electronics engineering fromTabriz University, Tabriz, Iran, in 2005 and 2007,respectively, where he is pursuing the Ph.D. degree.

His research interests are in the area of semicon-ductor optoelectronic devices.

Reza Maram Qartavol received the B.S. degreein electronics engineering from University of Kur-destan, Iran, in 2007. He is currently working towardthe M.S. degree in electronics engineering at thePhotonics and Nanocrystals Research Laboratory(PNRL), Faculty of Electrical and Computer En-gineering, University of Tabriz, Iran, where he isresearching quantum-dot semiconductor opticalamplifiers.

Hassan Rasooli Saghai received the B.Sc. degreein electronics engineering from Islamic Azad Uni-versity, Tabriz, Iran, the M.Sc. degree in electronicsengineering from Islamic Azad University, SouthTehran, Iran, and the Ph.D. degree in electronicsengineering from Islamic Azad University Scienceand Research, Iran, in 1996, 2000, and 2008, respec-tively.

Currently, he is a Postdoctoral Fellow in the Schoolof Engineering Emerging Technologies, university ofTabriz, Iran. He joined the Department of Electrical

Engineering, Islamic Azad University of Tabriz, in 2000 as a faculty member.His current research interests include quantum-dot based devices.