Tb/s Optical Logic Gates Based on Quantum-Dot ...

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

Tb/s Optical Logic Gates Based on Quantum-Dot Semiconductor Optical Amplifiers Ali Rostami, Hamed Baghban Asghari Nejad, Reza Maram Qartavol, and Hassan Rasooli Saghai

Abstract—The performance of an ultrafast all-optical logic gate based on quantum-dot semiconductor optical amplifier (QD-SOA) has been theoretically analyzed in this paper. We introduce a novel approach to accelerate the gain recovery process with a control pulse (CP) using the cross-gain modulation (XGM) effect. It is shown that the optical XOR gate in a Mach–Zehnder interferometer-based structure is feasible at Tb/s speeds with proper quality factor. The operation capability at 2.5 Tb/s with a -factor of 4.9 and 2 Tb/s with a -factor of 8.8 is reported for the first time. This capability indicates great potential for ultrafast all-optical signal processing and switching. Index Terms—All-optical processing, control pulse, quantumdot (QD) amplifier, Tb/s optical gate.

I. INTRODUCTION IGH-BIT-RATE semiconductor optical amplifier-based devices are essential in today’s optoelectronic systems since they can perform many functions ranging from linear applications such as linear amplification to ultrafast signal processing [1], [2]. Optical communication systems with a capacity of gigabits per second are commercially available and the capacity has been pushed above 10 Tb/s in research laboratories. As an optical switch or logic gate, semiconductor optical amplifier (SOA) has been utilized extensively in variety of configurations such as the symmetric Mach–Zehnder (SMZ) interferometer, the ultrafast nonlinear interferometer (UNI), and the terahertz optical asymmetric demultiplexer (TOAD) [3]–[5]. The speed of all-optical switches based on SOA is determined by the carrier dynamics of the SOA. Various schemes of all-optical logic gates like XOR operation using the nonlinearity of SOAs have been reported [6]–[9]. However these demonstrations are usually limited to 100 Gb/s by patterning effect due to the long carrier life time in the SOA active region. Thus, the predicted superiority of quantum dot SOAs because of their

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Manuscript received June 05, 2009; revised August 10, 2009. Current version published January 29, 2010. This work was supported in part by the ITRC under Grant 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 Technologies, University of Tabriz, Tabriz 51664, Iran (e-mail: [email protected]). H. B. A. Nejad and R. M. Qartavol are with the Photonic and Nanocrystal Research 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, University of Tabriz, Tabriz 51664, Iran. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JQE.2009.2033253

physical properties come into work. Quantum-dot (QD)-SOAs are supposed to have several advantages such as: negligible pattern effect due to compensation of the spectral holes by the carrier relaxation from excited state (ES), negligible cross talk between different wavelength channels due to spatial isolation of dots and prevention the carrier transfer among dots, and utilization of the cross gain modulation effect of two different wavelength channels in switching applications. The response time of gain saturation is 100 fs-1 ps which is enough for a gigabit to sub-terabit optical transmission system [2]. The main advantage of QD-SOAs, as compared to the bulk and quantum-well SOAs (QW-SOAs), is based on the existence of the gap between the QD levels and wetting layer (WL), and on the lower cross section of carrier-photon interaction which results, in particular, in shorter carrier relaxation times and lower gain saturation [10], [11]. The observed relaxation times in QD-SOAs, range from hundred of femtoseconds to tens of picoseconds which are significantly shorter than its value in QW-SOAs [12] and bulk SOAs [13]. However the main challenge in QD-based SOAs is still related to carrier relaxation from WL into ground or ES of QD because of the phonon bottleneck phenomenon peculiar to discrete energy levels [14], [15]. Considering the benefits of QD-based optical devices, all-optical logic gates based on QDs seem to be vital elements in ultrahigh speed networks as they can perform many critical functionalities. In [16] the capability of 250 Gb/s operation of QD-SOA-based logic gates has been predicted and in [1] it has been discussed and theoretically proved that high quality pattern-free operation of XOR logic gate and also an all-optical processor is limited to 200 Gb/s at 50 mA bias current which is limited by electron relaxation time from WL to ES. Thus, an upper limit has been concluded for SOA-based logic gates and systems. In this paper, we develop a theoretical approach for compensation of the carrier relaxation time into ES. In our model, we have considered two energy levels in both conduction and valence bands. It will be shown that ap(as depicted in Fig. 2) will plying a CP with energy of highly accelerate the recovery process of QD-SOA and will lead to high-bit-rate operation of QD-SOA-MZI structure in the presence of the CP. The arrival time of the CP will be discussed in the next sections and finally, the capability of 2.5 Tb/s XOR operation in a SOA-MZI based XOR logic gate will be investigated. The structure of this paper is as follows. In Section II the operation principles of QD-SOA-MZI XOR gate are presented and discussed. Section III is dedicated to operation theory of the QD-SOA and the rate equation model for the proposed idea. The achieved simulation results are presented in Section IV. Finally, Section V gives a brief summary of our work.

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

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

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

II. QD SOA-MZI-BASED XOR GATE The optical XOR gate in our study consists of a symmetrical MZI with one QD-SOA located in the same relative position of each arm as shown in Fig. 1 ([1] and [16]). For the Boolean , the input logic signals, A and B at waveoperation length , enter the arms of MZI via two multiplexers, respecenters to the structure tively. A probe signal at wavelength and splits into two equal parts in coupler C1. The wavelength and should be less than the homogeseparation between neous broadening of the single QD gain to ensure effective cross gain modulation. If the input signals A and B are identical, the QD-SOA-MZI is balanced and no signal emerges from XOR output. In contrast, if one of the input signals is zero while the other is one; a differential phase shift is introduced due to the cross-phase modulation (XPM) in the QD-SOA and the probe signal switches to the output consequently. The CPs at waveenter to each QD-SOA according the input signal length patterns (A, B) via the multiplexers. The time delay between control pulses and input signals, which affects the QD-SOA performance and hence the XOR gate operation, will be discussed in Section IV. The XOR output intensity can be expressed as [16]

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

(2) (3) where is time transformed by with the group of the light pulse, , and are velocity the photon densities of input signal, probe and CP, respecis modal gain, is the material absorption tively, coefficient, is modal absorption coefficient of CP and is the distance in longitudinal direction i.e., and stand 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 given by where is maximum modal gain [17] and is the electron (hole) occupation probability is the efin the ground state (GS). The term fective population inversion in GSs. The expressions of and are given in [18]. For simplicity, is assumed [19], [20]. Equations (3) may primitively be written as or in the other words,

(1) , are the integral of QD-SOA gains and where , are nonlinear phase shifts. and are the ratios of couplers C1 and C2 which are equally set to 0.5 for simplicity. III. THEORY OF OPERATION The output power, gain and phase characteristics of the QD-SOA can be obtained by solving the rate equations of the structure. To describe the control-pulse-assisted QD-SOA model, the two band model of Fig. 2 is considered where the transition of conduction band ground state (CBGS) to valence band ground state (VBGS) is assumed to be the main stimulated transition by input signal and the transition of valence band ES (VBES) to conduction band ES (CBES) is assumed to populate the CBES via absorption of CP.

and finally it can be described in the form presented in (3). The modal absorption coefficient of the CP may be where described as is the maximum modal absorption is the electron (hole) occupation probcoefficient and ability in the ES. QD-SOA dynamics relate to CP propagation term which describes the equation through and ES carrier dynamic, i.e., stand for optical gain and absorption (in the proposed model), respectively ( is presumed). Due to the larger effective mass of holes compared to electrons, and the resulting smaller level spacing, holes are expected to relax faster than electrons and therefore, electrons are assumed to limit the carrier dynamics [21]. Thus, the rate equations for the WL, ES and GS can be written as ([1], [19], and [24])

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(4)

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(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, is is the electron rethe spontaneous radiative lifetime in WL, is the electron escape laxation time from the ES to the GS, time from the GS to the ES, is the spontaneous radiative is the surface density of QDs where its lifetime in the QD. cm , is the electron density in typical value is 5 is the effective thickness of active layer, is the the WL, SOA material permittivity and is the velocity of light in free space. The last term in (5) and two last terms in (6) demonstrate the absorption of CP and stimulated emission in CBGS, respectively. For simplicity, we presume an ideal facet reflectivity and neglect the amplified spontaneous emission. The time-dependence of the integral QD-SOA gain and pulse phase-shift and can be expressed as , respectively, where is the linewidth enhancement factor. It has been discussed in several articles that linewidth enhancement factor (LEF) may vary in a large interval from the experimentally measured value of 0.1 up to giant values of 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 of InAs-InGaAs QD amplifiers. As a common model, carriers are captured into the CBES from the WL which serves as a carrier reservoir for the QD and after a stimulated depletion from CBGS, the CBES carriers are replaced by fast carrier transfer limits the gain dynamics as from the WL, in this manner it mentioned before. To investigate the effect of CP on gain characteristics of the QD-SOA, we have considered the energy separation between the CBES and CBGS and also VBES and to avoid the overlapping VBGS to be about problem at higher bit rates. The wavelengths of signal, probe m, m and CP are considered to be: m. For the following structure parameters and cm , cm , [19], [21], [24], [25]: cm , , ps, ns, ns, ns, ps, ps, m, m, m (the width of (the confinement factor), the state ocQD-SOA), cupation probabilities of electrons in the presence and without CP 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 the presence and without CP. The dashed lines correspond to input bit sequence at 1 Tb/s. The bias current is 50 mA, input signal, CP and probe signal powers are: 200 W, 250 W and 2 W, respectively.

Fig. 4. Electron state occupation probabilities of GS, f(t), and ES, h(t), in the presence and without CP. The dashed lines correspond to input bit sequence at 2 Tb/s. The bias current is 50 mA, input signal, CP and probe signal powers are: 200 W, 250 W and 2 W, respectively.

W and 2 Tb/s input bit sequences, 50 mA bias current, input signal, W CP and W probe signal are displayed in Figs. 3 and 4, respectively. At both bit rates of 1 Tb/s and 2 Tb/s the oscillation of ES and GS completely follows the input signal variation however at 2 Tb/s bit sequence, the population variation can’t reach to the final population value but still varies with relatively high ampli0.75 and ES 0.35 tude. The high population of GS is due to fast electron transition between ES and GS and absorption of the CP which compensates the relaxed population of ES to GS. The maximum value for state population probability of ES, h, versus increasing the CP power and in enough large values of CP power will tend to 0.5. This fact can be justified by considering the last term of (5). Whenever the h value tends to 0.5, the expression (1–2 h) tends to zero and in this case, the effect of last term in (5) (absorption of CP) on increasing the population of ES vanishes. Thus, temporal decrease of h motivates the term (1–2 h) to become positive and effective absorption of



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Fig. 5. Gain dynamics of QD-SOA following an input pulse with 1 ps FWHM and 200 W pulse power in presence and without considering the CP for two different input and CP temporal positions. The dotted line corresponds to the case that the CP isn’t applied.

Fig. 7. The effect of bias current on electron state occupation probabilities of GS, f(t), and ES, h(t), in the presence of the CP. The input bit sequence is 1 Tb/s. The bias current is 50 mA, input signal, CP and probe signal powers are: 200 W, 250 W and 2 W, respectively.

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

Fig. 8. XOR operation of QD-SOA-MZI structure for 1 Tb/s input bit sequence and 50 mA injected current. The input signal, CP and probe signal powers are: 200 W, 2 mW and 2 W, respectively.

CP will happened. It should be mentioned that the process of controlling the h value below 0.5 is related to XGM phenomenon. In fact, the influence of the CP on gain recovery process is similar to a fast current source which is applied when the gain dynamics reaches to its minimum value. In Fig. 5 two possible temporal positions of input signal and CP with 1 ps FWHM and also the related gain variations are illustrated. It can be concluded that applying the CP when the gain variation tends to zero (i.e., when the input pulse reaches to its maximum amplitude), will obtain the optimum gain recovery time. In this case, absorption of the CP will populate the CBES and hence the recovery process will accelerate. Otherwise, as it can be seen in Fig. 6, a variation in ES population appears which leads to longer recovery time (dashed curve in Fig. 5). However, the recovery process is still much faster compared to the case that no CP is applied in the same input power and injected current (dotted curve in Fig. 5).

The bias current in QD-SOAs is known to be an effective parameter to decrease the recovery time [16]. High injection current decreases the ES refilling time and therefore leads to faster recovery process. In Fig. 7 the influence of 20 mA and 50 mA bias currents on the state population dynamics is illustrated (in the presence of CP). Generally, the dynamic gain range is dependant to bias current. So, higher bias current is necessary in order to have acceptable gain and phase variations. The bold curve in Fig. 7 (20 mA bias current), describes the case that the CP rises the state occupation probability over the final steady state value and therefore increase the dynamic gain range. However when the input sequence remains zero for several bit periods, the dynamic range of the first coming pulses is limited due to low bias current. The results for the XOR logic operation with CW probe signal at 1, 2 and 2.5 Tb/s input sequences are displayed in Figs. 8–10,


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Fig. 9. XOR operation of QD-SOA-MZI structure for 2 Tb/s input bit sequence and 50 mA injected current. The input signal, CP and probe signal powers are: 200 W, 2 mW and 2 W, respectively.

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

Fig. 10. XOR operation of QD-SOA-MZI structure for 2.5 Tb/s input bit sequence and 50 mA injected current. The input signal, CP and probe signal powers are: 200 W, 2 mW and 2 W, respectively.

respectively. The results describe that the pattern effect is negligible at 1 Tb/s but in Figs. 9 and 10 it is seen that the form of XOR signal is distorted. pseudoIn order to obtain the eye diagram, we use a random RZ sequence input. The corresponding eye diagrams of the XOR gate output signal are shown in Fig. 11. A quantity known as Q is widely utilized to analyze and predict the signal quality for pseudo-random signals [26] and is defined as where and are the average power of output signals “1” and “0,” and are standard deviation of all “1” and “0,” respectively. As it described before, in a QD-SOA, bias current and electron relaxation time from WL to ES determine the SOA performance and hence high currents and faster relaxation times improve the Q factor. But beside the fact that too high current is prohibited for practical applications, the Q factor saturates above a specific bias current as reported in

[16]. Also the Q value is sensitive to the input pulsewidth and increasing the pulsewidth decreases the Q factor because of overlapping of two neighboring pulses. The Q factor is also dependant on parameter. Multilayer QD structures are considered as a technique to increase the modal gain due to increasing the parameter and therefore reducing the threshold current. As it can be seen in Fig. 11, because of ultrafast gain recovery in the presence of CP, at the bit rate of 1 Tb/s, the pattern effect is almost absent and the eye pattern is clearly open with Q of 28.4.Also for the bit rate of 2 Tb/s and 2.5 Tb/s the -factor drops to 8.8 and 4.9, respectively, and the eye is gradually closing due to pattern effect. Achieving to high speed signal processing, as it mentioned before, depends strongly on WL to ES and ES to GS relaxis not a limiting factor in conventional ation times. However, (according to the reported reQD-SOA’s operation 200 ([1], [19], [27]–[29]) which are 160 fs because sults for of longer WL to ES relaxation time. However, this parameter can be important in achieving high-speed operation in the prorelaxation posed approach as a higher limit. Increasing the , time and consequently decreases the quality factor of XOR output, as shown in Fig. 12. is the Boltzmann constant, T is the absolute temperature and is the energy separation between the ES and GS. V. CONCLUSION In this article, for the first time, we introduced a novel theoretical approach to compensate the slow carrier relaxation time from WL to ES (using XGM effect) which is the main limit to achieve to higher speeds in QD-SOAs. It concluded that the proposed approach accelerates the recovery process of the SOA. Applying a 2 mW CP to the two-energy-level-QD at certain



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

times enables the QD-SOA-MZI-based XOR gate to operate under 1, 2, and 2.5 Tb/s input bit sequences with Q factors of 28.4, 8.8, and 4.9, respectively. Also the eye patterns related to XOR operation presented. This capability of control-pulseassisted-QD-SOA is promising for ultra-high-speed all-optical logic gates, all-optical switching and processing. ACKNOWLEDGMENT The authors would also like to thank the editor of the journal and anonymous referees for the important comments that helped us to improve the content of this paper. REFERENCES [1] Y. Ben-Ezra, B. I. Lembrikov, and M. Haridim, “Ultrafast all-optical processor based on quantum-dot semiconductor optical amplifiers,” IEEE J. Quantum Electron., vol. 45, no. 1, pp. 34–41, Jan. 2009. [2] M. Sugawara, T. Akiyama, N. Hatori, Y. Nakata, H. Ebe, and H. Ishikava, “Quantum-dot semiconductor optical amplifiers for high-bit-rate signal processing up to 160 Gbs and a new scheme of 3R regenerators,” Meas. Sci. Technol., vol. 13, pp. 1683–1691, 2002. [3] J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A terahertz optical asymmetric demultiplexer (TOAD),” IEEE Photon. Technol. Lett., vol. 5, no. 6, pp. 787–790, Jul. 1993. [4] E. Jahn, N. Agrawal, M. Arbert, H. J. Ehrke, D. Franke, R. Ludwig, W. Pieper, H. G. Weber, and C. M. Weinert, “40 Gbit/s all-optical demultiplexing using a monolithically integrated Mach–Zehnder interferometer with semiconductor laser amplifier,” Electron. Lett., vol. 31, no. 21, pp. 1857–1858, Oct. 1995. [5] M. Eiselt, W. Pieper, and H. G. Weber, “SLALOM: Semiconductor laser amplifier in a loop mirror,” J. Lightw. Technol., vol. 13, no. 10, pp. 2099–2112, Oct. 1995. [6] T. Fjelde, D. Wolfson, A. Kloch, B. Dagens, A. Coquelin, I. Guillemot, F. Gaborit, F. Poingt, and M. Renaud, “Demonstration of 20 Gbit/s alloptical logic XOR in integrated SOA-based interferometric wavelength converter,” Electron. Lett., vol. 36, no. 22, pp. 1863–1864, Oct. 2000. [7] H. K. Jae, M. J. Young, T. B. Young, L. Seok, and H. W. Deok, “All-optical XOR gate using semiconductor optical amplifiers without additional input beam,” IEEE Photon. Technol. Lett., vol. 14, no. 10, pp. 1436–1438, Oct. 2002. [8] T. Houbavlis, K. Zoiros, K. Vlachos, T. Papakyriakopoulos, H. Avramopoulos, F. Girardin, G. Guekos, R. Dall’Ara, S. Hansmann, and H. Burkhard, “All-optical XOR in a semiconductor optical amplifier-assisted fiberSagnac gate,” IEEE Photon. Technol. Lett., vol. 11, no. 3, pp. 334–336, Mar. 1999.

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Ali Rostami received the Ph.D. degrees in photonic /electronic engineering from University of Amirkabir, Tehran, Iran, in 1998. He was in sabbatical leave in the University of Toronto, Toronto, ON, Canada, (2004–2005) at the Photonic Group. He is currently full Professor of Electronic Engineering and Photonics Science at the University of Tabriz, Tabriz, Iran. His teaching and research interests include optical integrated circuits and optoelectronic devices. He is a member of the Optical Society of America. He is the author and coauthor of more than 220 scientific international journal and conference papers and 4 text books. Also, he collaborates with some international journals as reviewer boards (more than 10 journals) and works as editorial committee of two Iranian journals. Dr. Rostami has served on several other committees and panels in government, industry, and technical conferences.

Hamed Baghban Asghari Nejad received the B.S. and M.S. degrees in electronics engineering from Tabriz University, Tabriz, Iran, in 2005 and 2007, respectively, where he is pursuing the Ph.D. degree. His research interests are in the area of semiconductor optoelectronic devices.

Reza Maram Qartavol received the B.S. degree in electronics engineering from University of Kurdestan, Iran, in 2007. He is currently working toward the M.S. degree in electronics engineering at the Photonics and Nanocrystals Research Laboratory (PNRL), Faculty of Electrical and Computer Engineering, University of Tabriz, Iran, where he is researching quantum-dot semiconductor optical amplifiers.

Hassan Rasooli Saghai received the B.Sc. degree in electronics engineering from Islamic Azad University, Tabriz, Iran, the M.Sc. degree in electronics engineering from Islamic Azad University, South Tehran, Iran, and the Ph.D. degree in electronics engineering from Islamic Azad University Science and Research, Iran, in 1996, 2000, and 2008, respectively. Currently, he is a Postdoctoral Fellow in the School of Engineering Emerging Technologies, university of Tabriz, 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.
