2778 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 23, NO. 9, SEPTEMBER 2005 Analytical Characterization of SOA-Based Optical Pulse Delay Discriminator Malin Premaratne, Senior Member, IEEE, and Arthur James Lowery, Senior Member, IEEE Abstract—Semiconductor optical amplifier (SOA)-based optical timing extraction and clock-recovery schemes offer compact size, low operating power, and added possibility for integration into an all-optical circuitry. In this paper, we analyze a device that could measure the relative delay between counterpropagating pulses incident on an SOA. Unlike previous designs based on differential photodiodes, our optical pulse delay discriminator (OPDD) uses the voltage difference between two contacts on the SOA. We therefore eliminate the two photodiodes and two optical couplers, making integration far easier. After giving a qualitative description of the operation of the proposed design, we carry out a comprehensive analytical analysis of the operation of the device performance. At each stage, we demonstrate the accuracy of the derived approximate formulas. An analytical expression for the transient response of OPDD shows it to be exponential with a time constant set by the carrier-recovery lifetime. We show that it is possible to reliably measure the incident delay between counterpropagating, periodic pulse trains by measuring the mean value (or low-pass-filtered value) of the induced voltage difference. Our analysis shows the OPDD has excellent linearity. Index Terms—Clock recovery, integrated optoelectronic cir- cuits, photonic circuits, semiconductor optical amplifiers (SOAs). I. I NTRODUCTION T HE comparison of phase and timing of modulated optical waveforms is critical to the design of all-optical clocks using phase-locked loops [1]. Optical timing extraction and clock recovery [2]–[5] play a significant role in applications such as demultiplexing [6] and 3R (reamplification, reshaping, and retiming) regeneration [7], [8]. Semiconductor optical am- plifier (SOA)-based schemes ([2], [4], [7]) have attracted much interest because of their compact size, low operating power, and added possibility for integration into an all-optical circuitry. The operation principles rely on nonlinear gain saturation and cross-gain modulation. [7], [9], [10]. Short picosecond pulse propagation in SOAs has been widely studied for applications in optical communications systems [9], [10]. Even though the main motive for such studies was to investigate the amplification properties of SOAs, it is clear that SOAs play a major role in optical signal processing [11], [12]. The effectiveness of SOAs in all-optical integrated circuitry results from their high-gain coefficients and low saturation power [9], [10]. In 2002, Awad et al. [7] demonstrated that by simply com- paring the time-averaged output powers at the ends of an SOA, Manuscript received March 1, 2005; revised April 6, 2005. The authors are with the Advanced Computing and Simulation Laboratory (AXL), Department of Electrical and Computer Systems Engineering, Monash University, Clayton, Victoria 3800, Australia. (e-mail: malin@eng.monash. edu.au; arthur.lowery@eng.monash.edu.au). Digital Object Identifier 10.1109/JLT.2005.853142 it is possible to measure the relative delay between pulses. Awad et al. [7] used couplers and photodiodes to detect the powers of the counterpropagating waves exiting the SOA as shown in Fig. 1. The photocurrents are fed into a low-speed differential amplifier to obtain a signal proportional to the relative timing of the pulses. In this paper, we use the detection properties of an SOA’s contact voltage [15], [16] to measure the relative delay between two pulse trains. This again relies on cross-gain modulation, but in our device, the longitudinal dependence of the gain also becomes important. The difference in the contact voltages at the ends of the SOA indicates which pulse traverses the SOA first. This is because the first pulse will receive the most gain, substantially reducing the carrier density by gain saturation at the end from which it exits. The second pulse will receive less gain, and so will reduce the carrier density at the end from which it exits. The contact voltages are dependent on the local carrier density, and therefore indicate which pulse was first. Furthermore, because the gain recovers between the pulses, closely spaced pulses will cause a greater voltage difference. This scheme was proposed and tested numerically in [4]; this paper develops expressions to confirm the simulations. These expressions give fresh insight into the operation of the optical pulse delay discriminator (OPDD). In Section II, we derive approximate expressions for the longitudinal carrier-density profile evolution and the related optical-gain response for three different cases of interest: Section II-A derives the response to a single pulse; Section II-B covers two identical counterprop- agating pulses; and Section II-C extends the derivation to two counterpropagating periodic pulse trains. In each of these cases, we demonstrate the accuracy and validity of the derivations using numerical calculations. In Section III, we introduce quan- titative expressions to compare the OPDD scheme and Awad’s scheme. In Section III-A, we derive explicit expressions for the transient response and show that it is exponential with a time constant given by the carrier-recovery lifetime of SOAs. In Section III-B, we demonstrate the linearity of the OPDD and derive an approximate analytical expression to characterize the linear region. Based on these observations, we give guidelines for designing OPDDs in Section IV. We conclude this paper in Section V. II. APPROXIMATE ANALYTICAL CHARACTERIZATION OF RESPONSE OF SOA TO SHORT PULSES In this section, we develop approximate analytical results to characterize the response of SOA when it is fed by a single short optical pulse, two identical counterpropagating pulses, and two 0733-8724/$20.00 © 2005 IEEE