IEEE JOURNAL zyxwvutsrqponmlkjihgf OF QUANTUM ELECTRONICS, VOL. 31, NO. 3, MARCH 1995 439 Pulse Buildup Dynamics of an Actively Mode-Locked Laser Diode Array in the External Cavity Chi-Luen Wang, Jahn-Chung Kuo, C.-S. Chang, and Ci-Ling Pan Abstract-Dynamic pulse evolution characteristics of an actively mode-locked laser diode array in the external cavity have been investigated. Numerical calculations based on modified traveling-wave rate equations reproduce experimentally observed pulse and spectral width evolution and show that the buildup time is about 45 round-trips. We have also performed a theoretical analysis to understand which of the laser operating parameters would affect the buildup dynamics. It is shown that either higher dc bias current or larger radiative recombination coefficient (which is inversely proportional to the excited-state lifetime) will render the laser exhibiting shorter steady-state pulse width and faster evolution to the steady state. Other parameters affecting the buildup, but to a lesser extent, include the radio-frequency (RF) modulation current, spontaneous emission coefficient, and gain coefficient. The power reflectivities of the output mirror and the antireflection coated diode facet, on the other hand, have little effect on the pulse width and buildup time for zyxwvutsrqponm single pulse generation. I. INTRODUCTION ECENTLY, SEVERAL GROUPS have investigated the R buildup dynamics of mode-locked laser systems as the laser output evolved from noise bursts to steady state pi- cosecond and femtosecond pulses [ll-[6]. It is hoped that, through these studies, one can elucidate the pertinent pulse shaping mechanisms. The buildup times for different types of mode-locked lasers are found to be quite different: The colliding-pulse mode- locked (CPM) ring dye lasers evolves to the steady state in about 1300 to 1500 round-trips [l], [2]. The buildup time for a synchronously pumped zyxwvutsrq R6G dye laser is ~800 round-trips [3]. For additive-pulse mode-locked (APM) or self-starting passively mode- locked Tisapphire lasers with intra-cavity saturable absorber, several tens of thousand round-trips are required [4]-[6]. The dynamics of AM mode-locked Ti:A1203 laser was analyzed theoretically by Reddy and Tatum [7]. Recently Ruan et al. [8] studied the pulse evolution in cw femtosecond Cr3+:LiSrA1Ftj lasers mode-locked with MQW saturable absorbers. They found that the pulse duration shortened rapidly within the first millisecond as the mode-locking mechanism developed the pulse train. Once mode-locked pulses were formed and the absorption Manuscript received October 21, 1992; revised October 7, 1994. This work was supported in part by the National Science Council of the Republic of China under Grants NSCIO-0 417-Em-05, -17 and NSC81-0 417-E049-629, The authors are with the Institute of Electro-optical Engineering, National IEEE zyxwvutsrqpon Log Number 9408596. -630. Chiao Tung University, Hsinchu, Taiwan 300, R.O.C. was saturated, a further period of =SO0 ms is required for the laser to settle at its steady state wavelength although the pulse duration is already determined. A number of authors have also investigated the pulse buildup dynamics of semiconductor lasers. Lau and co-workers [9] showed that the time constant for buildup in passively mode-locked monolithic quantum-well semiconductor lasers is on the order of 3.5 ns, or ~175 round-trips. This is significantly longer than the tum- on and turn-off time for comparable cw lasers. They also predict that, to decrease the pulse buildup time, the photon lifetime should be decreased and the gain, modulation of the gain and the ratio of the mode-locking frequency to the gain bandwidth should be increased. Experimentally, AuYeung et al. [lo] was the first to show that the buildup time for an actively mode-locked double-heterostructure GaAlAs laser was ~ 3 0 round-trips. The accuracy of their experimental results, however, was limited by the bandwidth of the detection system. The evolution process could not be resolved. In a numerical study, Demokan zyx [ 11 ] estimated that the buildup time of an actively mode-locked AlGaAs-GaAs laser with one perfectly antireflection (ARj- coated facet would be ~150 round-trips. Later, Blixt and Krotkus [ 121 showed both theoretically and experimentally that an actively mode-locked InGaAsP buried- heterostructure laser diode in the extemal cavity reached its steady state in 40 to 50 round-trips. On the other hand, numerical calculations of Bowers et al. [ 131 yielded a relatively slow buildup time of 62 ns, or nearly a lo00 roundtrips for their short-extemal cavity actively mode-locked InGaAsP laser modulated at 16 GHz. Broad area or phase-locked array of laser diodes generating impressively high output power are now commercially avail- able. Active mode-locking of a laser diode array with linear [ 141 or ring [ 151 external cavities have also been reported. The pulses generated were 61 and 26-ps wide with peak powers of 1.1 W and 30 mW, respectively. Recently, we have presented detailed experimental data on both the temporal and spectral evolution of picosecond pulses generated by an actively mode- locked laser diode array in an extemal cavity [ 161. During the first 40 ns after the laser onset, the pulse width shortened quickly and approached the steady state 45 ps pulse width in approximately 100 ns, or 45 roundtrips. Concurrently the number of clusters of the longitudinal-mode spectrum reduced and approached a steady-state spectral distribution with the pulse energy mainly distributed among a few clusters near the line center. In this paper, a simple model based on modified 0018-9197/95$04.00 zyxwvutsrq 0 1995 IEEE