Dynamic properties of two-state lasing quantum dot laser for external optical feedback resistant applications Jianan Duan ˚§ , Yueguang Zhou : , Heming Huang ˚ , Bozhang Dong ˚ , Cheng Wang : and Fr´ ed´ eric Grillot ˚; ˚ LTCI, T´ el´ ecom Paris, Institut Polytechnique de Paris, 91120 Palaiseau, France : School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China ; Center for High Technology Materials, The University of New-Mexico, Albuquerque, NM 87106, USA § jianan.duan@telecom-paris.fr Abstract—This work investigates the dynamics of two-state quantum dot lasers through semi-analytically solving a set of rate equations. Simulations reveal that the occurrence of excited state lasing reduces the damping factor and relaxation oscillation frequency of the laser while increases the linewidth enhancement factor associated to the ground state transition. These results are in good agreement with the experimental observation showing that the quantum dot laser becomes more sensitive to external optical feedback at excited state lasing threshold. This work brings novel insights in the understanding of quantum dot laser physics that are useful for designing feedback resistant lasers in photonic integrated technologies. Index Terms—Semiconductor lasers, quantum dots, linewidth enhancement factor, external optical feedback. I. I NTRODUCTION Silicon photonics has been introduced to achieve high performance and low cost photonic integrated circuits (PICs) [1]. However, the challenge in PICs is the parasitic reflections from on-chip components that feed light back into the laser source and cause strong laser destabilization. As on-chip optical isolators are complicated to fabricate, the development of highly optical feedback resistant laser sources is important. Quantum dot (QD) lasers directly grown on silicon have been shown much higher tolerance to external optical feedback than quantum well lasers, mostly attributing to the small linewidth enhancement factor (α H -factor) and the high damping factor [2]. However, owing to the slow carrier scattering rate and the unclamped gain dynamics, QD lasers can simultaneously emit on both ground state (GS) and excited state (ES) transitions. The critical feedback level (r crit ) is an important criterion, corresponding to the maximum feedback ratio that can be tolerated into a communication system for maintaining an error-free operation. Above r crit , the laser enters the coherence collapse regime which is typically determined at the point where the laser linewidth is significantly broadened. We exper- imentally found that the r crit of the QD laser strongly depends on the occurrence of the ES, demonstrating that the reflection tolerance is greatly degraded at ES lasing threshold of I ES th [3]. This work is therefore motivated by theoretically explaining this phenomenon. Simulations are in good agreement with the experiments, showing that the damping factor and relaxation oscillation frequency (ROF) significantly decrease while the α H substantially increases at the ES lasing threshold, which finally affects the laser’s resistance against external optical feedback. Fig. 1. (a) Schematic representation of the electronic structure and carrier dynamics into the quantum dot. (b) Rate equation model. II. RATE EQUATION MODEL OF QUANTUM DOT LASER Fig. 1(a) illustrates the schematic of the carrier dynamics of the QD laser, where both electrons and holes are treated as neutral excitons. The QD model consists of a two dimension carrier reservoir RS, a four-fold degenerate ES and a two- fold degenerate GS. The dynamics among the three level is characterised by capture time τ RS ES , relaxation time τ ES GS and escape time τ GS ES and τ ES RS . In addition, carriers in RS, ES and GS are also recombined spontaneously within spontaneous time τ spon RS,ES,GS respectively. The stimulated emissions are considered to occur in both ES and GS. The dynamics of carrier number N RS,ES,GS , the photon number S ES,GS , and the phase of the light φ ES,GS are described by a coupled rate equation model as shown in Fig. 1(b) [4]. Where I is the injected current, q is the elementary charge, ρ RS,ES,GS are the corresponding carrier occupation probabilities in RS, ES, and GS, Γ p is the optical confinement factor, τ p is the photon lifetime, β sp is the spontaneous emission factor, and v g is the group velocity of the light. α ES,GS are the intrinsic α H -factor of ES and GS, k RS,ES are the contributions of carrier variation in RS and ES to the α H of GS. g RS,ES,GS represent material gain of each state. F RS,ES,GS are carrier noise sources in RS, ES and GS, respectively. F S ES , F S GS , F φ ES and F φ GS are the corresponding photon and phase noise sources in ES and GS. The damping factor and ROF are extracted from the laser system modulation transfer function, while the α H is obtained from the frequency noise spectrum [4]. III. RESULTS AND DISCUSSION Fig.2 shows the bias current dependence of the damping and relaxation oscillation dynamics of the QD laser. At about 0.8ˆI ES th , the laser is overdamped with a damping factor as NUSOD 2020 79 978-1-7281-6086-3/20/$31.00 ©2020 IEEE Authorized licensed use limited to: Telecom ParisTech. Downloaded on February 17,2021 at 10:07:36 UTC from IEEE Xplore. Restrictions apply.