Mutual synchronization between quantum-dot passively mode-locked laser frequency combs: Theoretical approach

Abstract

A comprehensive theoretical framework is established for describing repetition-rate synchronization and partial optical coherence in two bidirectionally coupled quantum-dot passively mode-locked lasers (QD-PMLLs). Each laser is modeled as a two-section monolithic device composed of a forward-biased gain section and a reverse-biased saturable absorber. The coupled delay-rate equations incorporate the slowly varying complex optical fields, modal gain dynamics, absorber loss, photon decay, linewidth-enhancement factors, delayed optical coupling, coupling phase, and spontaneous-emission noise. In the weak mutual-injection limit, the full model is systematically reduced to an effective timing-phase description, yielding the locking relation , and hence the locking condition . Representative simulations establish that two initially detuned 10 GHz pulse trains are pulled into a single shared repetition frequency, with the locked frequency showing pronounced and controllable delay-dependent tunability. The synchronized state exhibits a marked reduction in root-mean-square timing jitter, whereas finite mutual optical coherence appears only when the optical carrier mismatch simultaneously lies within the coherent injection-locking bandwidth. Agreement with recent synchronization experiments on InAs/InGaAs QD-PMLL combs demonstrates that the model not only reproduces the central experimental trends but also clarifies the underlying hierarchy: repetition-rate locking is robust and readily achieved, delay tuning provides an effective control parameter, timing noise is strongly suppressed in the locked regime, and optical phase coherence is an additional conditional constraint rather than an automatic consequence of rate synchronization.