Modulation properties and nonlinear dynamics induced by optical feedback in distributed-feedback quantum cascade lasers

This study explores the dynamic behavior of distributed-feedback quantum cascade lasers (QCLs) through numerical simulations based on the Effective Semiconductor Maxwell-Bloch Equations (ESMBEs). First, we analyze the intrinsic intensity modulation response of QCLs, demonstrating that the modulation bandwidth is fundamentally constrained by the population grating induced by the standing-wave pattern in the QCL cavity, namely, spatial hole burning (SHB). We then extend the ESMBEs framework to incorporate the effects of an external target, enabling the investigation of multimode nonlinear dynamics in QCLs subject to external optical feedback (EOF). Our findings identify fast SHB and a non-zero linewidth enhancement factor as key physical mechanisms governing the emergence of complex multimode behavior and the eventual transition to chaos. Notably, we reveal that QCL destabilization under EOF arises from interactions between internal longitudinal modes and external cavity modes, rather than from undamped relaxation oscillations, as typically observed in conventional semiconductor lasers. Furthermore, we examine the evolution of the system's dynamics as a function of feedback strength, demonstrating the onset of photonic chaos at feedback levels two orders of magnitude higher than those required in traditional diode lasers, in agreement with experimental observations existing in the literature. Finally, we assess the correlation dimension of the attractor of the resulting nonlinear dynamics. Beyond fundamental insight, this work introduces the use of ESMBEs as a predictive framework for experimental interpretation and device design, enabling the engineering of QCLs for mid- and long-infrared free-space applications, including high-speed transmission, chaos-based LiDAR, and random number generation. (c) 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) license (https://creativecommons.org/licenses/by-nc-nd/4.0/).