Noise-Induced Direction Switching in Quantum Cascade Ring Lasers: A Stochastic Analysis of the Lang–Kobayashi Model

Abstract

Directional switching between clockwise (CW) and counterclockwise (CCW) modes in ring quantum cascade lasers (QCLs) governs stability, mode control, and sensing applications, yet its dependence on stochastic noise amplitude (σ) remains insufficiently understood. In this work, we investigate noise-induced switching using a Lang–Kobayashi–type model with delay coupling and complex Gaussian noise, extracting switching rates from time-domain simulations over σ = 5 × 10⁻⁵ to 30 (1 / √photon lifetimes) via a dwell-time–based detection method. We find that stochastic noise alone is sufficient to drive switching, with no transitions observed in the zero-noise limit. The switching rate exhibits rapid growth at low σ, followed by saturation at approximately 1.05 (1 / photon lifetime) for σ ≥ 3 (1 / √photon lifetimes), indicating a transition from a noise-limited to a dynamics-limited regime where switching is constrained by intrinsic system timescales. Model comparison using AIC and R² demonstrates that a Hill-type model (R² = 0.963) provides the most accurate and physically interpretable description, outperforming power-law, exponential (Kramers-type), and piecewise fits, while achieving predictive performance comparable to machine learning models (KNN and Random Forest) under Leave-One-Out Cross-Validation. These results establish directional switching in ring QCLs as a saturable, noise-driven process and provide a compact framework for predicting mode stability in noisy laser systems.