Finite-Time Dynamical Complexity Mapping of Frequency-Comb-Injected Semiconductor Lasers under Different Comb-Spacing Patterns

This work investigates how frequency-comb spacing patterns influence the nonlinear dynamics of optically injected semiconductor lasers through numerical simulation. Equal, unequal, and logarithmic comb-spacing configurations are compared over a detuning–injection parameter grid using bifurcation diagrams, time-domain analysis, and a finite-time reconstructed divergence diagnostic, denoted Λts, derived from the simulated field-amplitude sequence. The results show that irregular comb spacing modifies the distribution of high-complexity response regimes. Unequal spacing reduces the classified high-complexity fraction from 62.57% for the equal-spacing baseline to 57.29%, corresponding to an absolute reduction of 5.28 percentage points and a relative reduction of 8.44% under the adopted numerical conditions. It also produces a smoother diagnostic landscape, indicating fewer strongly irregular post-transient responses across the investigated parameter grid. Because Λ ts is derived from scalar time-series reconstruction rather than direct variational-equation integration, we use it as an auxiliary comparative diagnostic, not as a strict calculation of the maximum Lyapunov exponent λmax or as sole proof of deterministic chaos. These findings suggest that comb-spacing irregularity influences nonlinear response regimes; however, full Lyapunov-spectrum analysis is necessary for definitive chaos classification.