Nonlinear Dynamics in Semiconductor Lasers 2023 - Abstract
Seidel, Thomas
Passively mode-locked lasers can generate multiple pulses per round-trip. In this so-called harmonically mode-locked (HML) regime the pulses can interact with each other via the carriers (in particular, gain repulsion), overlapping tails and time-delayed feedback stemming from e.g. unwanted reflections of lenses. The latter results in small copies of the main pulses in the cavity which amplitude and position are controlled by the feedback rate η and the feedback time τƒ, respectively. The different interactions influence the two degrees of freedom of each pulse: phase and position. From symmetry considerations, we derive fixed points of the system corresponding to equidistant pulses with a phase difference of 2πρ/n, ρ=1,..,n. Starting from the Haus equation we derive an effective equation of motion (EOM) for the positions and phases of the n pulses in an HMLn; configuration in form of 2n ordinary differential equations. We can separate the phase independent force acting via the carriers (as they are only intensity dependent) from the phase dependent force stemming from tail overlap and time-delayed feedback. Comparisons between direct numerical simulations of the full Haus model with the simplified EOM exhibit excellent quantitative agreement. For the case of two coupled pulses we perform a detailed bifurcation analysis of the EOM as a function of the feedback parameters τ_ƒ (feedback position), η (feedback rate) and Ω (feedback phase). The analysis reveals multiple interesting regimes such as stable non-equidistant configurations, multistability between non-equidistant solutions as well as different kinds of periodic orbits. Again, we compare the results with the full Haus model and obtain excellent agreement. We use the knowledge obtained from the two-pulse-case to find corresponding regimes for higher pulse numbers. The resulting higher dimensionality of the phase space allows us to find additional regimes such as aperiodic solutions.