Time crystals transforming frequency combs in tunable photonic oscillators

The response of a tunable photonic oscillator, consisting of an optically injected semiconductor laser, under an injected frequency comb is considered with the utilization of the concept of the time crystal that has been widely used for the study of driven nonlinear oscillators in the context of mathematical biology. The dynamics of the original system reduce to a radically simple one-dimensional circle map with properties and bifurcations determined by the specific features of the time crystal fully describing the phase response of the limit cycle oscillation. The circle map is shown to accurately model the dynamics of the original nonlinear system of ordinary differential equations and capable for providing conditions for resonant synchronization resulting in output frequency combs with tunable shape characteristics. Such theoretical developments can have potential for significant photonic signal-processing applications.