No abstract

The concept of the Isochrons is introduced for the study of the phase response of an optically injected semiconductor laser. The global structure of the Isochrons and the corresponding phase response curves are numerically computed and systematically dissected in terms of their characteristics. Their paramount role in the synchronization properties under an external periodic modulation of the injection beam is shown along with their ability for providing conditions for stable phase locking and highly customizable periodic outputs with discrete equidistant spectra in the form of frequency combs. Potential applications related to remote clock synchronization for communications requiring coherent receivers as well as geolocation applications based on precise phase-shift measurements, are discussed.

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.

The Isochrons and Phase Response Curves of an Optically Injected Laser are presented, along with their role in the synchronization dynamics under a periodic electrooptic modulation, toward providing conditions for stable phase-locking and periodic outputs in the form of Frequency Combs.