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.

Spatial control of localized oscillations in arrays of coupled laser dimers.

Arrays of coupled semiconductor lasers are systems possessing radically complex dynamics that makes them useful for numerous applications in beam forming and beam shaping. In this work, we investigate the spatial controllability of oscillation amplitudes in an array of coupled photonic dimers, each consisting of two semiconductor lasers driven by differential pumping rates. We consider parameter values for which each dimer's stable phase-locked state has become unstable through a Hopf bifurcation and we show that, by assigning appropriate pumping rate values to each dimer, high-amplitude oscillations coexist with negligibly low-amplitude oscillations.

Solitary wave formation under the interplay between spatial inhomogeneity and nonlocality.

The presence of spatial inhomogeneity in a nonlinear medium restricts the formation of solitary waves (SW) on a discrete set of positions, whereas a nonlocal nonlinearity tends to smooth the medium response by averaging over neighboring points. The interplay of these antagonistic effects is studied in terms of SW formation and propagation. Formation dynamics is analyzed under a phase-space approach and analytical conditions for the existence of either discrete families of bright SW or continuous families of kink SW are obtained in terms of Melinikov's method.

The Asymmetric Active Coupler: Stable Nonlinear Supermodes and Directed Transport.

We consider the asymmetric active coupler (AAC) consisting of two coupled dissimilar waveguides with gain and loss. We show that under generic conditions, not restricted by parity-time symmetry, there exist finite-power, constant-intensity nonlinear supermodes (NS), resulting from the balance between gain, loss, nonlinearity, coupling and dissimilarity. The system is shown to possess non-reciprocal dynamics enabling directed power transport functionality.

Stability and dynamics of nonautonomous systems with pulsed nonlinearity.

We study the dynamics of a class of nonautonomous systems with pulsed nonlinearity that consist of a periodic sequence of linear and nonlinear autonomous systems, each one acting alone in a different time or space interval. We focus on the investigation of control capabilities of such systems in terms of altering their fundamental dynamical properties by appropriate parameter selections. For the case of single oscillators, the stability of the zero solution as well as the phase space topology is shown to drastically depend on parameters such as the frequency of the linear oscillations and the durations of the linear and nonlinear intervals.