Chaos and regularities in cavity assisted two-channel nonlinear coupler

Abstract

This paper presents a study of the dynamical behavior in a cavity-assisted two-channel Kerr nonlinear directional coupler. Applying a deterministic periodic laser pump to a two-channel coupled system led to a range of dynamic behaviors, encompassing periodicity, quasiperiodicity, chaoticity and hyperchaoticity. This is confirmed by the exploration of the Lyapunov exponents, Poincaré sections and bifurcation diagrams for resonance and low cavity detuning. For low cavity detuning, chaos arises when the laser pump’s amplitude is large. This is due to higher interactions between photons and the cavity, resulting in more photons inside and higher nonlinearity. On the other hand, the reduced interactions in high cavity detuning displayed regular behavior which is explained qualitatively.