Stability and interactions of transverse field structures in optical parametric oscillators near resonance detuning

Abstract

A Swift–Hohenberg-type equation is considered in two and three dimensions for an optical parametric oscillator near its resonance detuning limit. The stability and behaviour of solutions to this equation are characterized utilizing numerical simulations and linear stability analysis. The stability of one-dimensional solutions extended to higher dimensions is considered as well as localized structures (LS) and fronts. The interactions of the localized structures are responsible for creating a host of stable, self-organizing and nontrivial spatial patterns. One manifestation of the LS leads to the formation of dipoles, dipoles rings and dipole lines. Stable hexagonal patterns are also generated. Extensions to the three-dimensional setting give analogous results to the two-dimensional behaviour. The stable LS are promising candidates as optical bits for photonic applications.