Global bifurcations and homoclinic chaos in nonlinear panel optomechanical resonators under combined thermal and radiation stresses

Abstract

In this paper, we investigate the nonlinear interaction and time-evolution of confined optical, thermal and mechanical modes in a three-dimensional optomechanical resonator. We model a high-finesse cavity with a thin thermo-elastic panel placed at the center of two highly reflective mirrors that is subjected to an incoming continuous-wave electromagnetic field. The latter is constructed by constraining the light-structure interaction to a first-order scattering phenomenon in the classical interpretation modeled as a spatio-temporal perturbation around a time-harmonic field. We employ a Galerkin-based separation of variables decomposition on the resultant fields and replace them with their nonlinear modal counterparts. The resulting dynamical system is thus governed by the combined effects of thermal and radiation stresses which yield a complex spatially dependent self-excited bifurcation structure where Hopf bifurcations give rise to periodic limit-cycle solutions. In regions where coexisting solutions are found, homoclinic connections ensue codimension-two Bogdanov–Takens and Double-Hopf bifurcations and that for a range of control parameters a global homoclinic Shilnikov bifurcation culminates with a distinct period-doubling route to chaos. We note that the current formulation demonstrates the essential contribution of coupled thermal and radiation stresses to the bifurcation structure of nonlinear light-structure interaction systems and may shed light to modal energy transfer mechanisms and scattering phenomena.