Classical Non-Linearity Dynamics in a model with a different mechanism of optomechanical interaction

Most studies on cavity optomechanics focusing on energy exchange between optical and mechanical modes assume that the interaction is mediated by either the dependence of cavity frequency (dispersion coupling) or cavity decay rate (dissipation coupling) on mechanical oscillations. We introduce and investigate a system with a different mechanism of optomechanical interaction realized in systems with degenerate optical modes. Interaction with a moving mechanical oscillator in such systems result in coupling between degenerate optical modes in addition to changing their frequencies. We study the classical dynamics of a model consisting of two degenerate optical modes and a mechanical oscillator with two degrees of freedom. In the absence of a pump, the system exhibits a highly non-trivial nonlinear dynamic characterized by a bifurcation point where the linear dynamics loses its stability. Numerical simulations showed that in the stable regime, the dynamics can be described as nonlinear modulation of the amplitude of the linear oscillations. We derived an analytical expression for the modulation frequency, which turns out to be proportional to the amplitude of the initial mechanical displacement, determining the degree of nonlinearity in the system. Numerical studies of the system in the unstable regime showed a significant increase in the amplitude of mechanical oscillations responsible for the frequency pulling of optical modes. The study of this regime is ongoing.