Lagrangian approach for analysis of radiation pressure induced parametric instability in micro-resonators

We introduce a new scheme for determining radiation pressure coupling to microresonator devices. It is shown that for the input pump powers there exists a threshold value for instability behavior. Radiation pressure can couple mechanical modes of a cavity to it's optical modes, leading to parametric oscillation instability. Here we present an approximate analysis of such nonlinear effect with Hamilton's least action principle. Our Lagrangian includes no interaction term, but interaction between optical and mechanical modes has been taken into account through integration limit.