Dynamics and instabilities of nonlinear Fano resonances in photonic crystals

We study the dynamics of the nonlinear Fano resonance in the 2D photonic-crystal waveguides with a side-coupled cavity. The photonic crystal is created by a lattice of dielectric rods in air. The cavity is assumed to be nonlinear, which can be achieved by replacing a normal dielectric rod by a nonlinear rod. The stationary regime of the light transmission through such a structure can be studied by using the Green´s function approach. In particular, such a system shows a possibility of the nonlinear Fano resonance and bistable transmission. In order to study the full dynamical problem, here we generalize our approach by utilizing the time-dependent Green´s function formalism. By using the proper boundary conditions, we are able to obtain fast and accurate results which then verified by the numerical FDTD simulations. We perform two types of simulations for the Gaussian pulses and continuous waves.