Model of thermo-optic nonlinear dynamics of photonic crystal cavities

The wavelength scale confinement of light offered by photonic crystal (PhC) cavities is one of the fundamental features on which many important on-chip photonic components are based, opening silicon photonics to a wide range of applications from telecommunications to sensing. This trapping of light in a small space also greatly enhances optical nonlinearities and many potential applications build on these enhanced light-matter interactions. In order to use PhCs effectively for this purpose it is necessary to fully understand the nonlinear dynamics underlying PhC resonators. In this work, we derive a first principles thermal model outlining the nonlinear dynamics of optically pumped silicon two-dimensional (2D) PhC cavities by calculating the temperature distribution in the system in both time and space. We demonstrate that our model matches experimental results well and use it to describe the behavior of different types of PhC cavity designs. Thus, we demonstrate the model's capability to predict thermal nonlinearities of arbitrary 2D PhC microcavities in any material, only by substituting the appropriate physical constants. This renders the model critical for the development of nonlinear optical devices prior to fabrication and characterization.