Modeling nanosecond thermo-optic coupling dynamics in nanoscale resonators.

Due to their narrow spectral features, nanophotonic resonant systems can be strongly affected by thermo-optical effects. Accounting for these effects is key for reliable operation. Typical existing models use quasi-static approximations to predict the dynamics assuming slow temperature variation. This can be insufficient when the heat transfer time scales are comparable to those of the excitation source. Curently no models describe this transient thermo optical coupling. Here, we develop a semi-analytical approach to predict non-equilibrium thermo-optical coupling in a nanoscale resonator under pulsed excitation. Our formalism is based on a mutually coupled system of heat transfer and Maxwell equations. Optical heating serves as a heat source that in turn induces perturbations in optical properties. We show that the behaviour of the system vaies with the dimentionality and study the different possible interaction regimes. Our model is general and can be used for a variety of nanoscale resonators. Comparisons with rigorous numerical simulations show that our semi-analytical model is effective at predicting the behavior of real nanophotonic systems. Additionally, we discuss the applications of our approach to design optimal pulsed light absorbers and fast thermally tunable metasurfaces.