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 coupling. Modelling such effects is of great importance to predict system performance with high fidelity. At present most approaches rely on quasi-static models that predict dynamics assuming slow temperature variation. Such an approach is inadequate in nanostructures, where heat transfer time is comparable with that of optical processes. Currently there are no models that describe transient thermo-optical coupling. Here, we develop a semi-analytical approach that allows predicting thermo-optical coupling in resonant nanophotonic structures under pulsed excitation. Our formalism is based on a mutually coupled system of heat transfer and Maxwell equations. Hence, optical heating serves as a source of energy deposition, whereas heating could lead to shifts in optical properties. We account for the heat transfer using the Green’s function approach, which, as we show, changes form depending on the dimensionality of the problem. To account for optical processes, we make use of the slowly varying amplitude approximation. In this case a perturbative temporal coupled mode theoretical framework is developed.

We apply the model to several cases of interactions where the transient nature plays an important role. First, we study the absorption of a nanosecond laser pulse by a nanophotonic resonant system. In this case thermally induced refractive index modulations cause a shift of the resonant frequency leading to it’s mismatch with the excitation frequency. This mismatch leads to a change in the absorptivity throughout the duration of the pulse. We study how this dynamic variation affects the total absorption fraction of the pulse for different structure dimensionality, initial (unperturbed) resonant frequency and pulse duration. We find, that for optimal absorption the resonator frequency has to be detuned relative to the excitation frequency and the value of this detuning varies with dimensionality and pulse duration.

In addition to optimizing the nanophotonic systems themselves our model can be used to design the temporal shape of the excitation pulse. To demonstrate that we perform optimization of a thermally controllable metasurface transmission switch. Using a gradient optimization algorithm, we find the optimal temporal shape to switch the metasurface from a high transmission state to low transmission and back again within 16 ns while using minimal energy. Thermal switching at this speed is difficult due to thermal dissipation time limitations. This makes accounting for transient thermal behavior critical to optimal performance.

We compare our simple semi-analytical model to more rigorous numerical simulations of real nanophotonic devices. A good agreement between the two is observed.

In summary, we develop a semi-analytical model capable of predicting fast non equilibrium thermal effects in nanophotonic systems under arbitrary pulse excitation. We use the model to demonstrate the exciting transient thermal dynamics and perform optimization for several practical cases.