Simulating optical microcavities by inverting the thermal transfer function

Abstract

I present a reduced-order approach for incorporating distributed thermal dynamics into nonlinear optical-microcavity simulations without repeatedly solving the time-dependent heat equation. A harmonic finite-element heat solve is used to obtain the thermal transfer function, which is introduced into the time domain through either a rational approximation or an impulse-response convolution. The method is validated against heat-equation-coupled finite-element simulations for prescribed TE1-mode heating and for nonlinear silicon microcavity dynamics. For the feed-forward TE1 tests up to 100 MHz and simplified cavity dynamics, the error remains below 4%. The reduced models reproduce the local self-pulsation dynamics, although long-time phase alignment is sensitive to the spatial definition of the thermal transfer function and to impulse-response truncation. These results establish a physics-based route for retaining multi-timescale thermal memory while substantially reducing the cost of coupled optical--thermal simulations.