Modal Expansion of the Impulse Response Function for Predicting the Time Dynamics of Open Optical Cavities

TL;DR

This paper develops a modal expansion approach to predict the temporal dynamics of open optical cavities, providing analytical expressions for the impulse response function and clarifying the role of eigen-modes in transient versus permanent regimes.

Contribution

It introduces a novel modal expansion method for the impulse response of open optical cavities, with analytical derivations and validation for Fabry-Perot resonators.

Findings

Eigen-modes influence signals only during transients.

The modal expansion converges and accurately predicts cavity dynamics.

Analytical expressions for internal and scattered fields are derived.

Abstract

Light interaction with optical cavities is of fundamental interest to enhance the light-matter interaction and to shape the spectral features of the electromagnetic fields. Important efforts have been carried out to develop modal theories of open optical cavities relying on an expansion of the fields on the eigen-fields of the cavity. Here, we show how such an expansion predicts the temporal dynamics of optical resonators. We consider a Fabry-Perot cavity to derive the full analytical expressions of the internal and scattered field on the quasi-normal modes basis together with the complex eigen-frequencies. We evince the convergence and accuracy of this expansion before deriving the impulse response function (IRF) of the open cavity. We benefit from this modal expansion and IRF to demonstrate that the eigen-modes of the open cavity impact the signals only during the transient regimes and not in the permanent regime.