Computation of eigenfrequency sensitivities using Riesz projections for efficient optimization of nanophotonic resonators

TL;DR

This paper introduces a Riesz projection-based method for efficiently computing eigenfrequency sensitivities in resonant systems, specifically applied to optimize nanophotonic resonators' quality factors.

Contribution

The paper presents a novel approach using Riesz projections for calculating eigenfrequency sensitivities directly from Maxwell's equations, improving efficiency over finite difference methods.

Findings

The method accurately computes eigenfrequency derivatives.

It outperforms finite difference approaches in efficiency.

Successful optimization of a nanophotonic resonator's quality factor.

Abstract

Resonances are omnipresent in physics and essential for the description of wave phenomena. We present an approach for computing eigenfrequency sensitivities of resonances. The theory is based on Riesz projections and the approach can be applied to compute partial derivatives of the complex eigenfrequencies of any resonance problem. Here, the method is derived for Maxwell's equations. Its numerical realization essentially relies on direct differentiation of scattering problems. We use a numerical implementation to demonstrate the performance of the approach compared to differentiation using finite differences. The method is applied for the efficient optimization of the quality factor of a nanophotonic resonator.