A mathematical design strategy for highly dispersive resonator systems

TL;DR

This paper develops an asymptotic modeling approach for complex systems of dispersive resonators, enabling efficient design of resonator arrays with targeted frequency responses, demonstrated on halide perovskite resonators.

Contribution

It extends integral and asymptotic techniques to model many dispersive resonators with nonlinear frequency dependence, facilitating inverse design strategies.

Findings

Concise models for coupled resonators with small radii

Method for inverse design of resonator systems

Application to halide perovskite resonators

Abstract

Designing devices composed of many small resonators is a challenging problem that can easily incur significant computational cost. Can asymptotic techniques be used to overcome this often limiting factor? Integral methods and asymptotic techniques have been used to derive concise characterisations for scattering by resonators, but can these be generalised to systems of many dispersive resonators whose material parameters have highly non-linear frequency dependence? In this paper, we study halide perovskite resonators as a demonstrative example. We extend previous work to show how a finite number of coupled resonators can be modelled concisely in the limit of small radius. We also show how these results can be used as the basis for an inverse design strategy, to design resonator systems that resonate at specific frequencies.