# Non-Scattering Multi-Mirror Systems for Field Localization

## TL;DR

This paper introduces a novel non-scattering multi-mirror resonator system that allows independent control of inner cavity fields without disturbing the outer cavity, enhancing wave localization capabilities.

## Contribution

It proposes the concept of invisible, non-scattering cavities that can be nested like matryoshka dolls, enabling complex resonator designs without analytical complexity.

## Key findings

- Nested non-scattering cavities maintain high finesse.
- Independent control of inner cavity standing waves.
- System remains non-scattering despite multiple cavities.

## Abstract

Resonators composed of two mirrors, such as Fabry-Perot cavities, provide a simple but effective approach to achieve wave transmission with high finesse. Further increase of the quality factor requires reflectors with higher conductivity or multi-mirror solutions. However, the analytical complexity of resonators with more than two mirrors prevents the design of optimal structures without recurring to numerical methods. This work considers an alternative approach to this problem by using cavities which do not produce any electromagnetic scattering. We demonstrate that these invisible cavities can be placed inside one another, resulting in a `matryoshka-doll'-like resonator. The standing-wave distribution of the inner resonator can be controlled without disturbing that of the outer one, whereas the whole system remains non-scattering.