# A Topology-Controlled Photonic Cavity Based on the Near-Conservation of the Valley Degree of Freedom

## TL;DR

This paper introduces a new method for creating topologically nontrivial photonic cavities by exploiting the near-conservation of the valley degree of freedom, enabling energy localization through valley-flipping dynamics.

## Contribution

It presents a novel approach to localize topological photonic edge modes using valley degree of freedom conservation and geometric control of valley-flipping time.

## Key findings

- Energy localization at the mirror surface due to valley-flipping
- Designs for microwave and optical spectral ranges
- Analytic models for leaky and closed cavities

## Abstract

We demonstrate a novel path to localizing topologically-nontrivial photonic edge modes along their propagation direction. Our approach is based on the near-conservation of the photonic valley degree of freedom associated with valley-polarized edge states. When the edge state is reflected from a judiciously oriented mirror, its optical energy is localized at the mirror surface because of an extended time delay required for valley-index-flipping. The degree of energy localization at the resulting topology-controlled photonic cavity (TCPC) is determined by the valley-flipping time, which is in turn controlled by the geometry of the mirror. Intuitive analytic descriptions of the "leaky" and closed TCPCs are presented, and two specific designs--one for the microwave and the other for the optical spectral ranges--are proposed.