# Photonic bands, superchirality, and inverse design of a chiral minimal metasurface

## TL;DR

This paper reveals that a chiral metasurface exhibits a band structure in its chiro-optical response, with superchiral fields and anomalous polarization behaviors, and introduces an inverse design for a minimal unit cell geometry.

## Contribution

It introduces a novel inverse design method for a minimal chiral metasurface unit cell based on SVD analysis, connecting band structures to chiro-optical effects.

## Key findings

- Chiral metasurface exhibits a band structure in its optical response.
- Superchiral near-fields are excited at specific resonances.
- A minimal unit cell design is achieved using inverse design techniques.

## Abstract

Photonic band structures are a typical fingerprint of periodic optical structures, and are usually observed in spectroscopic quantities such as transmission, reflection and absorption. Here we show that also the chiro-optical response of a metasurface constituted by a lattice of non-centrosymmetric, L-shaped holes in a dielectric slab shows a band structure, where intrinsic and extrinsic chirality effects are clearly recognized and connected to localized and delocalized resonances. Superchiral near-fields can be excited in correspondence to these resonances, and anomalous behaviors as a function of the incidence polarization occur. Moreover, we introduce a singular value decomposition (SVD) approach to show that the above mentioned effects are connected to specific fingerprints of the SVD spectra. Finally, we demonstrate by means of an inverse design technique that the metasurface based on an L-shaped hole array is a minimal one. Indeed, its unit cell geometry depends on the smallest number of parameters needed to implement arbitrary transmission matrices compliant with the general symmetries for 2d-chiral structures. These observations enable more powerful wave operations in a lossless photonic environment.