# Fisher-Information Efficient Metagratings for Transverse Displacement Metrology at the Measurement Independent Shot-Noise Limit

## TL;DR

This paper establishes a fundamental precision limit for transverse displacement measurement using classical light, demonstrating that optimized metagratings can reach this limit efficiently by minimal photon detection, linked to specific resonant properties.

## Contribution

It derives a measurement independent precision bound for classical transverse displacement metrology and shows how optimized metagratings can achieve this bound efficiently.

## Key findings

- Achieves measurement independent shot-noise limit using classical sources.
- Optimized metagratings detect minimal photons while reaching the fundamental bound.
- Resonant properties like 0th dipole and anapole conditions are key to achieving the bound.

## Abstract

We derive the measurement independent precision bound for transverse displacement metrology using a classical source. Using tools from quantum estimation theory and metamaterial designs, we prove that the bound is achieved efficiently using optimized metagratings by detecting only a very small amount of photons used to probe the displacement, and we also reveal the direct link between the resonant property in the unit cell and the conditions to achieve the bound: one with the 0th dipole resonance and the other one with the anapole condition of the 1st dipole.