# Integrated optical force sensors using focusing photonic crystal arrays

## TL;DR

This paper introduces a fully integrated optical force sensor using focusing photonic crystal arrays on silicon nitride membranes, simplifying design and assembly for high-sensitivity force detection.

## Contribution

It presents the first simulation of a focusing mirror made from a suspended silicon nitride membrane, enabling compact, integrated optical force sensors without complex alignment.

## Key findings

- Simulated a focusing photonic crystal mirror made from silicon nitride.
- Designed an integrated Fabry-Pérot cavity sensor with simplified assembly.
- Proposed a sensor with cavity lengths from hundreds of micrometers to millimeters.

## Abstract

Mechanical oscillators are at the heart of many sensor applications. Recently several groups have developed oscillators that are probed optically, fabricated from high-stress silicon nitride films. They exhibit outstanding force sensitivities of a few aN/Hz$^{1/2}$ and can also be made highly reflective, for efficient detection. The optical read-out usually requires complex experimental setups, including positioning stages and bulky cavities, making them impractical for real applications. In this paper we propose a novel way of building fully integrated all-optical force sensors based on low-loss silicon nitride mechanical resonators with a photonic crystal reflector. We can circumvent previous limitations in stability and complexity by simulating a suspended focusing photonic crystal, purely made of silicon nitride. Our design allows for an all integrated sensor, built out of a single block that integrates a full Fabry-P\'{e}rot cavity, without the need for assembly or alignment. The presented simulations will allow for a radical simplification of sensors based on high-Q silicon nitride membranes. Our results comprise, to the best of our knowledge, the first simulations of a focusing mirror made from a mechanically suspended flat membrane with subwavelength thickness. Cavity lengths between a few hundred $\mu$m and mm should be directly realizable.