# Flexure-Tuned Membrane-at-the-Edge Optomechanical System

## TL;DR

This paper presents a novel flexure-tuned membrane-in-the-edge optomechanical system that allows full-range coupling control, avoids abrupt spectral discontinuities, and can achieve significantly enhanced strong coupling regimes compared to traditional membrane-in-the-middle setups.

## Contribution

It introduces a passively aligned, flexure-tuned cavity system with analytical models, enabling larger coupling strengths and smoother spectral behavior than existing MIM systems.

## Key findings

- Achieves >15 microns membrane travel with flexure tuning.
- Provides analytical expressions for optomechanical couplings.
- Potential for orders of magnitude larger coupling than MIM systems.

## Abstract

We introduce a passively-aligned, flexure-tuned cavity optomechanical system in which a membrane is positioned microns from one end mirror of a Fabry-Perot optical cavity. By displacing the membrane through gentle flexure of its silicon supporting frame (i.e., to ~80 m radius of curvature (ROC)), we gain access to the full range of available optomechanical couplings, finding also that the optical spectrum exhibits none of the abrupt discontinuities normally found in "membrane-in-the-middle" (MIM) systems. More aggressive flexure (3 m ROC) enables >15 microns membrane travel, milliradian tilt tuning, and a wavelength-scale (1.64 $\pm$ 0.78 microns) membrane-mirror separation. We also provide a complete set of analytical expressions for this system's leading-order dispersive and dissipative optomechanical couplings. Notably, this system can potentially generate orders of magnitude larger linear dissipative or quadratic dispersive strong coupling parameters than is possible with a MIM system. Additionally, it can generate the same purely quadratic dispersive coupling as a MIM system, but with significantly suppressed linear dissipative back-action (and force noise).