Title: Integrated optical force sensors using focusing photonic crystal arrays,
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-Pérot 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.