Integrated optical force sensors using focusing photonic crystal arrays
  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.
