Enhanced sensitivity of an all-dielectric refractive index sensor with optical bound state in the continuum

The sensitivity of a refractive index sensor based on an optical bound state in the continuum is considered. Applying Zel’dovich perturbation theory we derived an analytic expression for bulk sensitivity of an all-dielectic sensor utilizing symmetry protected in-$\mathrm{\Gamma }$ optical bound states in a dielectric grating. The upper sensitivity limit is obtained. A recipe is proposed for obtaining the upper sensitivity limit by optimizing the design of the grating. The results are confirmed through direct numerical simulations.