Refractive index sensing with optical bound states in the continuum

We consider refractive index sensing with optical bounds states in the continuum (BICs) in dielectric gratings. Applying a perturbative approach we derived the differential sensitivity and the figure of merit of a sensor operating in the spectral vicinity of a BIC. Optimisation design approach for engineering an effective sensor is proposed. An analytic formula for the maximal sensitivity with an optical BIC is derived. The results are supplied with straightforward numerical simulations.