Refractive-index sensing based on large negative Goos-Hänchen shifts of a wavy dielectric grating

A wavy dielectric grating hosts bound states in the continuum (BICs) at nonzero Bloch wave number. For an oblique incident optical field with parameters near to the BICs, the reflectance spectrum exhibits an ultrasharp Fano line shape, and the reflected beam has a large negative Goos-H\"anchen shift, due to excitation of the corresponding quasi-BIC with negative group velocity. Under incidence of a Gaussian beam with a sizable beam width, the excited quasi-BIC could travel a long distance along the direction of the Goos-H\"anchen shift, designated as ${L}_{\mathrm{GH}}$, before the energy is completely radiated. If the length between the termination of the wavy shape and the focus of the incident Gaussian beam is smaller than ${L}_{\mathrm{GH}}$, sizable energy flux can be coupled into the waveguide mode of the flat dielectric slab that is connected to the wavy dielectric grating. Measurement of the energy flux of the waveguide mode can sense the variation of the refractive index of the background medium. The proposed sensing scheme can be integrated with a waveguide in an optical circuit.