Bound states in the continuum in composite structures consisting of two dielectric diffraction gratings with Lorentzian line shape

We propose a simple analytical approximation of the spectrum of a dielectric grating with Lorentzian line shape in the reflection spectrum as a function of frequency and the tangential wave vector component of the incident wave. Using scattering matrix formalism we derive the reflection and transmission spectra of a composite structure consisting of two such identical diffraction gratings separated with a homogenous dielectric layer. By appropriately choosing the thickness of the intermediary layer one can achieve the formation of a bound state in the continuum (BIC) as well as high-Q quasi-BIC lines. The obtained results can find application in the design of optical filters and sensors.