Lines of Quasi-BICs and Butterworth Line Shape in Stacked Resonant Gratings: Analytical Description

We propose analytical approximations of the reflection and transmission spectra a stacked dielectric diffraction grating consisting two identical resonant guided-mode gratings with Lorentzian line shape. These approximations, derived using scattering matrix formalism, are functions both angular frequency ω tangential wave vector component kx incident wave. analytically demonstrate and, full-wave simulations rigorous coupled-wave analysis technique, numerically confirm that by proper choice thickness layer separating gratings, one can tailor optical properties structure. In particular, it is possible to obtain lines quasi-bound states in continuum ω–kx parameter space quality factor decaying proportionally kx−4 or kx−6. addition, structure be used as spectral spatial Butterworth filter operating reflection. The presented results may find application design filters sensors based on gratings.