Wavy optical grating: Wideband reflector and Fabry-Pérot bound states in the continuum
Ma Luo, Feng Wu
Abstract
In this paper, we theoretically and numerically investigate the resonant modes and reflectance of an optical grating consisting of a wavy dielectric slab by applying the spectral element method. The presence of the wavy shape transforms the waveguide modes into leaky resonant modes. A few resonant modes with specific longitudinal wave numbers have infinitely large-$Q$ factors, whereas the other resonant modes have finite-$Q$ factors. For the leaky resonant mode with a zero longitudinal wave number, the $Q$ factor is inversely proportional to the amplitude of the wavy shape. An array of multiple low-$Q$ wavy gratings has a high reflectance in a large bandwidth. A double-layer wavy grating forms a Fabry-P\'erot cavity, which hosts Fabry-P\'erot bound states in the continuum (BICs) at the resonant frequency. The $Q$ factor of the Fabry-P\'erot cavity can be tuned by adjusting the distance between the two wavy slabs. The wavy shape could be generated by a vibrational wave in a flat dielectric slab so that the BICs and wideband reflectance could be controlled on demand.