  In this study, 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 number have infinitely large Q factor, while
the other resonant modes have finite Q factor. For the leaky resonant mode with
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-Perot cavity, which hosts Fabry-Perot bound states in the continuum
(BICs) at the resonant frequency. The Q-factor of the Fabry-Perot 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 mode and wideband reflectance could be controlled on-demand.
