Acoustics of a Partially Partitioned Narrow Slit Connected to a Half-Plane: Case Study for Exponential Quasi-Bound States in the Continuum and their Resonant Excitation

Localized wave oscillations in an open system that do not decay or grow time, despite their frequency lying within a continuous spectrum of radiation modes carrying energy to from infinity, are known as bound states the continuum (BIC). Small perturbations typically delicate conditions for BIC almost always result waves weakly coupling with modes, leading leaky called quasi-BIC have large quality factor. We study asymptotic nature this weak case acoustic interacting rigid substrate featuring partially partitioned slit---a setup supports exponentially approach slit is made increasingly narrow. In limit, we use method matched expansions conjunction reciprocal relations those and resonant excitation. particular, derive approximation small imaginary part each wavenumber eigenvalue (inversely proportional factor), which beyond all orders expansion itself. Furthermore, amplitudes where they resonantly excited by plane at oblique incidence. These resonances occur narrow intervals physically manifested cylindrical-dipolar emanating aperture field enhancements inside slit. The approximations validated against numerical calculations.