Design of an acoustic energy distributor using thin resonant slits

Abstract

We consider the propagation of time-harmonic acoustic waves in a device made of three unbounded channels connected by thin slits. The wavenumber is chosen such that only one mode can propagate. The main goal of this work is to present a device which can serve as an energy distributor. More precisely, the geometry is first designed so that for an incident wave coming from one channel, the energy is almost completely transmitted in the two other channels. Additionally, adjusting slightly two geometrical parameters, we can control the ratio of energy transmitted in the two channels. The approach is based on asymptotic analysis for thin slits around resonance lengths. We also provide numerical results to illustrate the theory.

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

“…These studies exploit the conventional standing-wave resonances of a slit cavity, which are associated with cylindrical monopole-like radiation emitted from the slit aperture and quality factors and field enhancements that are algebraically large in the cavity aspect ratio. The asymptotic properties of such resonances have been studied extensively using various methods [47][48][49][50][51][52][53][54][55]. In this context, the present work shows that adding a partition to a slit introduces an extra set of resonances, which lie in the same frequency regime but are distinct in that they exhibit exponentially large quality factors and field enhancements and that cylindrical dipole-like radiation is emitted from the slit aperture.…”

“…In preparation for matching with the exterior region, we use (54) to extract from the solution (56) the far-field behaviour…”

“…Building on previous singular-perturbation analyses of resonant phenomena involving narrow slits [51][52][53][54]56], we shall use the method of matched asymptotic expansions [23] to construct approximations for the wave field by systematically relating asymptotic expansions whose domain of validity spatially overlap. Furthermore, as in [51,52,56], we shall use conformal mappings [57] to solve certain 'inner' problems that arise as part of the analysis, in this case associated with regions near the partition edge and slit aperture.…”

Acoustic passive cloaking using thin outer resonators

“…To cloak obstacles, we will work with thin outer resonators of width ε as depicted for example in Figures 17-20. We already used similar techniques in [20] and [17] to design respectively energy distributors and mode converters. Thus the present article constitutes somehow the third opus of the trilogy started with [20,17].…”

“…We already used similar techniques in [20] and [17] to design respectively energy distributors and mode converters. Thus the present article constitutes somehow the third opus of the trilogy started with [20,17]. In general, due to the geometrical properties of waveguides as in Figures 17-20, the thin resonators produce only a perturbation of order ε on the fields and so on the scattering coefficients.…”