Boundary-layer effects on electromagnetic and acoustic extraordinary transmission through narrow slits

Abstract

We study the problem of resonant extraordinary transmission of electromagnetic and acoustic waves through subwavelength slits in an infinite plate, whose thickness is close to a half-multiple of the wavelength. We build on the matched-asymptotics analysis of Holley & Schnitzer (2019 Wave Motion 91 , 102381 (doi:10.1016/j.wavemoti.2019.102381)), who considered a single-slit system assuming an idealized formulation where dissipation is neglected and the electromagnetic and acoustic problems are analogous. We here extend that theory to include thin dissipative boundary layers associated with finite conductivity of the plate in the electromagnetic problem and viscous and thermal effects in the acoustic problem, considering both single-slit and slit-array configurations. By considering a distinguished boundary-layer scaling where dissipative and diffractive effects are comparable, we develop accurate analytical approximations that are generally valid near resonance; the electromagnetic–acoustic analogy is preserved up to a single parameter that is provided explicitly for both scenarios. The theory is shown to be in excellent agreement with GHz-microwave and kHz-acoustic experiments in the literature.

Design of an acoustic energy distributor using thin resonant slits

“…This way of considering the problem is an essential ingredient of the analysis. From this respect, our work shares similarities with [22–24] (see also references therein). The difference is that we combine several thin slits and coupling effect can appear.…”

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

“…in the upper half-plane, which is derived from ( 51) and (53). It is easy to see that the solution is identical to that asymptotic behaviour, i.e.,…”

“…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.…”

“…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.…”

Electromagnetic field enhancement in a subwavelength rectangular open cavity

“…In [14,22,23], an asymptotic expansion method was proposed to study the solution of the Helmholtz equation in a domain including a single thin slot. A quantitative analysis was made for the field enhancement of the Helmholtz equation for a single narrow open slit [28,30], or periodic slits [12,31,32]. We refer [4,5] for the study of closely related Helmholtz resonators and resonances in bubbly media.…”