Resonances for Maxwell’s equations in a periodic structure

Abstract

This paper deals with the existence and the distribution of the resonances associated to the Maxwell system in a periodic infinite structure. By boundary integral operators method, we reduce our problem to the existence and distribution of the characteristic values of a family of periodic non-self adjoint integral operators. The distribution of resonances is completely shown and an algorithm to compute them is proposed.

An adaptive edge element method with perfectly matched absorbing layers for wave scattering by biperiodic structures

“…It is further assumed that ε (1) > 0 and µ (j) > 0, j = 1, 2. However ε (2) may be complex according to the substrate material used in Ω (2) . Due to the periodic structure, the usual Sommerfeld or Silver-Müller radiation condition is no longer valid.…”

“…Due to the periodic structure, the usual Sommerfeld or Silver-Müller radiation condition is no longer valid. Instead, the following radiation condition based on diffraction theory is employed: (E, H) is composed of bounded outgoing waves in Ω (1) and Ω (2) plus the incident wave (E I , H I ) in Ω (1) . Scattering theory in biperiodic structures has many important applications in micro-optics, where the biperiodic structures are also termed as 2D gratings or crossed gratings.…”

“…See Bao and Dobson [10] and Ammari and Bao [2] for additional discussions on the solvability of the variational problem in the isotropic case. The questions on existence and uniqueness in the present general case are open.…”

“…Now we turn to the introduction of absorbing PML layers. The computational domain Ω is surrounded with two PML layers of thickness δ (1) and δ (2) in Ω (1) and Ω (2) , respectively. The specially designed model medium in the PML layers should basically be chosen so that either the wave never reaches its external boundary or the amplitude of the reflected wave is so small that it does not essentially contaminate the solution in Ω.…”

Resonant frequencies for a narrow strip grating

“…We have previously [1] investigated the problem of resonances in a narrow slots grating. This grating is constituted by a parallel-plane waveguide in which periodically opened narrow slots, in"nite in one direction are seen.…”