Total Resonant Transmission and Reflection by Periodic Structures

TL;DR

This paper analyzes how periodic structures can cause sharp resonant transmission and reflection anomalies near guided modes, with conditions for total transmission or reflection and their mathematical characterization.

Contribution

It establishes sufficient symmetry conditions for total resonant transmission and reflection in 2D periodic structures, detailing their analytical properties near guided modes.

Findings

Total transmission and reflection occur at specific frequencies near guided modes.

The loci of these anomalies are real-analytic curves intersecting quadratically.

Multiple anomalies can be excited by a single guided mode.

Abstract

Resonant scattering of plane waves by a periodic slab under conditions close to those that support a guided mode is accompanied by sharp transmission anomalies. For two-dimensional structures, we establish sufficient conditions, involving structural symmetry, under which these anomalies are characterized by total transmission and total reflection at frequencies separated by an arbitrarily small amount. The loci of total reflection and total transmission are real-analytic curves in frequency-wavenumber space that intersect quadratically at a single point corresponding to the guided mode. A single anomaly or multiple anomalies can be excited by the interaction with a single guided mode.