A lattice model for resonance in open periodic waveguides

TL;DR

This paper introduces a discrete lattice model for resonant wave scattering in open periodic waveguides, explaining sharp transmission anomalies and field amplification through guided modes and bifurcation analysis.

Contribution

It presents a novel discrete lattice model that captures resonance phenomena in open waveguides, including bifurcation and guided mode behavior, which advances understanding of electromagnetic wave interactions.

Findings

Existence of standing and traveling guided modes.

Resonance initiated at a critical coupling strength.

Complex structure of transmission coefficient at resonance.

Abstract

We present a discrete model of resonant scattering of waves by an open periodic waveguide. The model elucidates a phenomenon common in electromagnetics, in which the interaction of plane waves with embedded guided modes of the waveguide causes sharp transmission anomalies and field amplification. The ambient space is modeled by a planar lattice and the waveguide by a linear periodic lattice coupled to the planar one along a line. We show the existence of standing and traveling guided modes and analyze a tangent bifurcation, in which resonance is initiated at a critical coupling strength where a guided mode appears, beginning with a single standing wave and splitting into a pair of waves traveling in opposing directions. Complex perturbation analysis of the scattering problem in the complex frequency and wavenumber domain reveals the complex structure of the transmission coefficient at resonance.