Complex Band Structure for Subwavelength Evanescent Waves

2024/09/22 by Yannick De Bruijn, De Bruijn, Yannick, Erik Orvehed Hiltunen +1 · 2 citations
Engineering · Materials Science · Physics and Astronomy · #Photonic and Optical Devices #Optical Coatings and Gratings #Photonic Crystals and Applications

paper · pdf · doi:10.48550/arxiv.2409.14537

Abstract

We present the mathematical and numerical theory for evanescent waves in subwavelength band gap materials. We begin in the one-dimensional case, whereby fully explicit formulas for the complex band structure, in terms of the capacitance matrix, are available. As an example, we show that the gap functions can be used to accurately predict the decay rate of the interface mode of a photonic analogue of the SSH-model. In two dimensions, we derive the band gap Green's function and characterise the subwavelength gap functions via layer potential techniques. By generalising existing lattice-summation techniques, we illustrate our results numerically by computing the complex band structure in a variety of settings.

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• Spectra and pseudospectra of non-Hermitian Toeplitz operators: Eigenvector decay transitions in banded and dense matrices
• Complex Band Structure and localisation transition for tridiagonal non-Hermitian k-Toeplitz operators with defects

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