A note on double Floquet-Bloch transforms and the far-field asymptotics of Green's functions tailored to periodic structures
Analysis of PDEs
2024-05-28 v2 Mathematical Physics
Complex Variables
math.MP
Abstract
We propose a general procedure to study double integrals arising when considering wave propagation in periodic structures. This method, based on a complex deformation of the integration surface to bypass the integrands' singularities, is particularly efficient to estimate the Green's functions of such structures in the far field. We provide several illustrative examples and explicit asymptotic formulae. Special attention is devoted to the pathological cases of degeneracies, such as Dirac conical points for instance.
Keywords
Cite
@article{arxiv.2402.08076,
title = {A note on double Floquet-Bloch transforms and the far-field asymptotics of Green's functions tailored to periodic structures},
author = {Andrey V. Shanin and Raphael C. Assier and Andrey I. Korolkov and Oleg I. Makarov},
journal= {arXiv preprint arXiv:2402.08076},
year = {2024}
}