Publication: Low-frequency scattering defined by the Helmholtz equation in one dimension
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Program
KU-Authors
KU Authors
Co-Authors
Loran, Farhang
Advisor
Publication Date
2021
Language
English
Type
Journal Article
Journal Title
Journal ISSN
Volume Title
Abstract
The Helmholtz equation in one dimension, which describes the propagation of electromagnetic waves in effectively one-dimensional systems, is equivalent to the time-independent Schrodinger equation. The fact that the potential term entering the latter is energy-dependent obstructs the application of the results on low-energy quantum scattering in the study of the low-frequency waves satisfying the Helmholtz equation. We use a recently developed dynamical formulation of stationary scattering to offer a comprehensive treatment of the low-frequency scattering of these waves for a general finite-range scatterer. In particular, we give explicit formulas for the coefficients of the low-frequency series expansion of the transfer matrix of the system which in turn allow for determining the low-frequency expansions of its reflection, transmission, and absorption coefficients. Our general results reveal a number of interesting physical aspects of low-frequency scattering particularly in relation to permittivity profiles having balanced gain and loss.
Description
Source:
Journal of Physics A: Mathematical and Theoretical
Publisher:
Institute of Physics (IOP) Publishing
Keywords:
Subject
Physics, Mathematical physics