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arXiv · 2509.10205

Low-Frequency Scattering of TE and TM Waves by an Inhomogeneous Medium with Planar Symmetry

Farhang Loran·Ali Mostafazadeh·Cem Yetişmişoğlu
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Abstract

Stationary scattering of TE and TM waves propagating in an isotropic medium with planar symmetry is described by Bergmann's equation in one dimension. This is a generalization of Helmholtz equation which allows for developing transfer matrix methods to deal with the corresponding scattering problems. We use a dynamical formulation of stationary scattering to study the low-frequency scattering of these waves when the inhomogeneities of the medium causing the scattering are confined to a planar slab. This formulation relies on the construction of an effective two-level non-Hermitian quantum system whose time-evolution operator determines the transfer matrix. We use it to construct the low-frequency expansions of the transfer matrix and the reflection and transmission coefficients of the medium, introduce a generalization of Brewster's angle for inhomogeneous slabs at low frequencies, and derive analytic conditions for transparency and reflectionlessness of PT-symmetric and non-PT-symmetric slabs at these frequencies. We also discuss the application of this method to deal with the low-frequency scattering of TE and TM waves when the carrier medium occupies a half-space and the waves satisfy boundary conditions with planar symmetry at the boundary of the half-space. Because acoustic waves propagating in a compressible fluid with planar symmetry are also described by Bergmann's equation, our results apply to the low-frequency scattering of these waves.

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Farhang Loran, Ali Mostafazadeh, Cem Yetişmişoğlu. 2025-09-12. Low-Frequency Scattering of TE and TM Waves by an Inhomogeneous Medium with Planar Symmetry. https://doi.org/10.1088/1751-8121%2Fae0848

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