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

• URL: http://arxiv.org/abs/2509.10205v2
• Date: Mon, 15 Sep 2025 09:38:55 GMT
• Title: Low-Frequency Scattering of TE and TM Waves by an Inhomogeneous Medium with Planar Symmetry
• Abstract summary: We study the low-frequency scattering of TE and TM waves when the inhomogeneities of the medium causing the scattering are confined to a planar slab.<n>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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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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