Research Project: Düşük Frekanslı Elektromanyetik Saçılmanın Dinamik Formülasyonu
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Contributors
Funders
ID
TB.00767
Authors
Mostafazadeh, Ali
Faculty Member
Publications
Dynamical formulation of low-frequency scattering in two and three dimensions
(American Physical Society (APS), 2025)
Loran, Farhang
Department of Physics
Department of Mathematics
Yes
Mostafazadeh, Ali
The transfer matrix of scattering theory in one dimension can be expressed in terms of the time-evolution operator of an effective nonunitary quantum system. In particular, it admits a Dyson series expansion which turns out to facilitate the construction of the low-frequency series expansion of the scattering data. In two and three dimensions, there is a similar formulation of stationary scattering in which the scattering properties of the scatterer are extracted from the evolution operator for a corresponding effective quantum system. We explore the utility of this approach to scattering theory in the study of the scattering of low-frequency time-harmonic scalar waves e-i omega t psi (r), with psi(r) satisfying the Helmholtz equation, [del 2 + k2 epsilon(r; k)]psi(r) = 0; omega and k being, respectively, the angular frequency and wave number of the incident wave; and epsilon(r; k) denoting the relative permittivity of the carrier medium, which, in general, takes complex values. We obtain explicit formulas for lowfrequency scattering amplitude, examine their effectiveness in the study of a class of exactly solvable scattering problems, and outline their application in devising a low-frequency cloaking scheme.
Low-frequency scattering of TE and TM waves by an inhomogeneous medium with planar symmetry
(Institute of Physics, 2025)
Loran, Farhang
Yetismisoǧlu, Cem
Department of Mathematics
Department of Physics
Yes
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.