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) Mostafazadeh, Ali; Loran, Farhang; Department of Physics; Department of Mathematics; Yes; College of Sciences
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) Mostafazadeh, Ali; Loran, Farhang ; Yetismisoǧlu, Cem ; Department of Mathematics; Department of Physics; Yes; College of Sciences
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.
