Spectral Analysis of Relativistic Dyadic Green's Function of a Moving Dielectric-Magnetic Medium

• Published in: IEEE transactions on antennas and propagation Vol. 59; no. 8; pp. 2973 - 2979
• Main Authors: Danov, T., Melamed, T.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Approximation methods; Dielectrics; Dyadic Green's function; Dyadics; Electric fields; Exact sciences and technology; Finite difference methods; Fourier transforms; Green's functions; Information, signal and communications theory; Magnetic fields; Materials; moving medium; plane-wave spectrum; Representations; Scalars; Signal and communications theory; Signal representation. Spectral analysis; Signal, noise; special relativity; Spectra; Telecommunications and information theory; Time domain analysis; Two dimensional; Fourier transformation; Isotropic medium; Special relativity; Spectrum analysis; Moving medium; Plane wave; Scalarization; plane-wave spectrum; Signal analysis; Green function; Dyadic Green's function
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2011.2158972

The present contribution is concerned with obtaining plane-wave spectral representations of the relativistic electric and magnetic dyadic Green's functions of an isotropic dielectric-magnetic medium (at the frame-at-rest) that is moving in a uniform velocity. By applying a simple coordinate transformation, scalarization of the EM vectorial problem is obtained in which the EM dyads are evaluated from Helmholtz's isotropic scalar Green's function. The spectral plane-wave representations of the dyadic Green's functions are obtained by applying the spatial 2D Fourier transform to the scalar Green's function. We investigate these spectral representations in the under and over phase-speed regimes, as well as 2D and 3D formulations and discuss the associated wave phenomena.