The Green-function transform and wave propagation

Frontiers in Physics

Sheppard, Colin J. R.¹  Kou, Shan S.²  Lin, Jiao² 

[1] Department of Nanophysics, Istituto Italiano di Tecnologia, Genova, Italy;School of Physics, The University of Melbourne, Melbourne, VIC, Australia

关键词: Fourier Analysis;    electromagnetic wave propagation;    Diffraction and scattering;    Fourier optics;    green function;   

DOI  :  10.3389/fphy.2014.00067

学科分类：物理（综合）

来源: Frontiers

【 摘 要 】

Fourier methods well known in signal processing are applied to three-dimensional wave propagation problems. The Fourier transform of the Green function, when written explicitly in terms of a real-valued spatial frequency, consists of homogeneous and inhomogeneous components. Both parts are necessary to result in a pure out-going wave that satisfies causality. The homogeneous component consists only of propagating waves, but the inhomogeneous component contains both evanescent and propagating terms. Thus we make a distinction between inhomogeneous waves and evanescent waves. The evanescent component is completely contained in the region of the inhomogeneous component outside the k-space sphere. Further, propagating waves in the Weyl expansion contain both homogeneous and inhomogeneous components. The connection between the Whittaker and Weyl expansions is discussed. A list of relevant spherically symmetric Fourier transforms is given.

【 授权许可】

CC BY