The Green-function transform and wave propagation

Colin J. R. Sheppard, Shan S. Kou, Jiao Lin
2014 Frontiers in Physics  
We review Fourier methods used in the disciplines of electromagnetism and signal processing, with a view to reconciling differences in approach. In particular, 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
more » ... 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.
doi:10.3389/fphy.2014.00067 fatcat:xgy2beqzize2zmueashc75hvny