The Green-function transform and wave propagation
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2014-11-01
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| Series: | Frontiers in Physics |
| Subjects: | |
| Online Access: | http://journal.frontiersin.org/Journal/10.3389/fphy.2014.00067/full |
| _version_ | 1828389158002884608 |
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| author | Colin eSheppard Shanshan eKou Jiao eLin |
| author_facet | Colin eSheppard Shanshan eKou Jiao eLin |
| author_sort | Colin eSheppard |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T06:25:17Z |
| format | Article |
| id | doaj.art-12c32a55d1dd42518edefa73ac1c2ab1 |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-12-10T06:25:17Z |
| publishDate | 2014-11-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-12c32a55d1dd42518edefa73ac1c2ab12022-12-22T01:59:13ZengFrontiers Media S.A.Frontiers in Physics2296-424X2014-11-01210.3389/fphy.2014.00067111378The Green-function transform and wave propagationColin eSheppard0Shanshan eKou1Jiao eLin2Italian Institute of TechnologyThe University of MelbourneThe University of MelbourneFourier 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.http://journal.frontiersin.org/Journal/10.3389/fphy.2014.00067/fullFourier Analysisgreen functionelectromagnetic wave propagationDiffraction and scatteringFourier optics |
| spellingShingle | Colin eSheppard Shanshan eKou Jiao eLin The Green-function transform and wave propagation Frontiers in Physics Fourier Analysis green function electromagnetic wave propagation Diffraction and scattering Fourier optics |
| title | The Green-function transform and wave propagation |
| title_full | The Green-function transform and wave propagation |
| title_fullStr | The Green-function transform and wave propagation |
| title_full_unstemmed | The Green-function transform and wave propagation |
| title_short | The Green-function transform and wave propagation |
| title_sort | green function transform and wave propagation |
| topic | Fourier Analysis green function electromagnetic wave propagation Diffraction and scattering Fourier optics |
| url | http://journal.frontiersin.org/Journal/10.3389/fphy.2014.00067/full |
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