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Considerations to Rayleigh's hypothesis

Rother, Tom and Wauer, Jochen (2009) Considerations to Rayleigh's hypothesis. Optics Communications, 282, pp. 339-350. Elsevier. DOI: 10.1016/j.optcom.2008.10.023.

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Abstract

In 1907 Lord Rayleigh published a paper on the dynamic theory of gratings. In this paper he presented a rigorous approach for solving plane wave scattering on periodic surfaces. Moreover he derived explicit expressions for a perfectly conducting sinusoidal surface, and for perpendicular incidence of the electromagnetic plane wave. This paper was criticized by Lippmann in 1953 for he assumed Rayleigh's approach to be incomplete. Since this time there have been published several arguments, proofs, and discussions concerning the correctness and the range of validity of Rayleigh's approach not only for plane wave scattering on gratings but also for light scattering on nonspherical structures, in general. In the paper at hand we will discuss the different point of views on what is called ''Rayleigh's hypothesis'' as well as the relevance of a found theoretical limit for its validity. Furthermore we present a numerical treatment of the original scattering problem of a p-polarized plane wave perpendicularly incident on a perfectly conducting sinusoidal surface (i.e., the scalar Dirichlet problem). In doing so we emphasizes the near-field solution especially within the grooves of the grating up to points on the surface, and below the surface. Two different Green's function formulations of Huygens' principle are used as starting points. One of this formulation results in the general T-matrix approach which is considered to be affected by Rayleigh's hypothesis especially for near-field calculations. The other formulation provides a conventional boundary integral equation which is in accordance with Lippmann's point of view and free of problems with Rayleigh's hypothesis. But the obtained results show that Lippmann's argumentation do not withstand a critical numerical analysis, and that the independence of least-squares approaches from Rayleigh's hypothesis, as understood and proven by Millar, seems to hold also for certain methods which does not fit into such an approach.

Document Type:Article
Title:Considerations to Rayleigh's hypothesis
Authors:
AuthorsInstitution or Email of Authors
Rother, TomUniversität Leipzig
Wauer, JochenUNSPECIFIED
Date:February 2009
Journal or Publication Title:Optics Communications
Refereed publication:Yes
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:282
DOI:10.1016/j.optcom.2008.10.023
Page Range:pp. 339-350
Editors:
EditorsEmail
Elsevier, UNSPECIFIED
Publisher:Elsevier
Status:Published
Keywords:Rayleigh's hypothesis, plane wave scattering, gratings
HGF - Research field:Aeronautics, Space and Transport (old)
HGF - Program:Space (old)
HGF - Program Themes:W EO - Erdbeobachtung
DLR - Research area:Space
DLR - Program:W EO - Erdbeobachtung
DLR - Research theme (Project):W - Vorhaben Entwicklung von Atmosphärenprozessoren (old)
Location: Neustrelitz
Institutes and Institutions:Remote Sensing Technology Institute > Atmospheric Processors
Deposited By: Dr.rer.nat. Tom Rother
Deposited On:02 Apr 2009
Last Modified:26 Feb 2013 15:00

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