Loughborough University
Leicestershire, UK
LE11 3TU
+44 (0)1509 263171
Loughborough University

Loughborough University Institutional Repository

Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/11796

Title: Construction of trapped modes for wave guides and diffraction gratings
Authors: McIver, P.
Linton, C.M.
McIver, M.
Keywords: Eigenvalues
Unbounded domain
Gratings
Issue Date: 1998
Publisher: © Royal Society Publishing
Citation: MCIVER, M., LINTON, C.M. and MCIVER, M., 1998. Construction of trapped modes for wave guides and diffraction gratings. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 454 (no.1978), pp.2593-2616.
Abstract: This paper describes various methods for the construction of trapped-mode solutions within wave guides and along diffraction gratings; in the latter case the solutions are often called Rayleigh-Bloch waves. One of the main results is the explicit construction of a number of new trapped-mode solutions within a wave guide that correspond to eigenvalues that are embedded in the continuous spectrum of the relevant operators. The method of construction is to take 'trial' solutions of the field equation that satisfy the required conditions on the guide walls and have the correct decay at large distances and then to identify lines that can be interpreted as the boundary of a structure within the wave guide. The same idea is also investigated for Rayleigh-Bloch waves within the context of diffraction gratings. Sensible choices of trial function are made by reference to solutions for a grating of circular cylinders, obtained by a multipole expansion method, and an approximate solution for more general geometries.
Description: This article is closed access.
Version: Closed access
DOI: 10.1098/rspa.1998.0272
URI: https://dspace.lboro.ac.uk/2134/11796
Publisher Link: http://rspa.royalsocietypublishing.org/
http://dx.doi.org/10.1098/rspa.1998.0272
ISSN: 1364-5021
Appears in Collections:Closed Access (Maths)

Files associated with this item:

File Description SizeFormat
McIverP&M_LintonCM_1998.pdfPublished version660.83 kBAdobe PDFView/Open

 

SFX Query

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.