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Two-dimensional, phase modulated lattice sums with application to the Helmholtz Green's function

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journal contribution
posted on 19.03.2015 by Christopher Linton
A class of two-dimensional phase modulated lattice sums in which the denominator is an indefinite quadratic polynomial Q is expressed in terms of a single, exponentially convergent series of elementary functions. This expression provides an extremely efficient method for the computation of the quasi-periodic Green's function for the Helmholtz equation that arises in a number of physical contexts when studying wave propagation through a doubly periodic medium. For a class of sums in which Q is positive definite, our new result can be used to generate representations in terms of Θ-functions which are significant generalisations of known results.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Mathematical Physics

Volume

56

Issue

1

Citation

LINTON, C.M., 2015. Two-dimensional, phase modulated lattice sums with application to the Helmholtz Green's function. Journal of Mathematical Physics, 56 (1), 013505.

Publisher

© AIP Publishing LLC

Version

VoR (Version of Record)

Publication date

2015

Notes

The following article appeared in Journal of Mathematical Physics, 2015, 56 (1), 013505 and may be found at http://dx.doi.org/10.1063/1.4905732. Copyright 2015 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

ISSN

0022-2488

Language

en

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