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

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.
Authors:
 [1]
  1. Department of Mathematical Sciences, Loughborough University, Leicestershire LE11 3TU (United Kingdom)
Publication Date:
OSTI Identifier:
22403088
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CALCULATION METHODS; EQUATIONS; PERIODICITY; POLYNOMIALS; TWO-DIMENSIONAL CALCULATIONS; WAVE PROPAGATION