Two-dimensional, phase modulated lattice sums with application to the Helmholtz Green’s function
Journal Article
·
· Journal of Mathematical Physics
- Department of Mathematical Sciences, Loughborough University, Leicestershire LE11 3TU (United Kingdom)
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.
- OSTI ID:
- 22403088
- Journal Information:
- Journal of Mathematical Physics, Vol. 56, Issue 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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