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

Journal Article · Thu Jan 15 00:00:00 EST 2015 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4905732· OSTI ID:22403088

Linton, C. M., E-mail: [e-mail] ^[1]

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1. 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

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CALCULATION METHODS
EQUATIONS
PERIODICITY
POLYNOMIALS
TWO-DIMENSIONAL CALCULATIONS
WAVE PROPAGATION