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Lattice sums for gratings and arrays (2000)

McPhedran, R. C. ; Nicorovici, N. A.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 41 (2000), S. 7808-7816

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ISSN: 1089-7658

Source: AIP Digital Archive

Topics: Mathematics , Physics

Notes: Lattice sums arising in quasiperiodic Green's functions for the Helmholtz equation, over general two-dimensional arrays are investigated. The array sums are related to those over a single quasiperiodic line of sources, and their difference is be expressed in terms of exponentially convergent series. It is shown that our expressions can be used to generate the sums pertaining to the case of photonic gap states, associated with complex quasiperiodicity (Bloch) vectors. The accuracy and computational speed of our expressions are illustrated. © 2000 American Institute of Physics.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.1310361

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