Lattice sums for gratings and arrays

Citation
Rc. Mcphedran et al., Lattice sums for gratings and arrays, J MATH PHYS, 41(11), 2000, pp. 7808-7816
Citations number
18
Categorie Soggetti
Physics
Journal title
JOURNAL OF MATHEMATICAL PHYSICS
ISSN journal
00222488 → ACNP
Volume
41
Issue
11
Year of publication
2000
Pages
7808 - 7816
Database
ISI
SICI code
0022-2488(200011)41:11<7808:LSFGAA>2.0.ZU;2-4
Abstract
Lattice sums arising in quasiperiodic Green's functions for the Helmholtz e quation, over general two-dimensional arrays are investigated. The array su ms are related to those over a single quasiperiodic line of sources, and th eir difference is be expressed in terms of exponentially convergent series. It is shown that our expressions can be used to generate the sums pertaini ng to the case of photonic gap states, associated with complex quasiperiodi city (Bloch) vectors. The accuracy and computational speed of our expressio ns are illustrated. (C) 2000 American Institute of Physics. [S0022- 2488(00 )00611-3].