Lattice sums for gratings and arrays

DOI10.1063/1.1310361zbMath0980.35007OpenAlexW2072319428MaRDI QIDQ2738282

Nicolae-Alexandru P. Nicorovici, Lindsay C. Botten, K. A. Grubits, R. C. McPhedran

Publication date: 30 August 2001

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.1310361

zbMATH Keywords

Bloch vectorsphotonic gap statesquasiperiodic Green's functions for the Helmholtz equation

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Miscellaneous applications of number theory (11Z05)

Related Items (12)

The split ring resonator ⋮ A new integral representation for quasi-periodic fields and its application to two-dimensional band structure calculations ⋮ A fast direct solver for scattering from periodic structures with multiple material interfaces in two dimensions ⋮ Evaluation and regularization of phase-modulated Eisenstein series and application to double Schlömilch-type sums ⋮ A fast summation method for oscillatory lattice sums ⋮ Fast algorithms for Helmholtz Green's functions ⋮ A note on quasiperiodic Green's functions for arrays ⋮ A new integral representation for quasi-periodic scattering problems in two dimensions ⋮ Sums of spherical waves for lattices, layers, and lines ⋮ One- and two-dimensional lattice sums for the three-dimensional Helmholtz equation ⋮ Neumann series and lattice sums ⋮ A fast method for imposing periodic boundary conditions on arbitrarily-shaped lattices in two dimensions

Cites Work

• Elementary function representations of Schlömilch series
• The Green's function for the two-dimensional Helmholtz equation in periodic domains
• Integral representations of harmonic lattice sums

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