Separation of variables in the computation of spectra in 2-D photonic crystals
Ponomarev, Igor
Ponomarev, Igor
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2000
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Band gap structure,Cubic lattice,Electromagnetic spectrum,Electromagnetic waves,Maxwell operator,Numeric computation,Photonic crystals,Separation of variables
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Citation
Ponomarev, I. (2001). Separation of Variables in the Computation of Spectra in 2-D Photonic Crystals. SIAM Journal on Applied Mathematics, 61(4), 1202-1218.
Abstract
The spectrum of the Maxwell operator corresponding to propagation of electromagnetic waves in periodic dielectric media of square geometry is analyzed. In the 2-D case the Maxwell operator splits into two scalar operators corresponding to so-called TE and TM modes of propagating electromagnetic wave. In the present paper we show that both of these operators can be slightly modified in such a way that separation of variables can be used. The eigenfunctions and the spectra for the modified operators are then used to obtain Rayleigh-Ritz-type estimates of the spectrum of the Maxwell operator. (See, for example, [Meade, Winn, and Joannopoulos, Photonic Crystals, Princeton University Press, 1995].) © 2000 Society for Industrial and Applied Mathematics.
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Society for Industrial and Applied Mathematics Publications
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SIAM Journal on Applied Mathematics
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0036-1399