00-181 A. Tip, J. M. Combes, A. Moroz
Bloch decomposition and band structure for absorptive photonic crystals (485K, pdf) Apr 14, 00
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Abstract. We show that dielectric photonic crystals do not have band gaps in frequency regions where absorption takes place, i.e. where the frequency-dependent electric permeability $\varepsilon (\QTR{bf}{x},\omega )$ has a non-zero imaginary part. Under these circumstances real eigenvalues of the Helmholtz operator in the Bloch-decomposed formalism are absent. We find, using a suitable analytic continuation procedure, that the former change into resonances, i.e., complex numbers depending on $\QTR{bf}{k}$, the wave vector from the first Brillouin zone, thus leading to complex bands in the lower half plane.

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