A Tip et al 2000 J. Phys. A: Math. Gen. 33 6223 doi:10.1088/0305-4470/33/35/311
A Tip1, A Moroz1,2,5 and J M Combes3,4
Show affiliationsThe band structure of absorptive dielectric photonic crystals is investigated. Provided the frequency-dependent electric permeability ε(x,ω) satisfies certain analyticity requirements as a function of frequency, we show that no bandgaps exist in frequency regions where absorption takes place, i.e. where ε(x,ω) has a non-zero imaginary part. In this case real eigenvalues of the Helmholtz operator in the Bloch-decomposed formalism are absent. Using a suitable analytic continuation procedure, we find that the former change into resonances, i.e. complex numbers depending on k, the wavevector from the first Brillouin zone, thus leading to complex bands in the lower half plane. This is confirmed numerically for a simple, one-dimensional example.
82D25 Crystals (For crystallographic group theory, see 20H15)
Issue 35 (8 September 2000)
Received 28 April 2000
A Tip et al 2000 J. Phys. A: Math. Gen. 33 6223
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