Band structure for absorptive photonic crystals

A. Tip and A. Moroz, FOM-Instituut voor Atoomen Molecuulfysica, Kruislaan 407, 1098SJ Amsterdam, The Netherlands

J-M Combes, Départment de Mathémaiques, Université de Toulon et du Var, 83130 La Garde, France

Absorptive photonic crystals pose new problems that there are at present actively studied. Only recently their quantizatio has been treated in full generality [1,2]. Here we discuss another important problem: their band structure. using a formalism{2} developed by one of us (AT), we define band gaps in teh absorptive case as natural generalizations of non-absorptive ones. We find that no such gaps appear in absorptive frequency intervals. In addition, the Block-decomposed Helmholtz operator has no real eigenvalues. next we use an analytic continuation technique[3] due to one of us (JMC) to retrieve the eigenvalues as resonances in the complex plane, quite analoguous to Feshbach resonances in atoms. Some numerical examples for a one-dimensional model are given.

References

[1] H. T. Dung, L. Knöll, and D.-G. Welsch, Phys. Rev. A 57, 3931 91998).

[2] A. Tip, Phys. Rev. A 57, 4818 (1998).

[3] J. Aguilar and J.-M. Combes, Commun. Math. Phys. 22, 269 (1971).