Giuseppe De Nittis, Max Lein
In this work, we establish effective dynamics for light from a limited frequency range propagating in an isotropic photonic crystal that is modulated on the macroscopic level. We do that by reformulating the dynamical Maxwell equations as a Schr\"odinger-type equation and adapting space-adiabatic perturbation theory. Just like in the case of the Bloch electron, we obtain a simpler, effective Maxwell operator which governs the dynamics for states from a relevant almost invariant subspace. A correct physical interpretation for the effective dynamics necessitates to establish two additional facts about the almost invariant subspace: (1) its elements need to verify the source-free condition and (2) it must contain real-valued elements.
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http://arxiv.org/abs/1307.1642
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