• DOI:10.1007/s00220-014-2083-0
• Corpus ID: 119719544

Effective Light Dynamics in Perturbed Photonic Crystals

@article{DeNittis2013EffectiveLD,
  title={Effective Light Dynamics in Perturbed Photonic Crystals},
  author={Giuseppe De Nittis and Max Lein},
  journal={Communications in Mathematical Physics},
  year={2013},
  volume={332},
  pages={221-260}
}

• G. De Nittis, Max Lein
• Published 5 July 2013
• Physics
• Communications in Mathematical Physics

In this work, we rigorously derive effective dynamics for light from within a limited frequency range propagating in a photonic crystal that is modulated on the macroscopic level; the perturbation parameter $${\lambda \ll 1}$$λ≪1 quantifies the separation of spatial scales.We do that by rewriting the dynamical Maxwell equations as a Schrödinger-type equation and adapting space-adiabatic perturbation theory. Just like in the case of the Bloch electron, we obtain a simpler, effective Maxwell operator for states from within a relevant almost invariant subspace. A correct physical interpretation for the effective dynamics requires establishing two additional facts about the almost invariant subspace: (1) The source-free condition has to be verified and (2) it has to support real states. The second point also forces one to consider a multiband problem even in the simplest possible setting; This turns out to be a major difficulty for the extension of semiclassical methods to the domain of photonic crystals.