Communications in Mathematical Physics

, Volume 332, Issue 1, pp 221–260 | Cite as

Effective Light Dynamics in Perturbed Photonic Crystals

Article

Abstract

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 \({\lambda \ll 1}\) 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.

Keywords

Vector Bundle Photonic Crystal Pseudodifferential Operator Topological Insulator Selfadjoint Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department MathematikUniversität Erlangen-NürnbergErlangenGermany
  2. 2.Department of MathematicsUniversity of Toronto, Bahen CentreTorontoCanada

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