Effective Light Dynamics in Perturbed Photonic Crystals
de Nittis G, Lein M (2014)
Publication Status: Published
Publication Type: Journal article
Publication year: 2014
Journal
Publisher: Springer Verlag (Germany)
Book Volume: 332
Pages Range: 221-260
Journal Issue: 1
DOI: 10.1007/s00220-014-2083-0
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 quantifies the separation of spatial scales.We do that by rewriting the dynamical Maxwell equations as a Schrodinger-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.
Authors with CRIS profile
Involved external institutions
Canada (CA)How to cite
APA:
de Nittis, G., & Lein, M. (2014). Effective Light Dynamics in Perturbed Photonic Crystals. Communications in Mathematical Physics, 332(1), 221-260. https://doi.org/10.1007/s00220-014-2083-0
MLA:
de Nittis, Giuseppe, and Max Lein. "Effective Light Dynamics in Perturbed Photonic Crystals." Communications in Mathematical Physics 332.1 (2014): 221-260.
BibTeX: Download