Localization of Classical Waves II: Electromagnetic Waves |
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Authors: | Alexander Figotin Abel Klein |
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Institution: | Department of Mathematics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA.?E-mail:figotin@mosaic.uncc.edu, US Department of Mathematics, University of California at Irvine, Irvine, CA 92697-3875, USA.?E-mail: aklein@math.uci.edu, US
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Abstract: | We consider electromagnetic waves in a medium described by a position dependent dielectric constant . We assume that is a random perturbation of a periodic function and that the periodic Maxwell operator has a gap in the spectrum, where . We prove the existence of localized waves, i.e., finite energy solutions of Maxwell's equations with the property that almost
all of the wave's energy remains in a fixed bounded region of space at all times. Localization of electromagnetic waves is
a consequence of Anderson localization for the self-adjoint operators . We prove that, in the random medium described by , the random operator exhibits Anderson localization inside the gap in the spectrum of . This is shown even in situations when the gap is totally filled by the spectrum of the random operator; we can prescribe
random environments that ensure localization in almost the whole gap.
Received: 1 July 1996 / Accepted: 15 August 1996 |
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