Math @ Duke

Publications [#244175] of Stephanos Venakides
Papers Published
 Shipman, SP; Venakides, S, Resonance and bound states in photonic crystal slabs,
SIAM Journal on Applied Mathematics, vol. 64 no. 1
(2003),
pp. 322342, ISSN 00361399 [doi]
(last updated on 2018/08/20)
Abstract: Using boundaryintegral projections for timeharmonic electromagnetic (EM) fields, and their numerical implementation, we analyze EM resonance in slabs of twophase dielectric photonic crystal materials. We characterize resonant frequencies by a complex FloquetBloch dispersion relation ω = W (β) defined by the existence of a nontrivial nullspace of a pair of boundaryintegral projections parameterized by the wave number β and the timefrequency ω. At resonant frequencies, the crystal slab supports a sourcefree EM field. We link complex resonant frequencies, where the imaginary part is small, to resonant scattering behavior of incident source fields at nearby real frequencies and anomalous transmission of energy through the slab. At a real resonant frequency, the sourcefree field supported by the slab is a bound state. We present numerical examples which demonstrate the effects of structural defects on the resonant properties of a crystal slab and surface waves supported by a dielectric defect.


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