17 research outputs found

    Higher-Order Methods for Solving Maxwell\u27s Equations in the Time-Domain

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    Electromagnetic interaction of split-ring resonators: The role of separation and relative orientation

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    Extinction cross-section spectra of split-ring-resonator dimers have been measured at near-infrared frequencies with a sensitive spatial modulation technique. The resonance frequency of the dimer\u27s coupled mode as well as its extinction cross-section and its quality factor depend on the relative orientation and separation of the two split-ring resonators. The findings can be interpreted in terms of electric and magnetic dipole-dipole interaction. Numerical calculations based on a Discontinuous Galerkin Time-Domain approach are in good agreement with the experiments and support our physical interpretation

    Nonlinear Wave Interaction In Photonic Band Gap Materials

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    We present detailed analytical and numerical studies of nonlinear wave interaction processes in one-dimensional (1D) photonic band gap (PBG) materials with a Kerr nonlinearity. We demonstrate that some of these processes provide efficient mechanisms for dynamically controlling so-called gap-solitons. We derive analytical expressions that accurately determine the phase shifts experienced by nonlinear waves for a large class of non-resonant interaction processes. We also present comprehensive numerical studies of inelastic interactions, and show that rather distinct regimes of interaction exist. The predicted effects should be experimentally observable, and can be utilized for probing the existence and parameters of gap solitons. Our results are directly applicable to other nonlinear periodic structures such as Bose-Einstein condensates in optical lattices. © 2006
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