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Nonlinear Effects in One-Dimensional Photonic Lattices

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Book cover Nonlinearities in Periodic Structures and Metamaterials

Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 150))

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Abstract

Optical waves propagating in photonic periodic structures are known to exhibit a fundamentally different behavior when compared to their homogeneous counterparts in bulk materials. In such systems the spatially periodic refractive index experienced by light waves is analogous to the situation in crystalline solids, where electrons travel in a periodic Coulomb potential [1]. Consequently, the propagating extended (Floquet Bloch) modes of a linear periodic optical system form a spectrum that is divided into allowed bands, separated by forbidden gaps, too, and the two different physical systems share most of their mathematical description. Photonic band-gap materials, which may be artificially fabricated to be periodic in three, two, or only one dimension, hold strong promise for future photonic applications like miniaturized all-optical switches, filters, or memories [2]. Here novel opportunities are offered when nonlinear material response to light intensity is taken into account. When studying such nonlinear photonic crystals it turns out that light propagation is governed by two competing processes: linear coupling among different lattice sites and energy localization due to nonlinearity. For an exact balance of these counteracting effects self-localized states can be obtained, which are called lattice solitons [3–6].

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  1. Institute of Physics and Physical Technologies, Clausthal University of Technology, Leibnizstr. 4, 38678, Clausthal-Zellerfeld, Germany

    Detlef Kip & Milutin Stepić

  2. Vinča Institute of Nuclear Sciences, 522, 11001, Belgrade, Serbia

    Milutin Stepić

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  1. Detlef Kip
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  1. Inst. Angewandte Physik, Universität Münster, Corrensstr. 2-4, Münster, 48149, Germany

    Cornelia Denz

  2. MPI für Physik Komplexer Systeme, Nöthnitzer Str. 38, Dresden, 01187, Sachsen, Germany

    Sergej Flach

  3. Research School of Physical Sciences &, Engineering, Australian National University, Canberra, 0200, Aust Capital Terr, Australia

    Yuri S. Kivshar

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Kip, D., Stepić, M. (2010). Nonlinear Effects in One-Dimensional Photonic Lattices. In: Denz, C., Flach, S., Kivshar, Y. (eds) Nonlinearities in Periodic Structures and Metamaterials. Springer Series in Optical Sciences, vol 150. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02066-7_1

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