Complex Nonlinear Photonic Lattices: From Instabilities to Control

Abstract

Nonlinear periodic structures have become an active area of research due to many exciting possibilities of controlling wave propagation, steering and trapping. Periodicity changes the wave bandgap spectrum and therefore strongly affects propagation and localization, leading to the formation of discrete and gap solitons which have already been studied in several branches of science [1–4]. In optics, a periodic modulation of the refractive index can either be prefabricated as in photonic crystals [5] or optically induced in photorefractive materials [6–9]. Until now, several different approaches for the fabrication of photonic crystals exist [10–12]. Although these mechanisms enable a precise material structuring with periodicities adequate for optical waves, they do not allow for flexible changes of structural parameters (e.g., lattice period or modulation depth). In contrast, the optical induction in photorefractive crystals provides highly reconfigurable, wavelength-sensitive nonlinear structures which can be induced at very low power levels. When dealing with optically induced photonic lattices in these photorefractive materials, it is crucially important to consider the anisotropic properties of photorefractive crystals. The light-induced refractive index change strongly depends on orientation as well as polarization of the lattice wave [13, 14]. In particular, its orientation with respect to the c-axis of the crystal determines the symmetry of the induced pattern [15]. The shape of the induced refractive index pattern also changes with increasing lattice strength depending on the saturation of the photorefractive nonlinearity. For instance, an ordinarily polarized light pattern created by several interfering plane waves induces a change of the refractive index while propagating linearly along the crystal. The lattice wave does not ‘feel’ the periodic modulated refractive index during propagation. If the lattice is weak, i.e. it is not affected by the saturation of the photorefractive nonlinearity, the light-induced refractive index follows the light intensity distribution and forms a two-dimensional photonic lattice, being uniform in the direction of propagation. Many exciting features of non-linear light propagation have been investigated in these lattices and have been presented in chapter 5.