Photonic Lattices

Photonic crystals represent a special type of optical waveguides in which it is possible to completely control the propagation of light by changing the parameters of the system, such as refractive index and grating period of the medium. Due to the periodicity of the system, corresponding energy spectrum related to the allowed and forbidden bands for the propagation of light can be defined. This zonal structure resembles to that developed in the solid state physics for electrons moving through the crystalline lattice. Depending on the structure of photonic crystals, three types can be distinguished: one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) photonic crystals. With the increase of dimensionality of the system its energy spectrum becomes more complex, which in turn increases the ability to control linear and nonlinear propagation of light.

1D photonic crystals are lattices composed of mutually parallel optical waveguides placed at certain distance, so the weak (linear) coupling between neighboring elements of the lattice is provided. In these periodic systems different effects, such as Bloch oscillations, discrete diffraction and various localized structures may occur. Such phenomena have no counterpart in homogenous systems. The presence of nonlinearities in mentioned lattices can lead to the formation of spatially localized structures - solitons, either within the semi-infinite forbidden band (discrete solitons), or within gaps of energy spectrum (gap solitons).

The different geometry of photonic systems significantly influences the type of localized solutions that may occur in the observed photonic lattices. Some examples of 1D photonic crystals are lattices with defects and binary lattices. Defects in photonic lattices represent irregularities in the grating periodicity. They can occur as a result of concatenation of two (not necessarily identical) waveguide gratings whose mutual distance can be controlled during the manufacturing process. Binary lattice is a special type of superlattices in which is introduced periodical change in the width of the lattice channels (so the distance between the channels remains the same) or in the distance between the channels, whereby the width of the channels is kept constant.

Moreover, for particular geometries, conditions neccessary for destructive wave interference can be achived without presence of disorder, defects or nonlinearity. Such systems are known as flat band systems, due to their energy spectra containing a perfectly flat energy band that provides diffractionless light propagation.

One of our research interests is to examine the linear and nonlinear effects accompanying the propagation of visible laser light through a different (1D) photonic lattices made of material with a saturable nonlinearity, such as, for example, lithium niobate (LiNbO3). Due to the nonlinear response of these materials to the intensity of incident radiation, the light passing through the photonic lattice causes local change in refractive index, providing necessary conditions for the self-localization along the lattice. Beside this, we are also studying localization phenomena in linear and nonlinear photonic lattices with defects, disorder or specific geometry.

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