Nonlinear light propagation in photonic crystal fibers filled with nematic liquid crystals

In this work nonlinear light propagation in a photonic crystal fiber (PCF) infiltrated with a nematic liquid crystal (NLC) is presented. Such a photonic structure, called the photonic liquid crystal fiber (PLCF), combines the passive PCF and the active NLC guest mixture. The analyzed configuration with a periodic modulation of spatial refractive index distribution corresponds to the matrix of waveguides. This kind of structure can be controlled by optical power and additionally by temperature and it allows for studying variety of discrete optical phenomena. For properly chosen parameters of the analyzed fiber, discrete diffraction in the linear case and generation of the discrete spatial soliton in nonlinear regime can be obtained. In this paper a possibility of the transverse light localization and delocalization due to both focusing and defocusing Kerr-type nonlinearity was analyzed. In the case of the positive nonlinearity the refractive index increases as a function of light intensity in such a way that the stronger guiding of the light within NLC cores is obtained. Light modifies the refractive index distribution inducing a defect in the periodic structure. That can lead to the situation in which light becomes self-localized and its diffractive broadening is eliminated. Eventually the discrete soliton can be created. In the case of negative nonlinearity, the difference between NLC waveguides and glass refractive indices decreases and the beam guidance becomes weaker for higher light intensities. In such a case the generation of the bright soliton is possible only in the regime of negative discrete diffraction: However, in the case of defocusing nonlinearity a decrease of refractive index with the optical power can lead to the bandgap shifting. The incident beam with a frequency initially within a bandgap is then turned outside the bandgap resulting in changing of the propagation mechanism to the modified total internal reflection.