Dynamics Of Optical Solitons In Modulated Optical Lattices

In nonlinear materials, when the natural diffraction of light is balanced by the self-focusing effect, the beam will be self-trapped and does not spread in the transverse direction with the propagation distance. Such nonlinear modes are called spatial soli-ton. In 2003, the method for realizing optical lattices with variable modulation depths and periods was reported. Since then, special attention has been paid to lattice solitons. Many properties of solitons that cannot be observed in bulk uniform nonlinear media have been discovered in modulated lattices. With the advancement of optically-induced method and lithography technology,the recent years have witnessed the transition of optical lattice solitons from periodic to nonperiodic linear refractive index modulation, such as radial symmetry modulation Bessel lattices, Mathieu lattices, parabolic lattices and chirped lattices etc. In physics, optical lattices with periodic refractive modula-tion correspond to a band-gap structure. Lattice solitons emerge as localized nonlinear modes in gaps of lattice spectrum. However, nonperiodic lattices have no correspond-ing band-gap structures. On the other hand, defects and defect states exist in a variety of lattice modulated linear and nonlinear systems, including solid state physics, photonic crystals, and Bose-Einstein condensates.They provide novel physics for the formation, manipulation, reconstruction of op-tical solitons and enrich the potential applications of solitons as information storage bits in all-optical drive, light switching and optical communication etc. Our main work focuses on propagation dynamic of solitons in modulation optical lattices. It includes following three parts:1. Two-color solitons in chirped photonic lattices.How are the properties of two-color localized nonlinear modes supported by one-dimensional chirped photonic lattices imprinted in quadratic media? When chirp rate and phase mismatch on the two-color solitons are varied, what is going to happen? The results were shown:various families of two-color soliton solutions are found. In con-trast to the unchirped lattices, chirped lattices can enhance the stability of two-color solitons. Odd solitons can be completely stable provided that the chirp rate exceeds a critical value, even for varying phase mismatches. We also study the excitation, unpack-ing, and oscillation of two-color solitons in chirped lattices. Our results may enrich the potential applications of two-color solitons in all-optical communications. Also, our results presented here might be relevant to suitable atomic-molecular Bose-Einstein condensates held in optical chirped lattices.2. Spatial solitons in photonic lattices with large-scale defects.We address the existence, stability and propagation dynamics of solitons supported by large-scale defects surrounded by the harmonic photonic lattices imprinted in the defocusing saturable nonlinear media. Several families of soliton solutions, including flat-topped, dipole-like and multipole-like solitons, can be supported by the defected lattices with different height of defects. The width of existence domain of solitons is solely determined by the saturable parameter. The existence domain of various types of solitons can be shifted by the variation of defect size, lattice depth and soliton order. We show that the solitons in our model are stable in a wide parameter window provided that the propagation constant exceeds a critical value, which is in sharp contrast to the stability of soliton trains supported by periodic lattices imprinted in defocusing saturable nonlinear media.3. Multi-peaked fundamental and vortex solitons in azimuthally modulated Bessel lattices in defocusing media. We demonstrate the existence, the propagation, the stability of azimuthon-like solitons and azimuthons supported by azimuthally modulated Bessel lattices imprinted in defocusing media. The so-called azimuthons is a novel class of spatially local-ized self-trapped ringlike singular optical beams in nonlinear media. This concept provided an important missing link between the radially symmetric vortices and ro-tating soliton clusters. The aim of this section is two-fold:Firstly, we investigated a class of self-tapped optical structures azimuthon-like solitons supported by the first-order azimuthally modulated Bessel lattices imprinted in defocusing nonlinear media, whose profiles resemble the "azimuthons" proposed by A. S. Desyatnikov in 2005. Azimuthon-like solitons are stable in their entire existence domains. Secondly, We found azimuthons with high topological charges in Bessel lattices modulated azimuthally and elucidated their existence and stability properties. We revealed that the "stability rule" of azimuthons in defocusing cubic media is quite the reverse comparing with the cases in the focusing media. The result is in good agreement with the conclusion given by B. Terhalle et al. where the stability of discrete vortex solitons supported by hexag-onal photonic lattices in focusing media is opposite to the stability in the defocusing one. Note that stable azimuthons are only found in media with nonlocal responses after 2005. Thus, to the best of our knowledge, our study provides the first example of stable azimuthons in nonlinear media with a local response.