Exploring Attribute Of Optical Soliton In Finite And Defect Modulation Lattices

When the natural diffraction of light is balanced by the self-focusing effect in-duced by the nonlinear response of media, light becomes " self-trapped" at a narrow width and does not spread in the transverse direction when propagation in nonlinear materials. This is called a spatial soliton. Spatial solitons are under intensive study these day due to their novel physics. In particular, as the method for realizing optical lattices was reported in2003. Various families of novel solitons that can not be ob-served in bulk uniform media have been discovered in modulated optical lattices. More and more attention are paid on researching the lattice solitons.With the development of material science, optically-induced method and lithog-raphy technology, various kinds of new lattices are realized. The structure of optical lattices have made the transition from periodic to nonperiodic modulation, and from one-dimensional to multi-dimensional systems. In my viewpoint, there are many more undiscovered phenomenons of solitons in one-dimensional modulated optical lattices. Take the periodic modulated lattices for example, the existence and stability of these lattice solitons always depend on the band-gap structure which correspond to lattices. Lattice solitons can only be found in gaps of lattice spectrum, and their physics are decided by the propagation constant. If take finite lattices instead of infinite ones, are these solitons under the influence of band-gap structure?Our main work focuses on propagation dynamic of solitons in finite modulation optical lattices, and solitons in combined lattices. It includes following two parts: 1. Symmetric and antisymmetric solitons in finite lattices.We propose a simple model for the realization of symmetrically and antisymmet-rically shape-preserving nonlinear waves with nonvanishing intensities at infinity. A finite lattice embedded into a defocusing saturable medium can support various fami-lies of novel solitons, including out-ofphase and in-phase solitons with symmetric and antisymmetric profiles. Although the lattice is finite, the existence and stability of soli-tons depend strongly on the band-gap structure of the corresponding infinite lattice. Saturable nonlinearity enhances the pedestal height and renormalized energy flow of solitons evidently. In particular, increasing the lattice site number or saturation degree of nonlinearity can considerably suppresses the instability of solitons. In addition, we find two branches of in-phase solitons in finite lattices and one branch of them can be dynamically stable. Our findings may provide a helpful hint for linking the solitons supported by infinite and finite lattices.2. Surface defect kink solitons.We reveal the existence of dynamically stable nonlinear defect kink modes at an interface separating a defocusing Kerr medium and an imprinted semi-infinite lattice with a positive or negative defect covering a single or several lattice sites. Increasing the number of defect sites equivalently results in a band-gap shift of lattice which in return alters the existence domain and stability properties of defect solitons. Negative defects can weaken the interaction between the oscillatory tails in neighboring lattice sites and thus lead to a significant suppression on the instability of defect solitons, especially for in-phase solitons. Our results provide an effective way for the realization of stable in-phase kink solitons.