Discrete Solitons In Saturable Nonlinearity Media With Parity-time Symmetric Lattices

When strong beams propagate in discrete nonlinear wave guides, there occurs coupled effect, discrete diffraction and media nonlinearity. A self-trap beam also called discrete solitons can be formed due to the delicate balance between discrete diffraction and nonlinearity. Mathematically, discrete solitons are travelling wave solutions of discrete nonlinear Schrodinger equations which generally have no analytical solutions and can only be solved by numerical method through computer. Discrete solitons can exist in media with Kerr, photorefractive and liquid-crystal and have many potential applications such as optical communication, optical switch and particle control. In recent year, since a waveguide called PT symmetric waveguide based on parity-time symmetry theory is proposed, discrete PT solitons become a hot topic. Many topics on discrete PT symmetric solitons have been reported such as Kerr media, necklace structures, alternating coupling coefficients and so on, while discrete solitons in saturable nonlinearity media with parity-time symmetric lattices are not discussed yet. Our subject focuses on the existence and stability of discrete solitons in saturable nonlinearity media with parity-time symmetric lattices.Firstly, history and background of optical solitons are studied, also the progress and the issues of optical solitons. And schematic and research significance of PT discrete solitons are as follow. Secondly, nonlinear Schrodinger equations with continuous and discrete are introduced; discrete diffraction, coupled theory and PT theory are also discussed. Numerical method such as Newton method, numerical analytical method and fourth order Runge-Kutta are emphasized. Finally, discrete Schrodinger nonlinear equations with saturable nonlinearity and parity-time symmetric are studied. Existence and stability of discrete PT soliton are obtained. Also, fourth order Runge-Kutta is used to stimulate the propagation of discrete PT solitons.The research shows that there exist two kinds of discrete solitons (plus and minus solutions), they share the same parameters but different energy flows. Plus solitons are always larger than those of minus solitons. These two kinds of solitons can be stable when stability parameters are more than zero. In most case, plus solitons are more stability while stable minus solitons only exist in small coupling coefficients. Discrete solitons with large degree of saturable nonlinearity have large energy flow. The degree of the saturable nonlinearity can affect the stability parameter; can also affect the stability of solitons. The stability lost with the increase of the coupling efficient due to the fact that the interaction between two nearby waveguides become larger and there occurs energy transfer easily.