Dynamic Analysis Of Solitons In PT-symmetric Optical Lattices Barrier

In the classical optics, the transmission equation of beam is similar to the nonlinear Schrodinger equation in terms of mathematical expression, with both scalar approximation and paraxial approximation. When gain and absorption are periodic anti-symmetry, the beam which propagating in PT symmetric photonic crystal lattice is equivalent to a quantum system‘s potential function with symmetric parity time(PT symmetric). The non-Hermitian-Hamitonian operator corresponding to the beam has all positive real energy spectrum in specific conditions. The liner and nonlinear propagation characteristics of beams in PT-symmetric optical lattice have remarkable value both in research and application, which enable PT symmetric photonic lattice becoming a hot subject of the field of nonlinear optics around the world, currently.First, we consider a kind of optical lattice barrier with PT symmetry, which can be induced by light in photorefractive materials, and the gain and loss of the barrie r can be achieved by doping. Transmission dynamics phenomena of the ground state soliton through the barrier is analyzed by split-step-Fourier transform method. The influence of five control parameters, such as the lattice period, the modulation depth of refractive index, the intensity of gain/loss, the position of soliton’s incident point and the barrier length, on the dynamics of the soliton is taken in consideration. It turns out that, when soliton traversing through PT symmetric lattice barrier, different degrees of deflection occurs and the energy of the soliton changes. And when the width of the soliton is about a lattice period, the self- deflection is most obvious. The deflection and energy transfer is caused by the reaction formation of the left and right wings of the soliton which leads to spatial uneven distribution. Based on scanning the five control parameters, we analyze and discuss the dynamics of the soliton transmission in detail.In order to find the physical mechanism of soliton transmissio n deflection, we discuss the corresponding solution of soliton supported by different modulation depth, lattice frequency, and gain/loss intensity of PT lattice. We analyze the lattice band gap structure by using the plane wave expansion, and calculate the soliton solution by improved iterative method. As a result, the influence of the modulation depth, lattice frequency, and gain/loss intensity of the PT lattice have the same trend as the transmission deflection. By comparing the evolution of soliton solution of the linear and nonlinear modulated by PT lattice, we find that the solut ion changes from single hump to multi-peak solution, and the energy of the solution becomes decrease, and the variety of the soliton solution power is unstable.