Study On The Optical Soliton Waves In PT Symmetric Optical Lattice

In this dissertation,we have studied the complex soliton wave in PT(parity-time)symmetric optical lattice.The PT lattice is formed by modulating the complex refractive index in the optical medium.The optical waveguide array is different from the traditional one.It is shown that the gain and loss properties are similar to those of real media,so it is of great practical significance to study soliton waves in the PT lattice.The solitons in the PT lattice satisfy the complex structure,that is,the PT lattice solitons have both real and imaginary components.The complex structure makes the soliton form rich and varied,and the soliton theory can be well improved.In the field of nonlinear optics,the description of soliton model equation is mainly nonlinear Schrodinger(NLS)equation,and solution of the equation is the soliton.We use some numerical algorithms to solve the NLS equation,which includes Newton iteration method,the square operator method(SOM)and the modified square operator method.In order to analyze the stability of solitons,the split step Fourier algorithm(Split-step FFT)and the four order Runge Kutta method can be used to simulate the soliton transmission.The key to the study of lattice solitons is to obtain the band gap structure.Because the different band gaps exist different solitons.The band gap can be obtained by the plane wave expansion method.The soliton model discussed in this dissertation is the PT symmetric lattice in the diffusive nonlinear media driven by the quadratic electro-optic effect.The so-called diffusion refers to the change of the refractive index of a point in the media is not only related to the intensity of the point,but also the light intensity distribution near the point and even the whole medium.The results show that the soliton solutions of PT symmetry can be obtained in the nonlinear diffusion media.The real part of these solitons is even symmetry,and the imaginary part is odd symmetry.When the nonlinearity is self-focusing,solitons exist in the semi-infinite gap,and the existence and stability interval is limited.When the nonlinearity is self-defocusing,soliton-s can only be found in the first gap.The energy of solitons in nonlinear diffusion increases sharply and becomes unstable in a certain interval.We also discuss the non-PT symmetric solitons in PT symmetric lattices pioneering.We find that a series of asymmetric PT optical solitons with continuous change according to certain laws exist along with the PT symmetric solitons.That isto say,for certain propagation constant,if there is a PT symmetric soliton,there will be a series of corresponding asymmetric solitons.These asymmetric solitons evolve with the energy ratio of the real part to imaginary part in a fixed range.The most important is that when the propagation constant is determined,the intensity of these asymmetric solitons is exactly the same as that of the PT symmetric solitons.It also implies that the derived asymmetric solitons have the same stability as the PT symmetric solitons.And this can be confirmed by simulating soliton transmission with the method of split-step Fourier.It means that it is able to transmit more widely and more common form of solitons in the PT symmetric lattice.It will greatly enrich the types of PT solitons.