The Mode Characteristics Of Nonlinear Waveguide

All-optical signal processing is widely used in the field of optical computing and optical communication, so the design for nonlinear optical waveguide device becomes an important subject. The study on the transmission characteristics of nonlinear optical waveguide has been carried out for many years, and various ways have also been given to solve the nonlinear dispersion equation. Given the fact that the previous study of nonlinear waveguide is more focused on the transmission characteristics of TE mode, this thesis is expanding the study further to the transmission characteristics of TM mode.This thesis is taking the most basic three layer slab dielectric waveguide as the object of study, and considering the nonlinear effect of dielectric; using classic Maxwell electromagnetic field theory as the study basis to deduce the Helmholtz equation based on boundary condition of electromagnetic field.This article is focusing on the transmission characteristics of optical wave in nonlinear dielectric waveguide. For the nonlinear Helmholtz equation solution,multiple study methods are used and compared in the article, for instance transmission matrix method, accurate solution, finite difference method and SVEA, etc.The first method is transmission matrix method which is in corresponding to three layer slab waveguide. If a core zone dielectric is nonlinear Kerr dielectric, then sub-layer separation method is applied. By dividing it into multiple layers, each layer is considered as an even linear dielectric. Then using the transmission matrix method along with boundary condition to deduce the Mode Eigen equation of waveguide, in this way the various modes(TE mode, TM mode) characteristics are explored and the electromagnetic field distribution is analyzed.This article also explored the transmission characteristics of three layer nonlinear waveguide TE mode through accurate solution. Based on the nonlinear Helmholtz equation of TE mode, I firstly studied the influence thatintegration constant exerted on nonlinear equation, then through the field strength relationship between two side boundaries at the core zone Kerr dielectric layer, the article finally gave the Mode Eigen equation of nonlinear waveguide TE mode. The thesis also analyzed the electromagnetic field distribution by studying TE mode characteristics with a self-made Legendre elliptic function.Exchange the differential equation into difference equation and deduce nonlinear Helmholtz equation through the method of numerical iteration.Based on the slowly varying envelope approximation(SVEA), the transmission characteristic of the TE mode in the nonlinear thin film waveguide is studied.The study found that for the Kerr medium whose core area is self-focusing, with the increase of the light power intensity, effective refractive index of guided wave increases and the transmission power rate in the core area increases, the self-focusing effect is more obvious.