Linearization Of Nonlinear Optical Cross Mode Modulation And Its Applications

At present,the transmission capacity of single-mode fiber-optic communication systems is close to the Shannon limit.In order to further expand the optical communication system to support the growing demand for data transmission,space division multiplexing technology has received extensive attention in recent years.However,it is very challenging to analyze the inevitable nonlinear interaction between multiple modes simply and intuitively.Meanwhile,nonlinear cross-mode modulation(XMM)generally exists in materials with third-order nonlinear polarization due to automatic phase matching.When the number of interacting modes in the system is large,using the traditional numerical simulation method,namely multimode nonlinear Schr(?)dinger equations(MM-NLSE),is complicated and timeconsuming to simulate the evolution of the light under the influence of the XMM effect,and the most important thing is that such approach lends no insight to the physical beyond.Therefore,it is of great practical significance to develop a linear method to find out the hidden linear characteristics of the nonlinear system,so as to solve the evolution of the light analytically with the transmission and display the physics beyond intuitively.In addition,after linearizing the nonlinear effects,we can describe the complex nonlinear system with a simple linear method.Due to the difficulties in experimental and theoretical studies,most topological photonics research is based on linear effects,however nonlinearities may introduce more novel physical phenomena.Therefore,applying the linearization model in the complex nonlinear topological photonic system is helpful to analyze the tune of the topological phase of the topological photonic system introduced by nonlinear effects,which has important scientific significance and potential for application.In this thesis,the linearization of XMM effect in multimode nonlinear optical waveguides and its application in nonlinear systems are studied.Firstly,for the application scenario of optical fiber,a linearization model of XMM effect in degenerate mode group with random mode coupling is constructed and verified by simulation.Then,for the application scenario of mode preserving waveguides,the space-dependent Hamiltonian of the XMM effect without random mode coupling is derived,and the mode evolution of the probe light under different initial states of pump light is analyzed in detail.In terms of applications,the fast system design of arbitrary vector mode conversion is realized based on the the linearized model.Furthermore,by combining the linearized model with the nonlinear topological photonic system,a detailed theoretical and simulation research on the optically reconfigurable spin-valley Hall effect based on the XMM effect is carried out.The main research results of this thesis are as follows:Firstly,based on the coupled mode theory,a linearization method is proposed to linearize the XMM effect in degenerate mode group with random mode coupling in fibers,and based on this,a fast design method for arbitrary vector mode conversion is proposed.In the case of pump-probe situation,an equivalent linear system to the probe light is constructed by decoupling the pump light and the probe light in the nonlinear optical systems.Based on the linear superposition principle of linear systems,the shortcomings of complex and timeconsuming in solving XMM effect based on MM-NLSE is solved.The research shows that the Hamiltonian of the system to the probe light is determined by the initial state of the pump light.Additionally,the mode of the pump light is always one of the eigenstate of the nonlinear system,and the eigenvalue corresponding to the pump light mode is twice that of the other eigenstates.The Hamiltonian method is helpful to understand the physical nature beyond the field evolution process intuitively.Secondly,for mode preserving waveguides,a mathematical framework for linearizing the XMM effect in the mode group without random mode coupling is proposed,and the model is verified by comparing with the precession equation and the nonlinear coupled mode equation.With the help of the Poincaré sphere,the evolution of the mode of the probe light under different initial states of the pump light is displayed intuitively.The research show that the Hamiltonian of the pump light can be diagonalized in two special cases,i.e.,degenerate and non-degenerate.In these cases,the Hamiltonian of the probe light is determined by the initial state of the pump light and evolves periodically with the transmission distance,which is fundamentally different from the previous Hamiltonian with random mode coupling.Thirdly,based on the linearized model,a large-capacity optically reconfigurable topological photonic integrated device is designed.An experimentally feasible scheme for realizing optically reconfigurable spin-valley Hall effect is proposed by exploiting the Kerr nonlinear effect(the XMM effect)of coupled microring resonators.The research shows that the optical nonlinear effect can be used as a flexible means to optically control the Hamiltonian of the probe light.For example,changing the initial input pumping conditions can change the topological properties of the system.Based on the microring resonator array,simultaneously independent manipulation of the two topological degrees of freedom(i.e.,spin and valley)is achieved for the first time in the optical system,thereby doubling the topological transmission channel of the optical communication system.