A Study On Full-vectorial Mode-solver For Optical Waveguides Based On Meshless Finite Cloud Method

Recently,with the in-depth development of emerging Internet of Things,5G wireless communications,high-performance computing and other information technologies,Photonic Integrated Circuits(PICs)have become the technical basis of such new systems.In order to meet the requirements of highly integrated and high-performance PICs,various novel optical waveguide structures have been proposed.The performance improvement and structure optimization of optical waveguides are closely related to the full-vectorial mode solver(mode analysis).Accurate and efficient numerical analysis methods play an irreplaceable role in the mode analysis of optical waveguides.With the application of new materials and the proposal of new structures,the computational accuracy and efficiency of traditional meshed numerical methods cannot meet the needs of waveguide mode analysis,so it is urgent to find new numerical schemes.Based on the practical design of optical waveguides,a novel meshless finite cloud numerical method is proposed in this paper.A variety of full vector mode solvers of optical waveguides,including isotropic,anisotropic,flexural and nonlinear,are constructed.The mode field distribution and effective refractive index of corresponding waveguides are given.The results are compared with the published results,and the effectiveness and reliability of the method in this paper are verified.Firstly,the development of integrated optics is summarized,mainly focusing on the commonly used material platforms,including semiconductor materials,dielectric materials,polymer materials,glass materials,magnetic materials and so on,the integration of silicon-based PIC and waveguide structures manufactured by different materials.Besides,several numerical analysis methods and research statutes of optical waveguides and photonic devices are then systematically summarized,and the main contents and innovations of this thesis are also given.Then,the basic theory of optical waveguide is introduced,and the electromagnetic equations used for the modal analysis of optical waveguides and photonic devices with different media are derived.The commonly used boundary conditions for numerical analysis of different dielectric waveguides are briefly described.And,several kinds of approximate discretization schemes commonly used in meshless method are introduced in detail.Through analyzing and comparing the advantages and disadvantages of different schemes,the research tools in this paper are introduced.For the classical isotropic straight waveguide structure,a full vector meshless finite cloud(FC)mode solver of magnetic field component is constructed.This mode solver utilizes the collocation method to construct unconstrained interpolated nodes.Two typical numerical tests show that the computational accuracy of the mode solver is highly consistent with that of the standard film mode matching method,and superior to the mesh-based numerical methods,while maintaining fast convergence characteristics.For the isotropic bent waveguide structures,two full-vectorial meshless FC mode solvers based on magnetic field and electric field components are respectively proposed.These two mode solvers construct computational nodes via a non-uniform node distribution,so that the shackles of the boundary nodes are thus bypassed in construction of interior nodes,and the better computational efficiency can be achieved while accurately solving the fundamental and high-order modes of the bent waveguides.These two mode solvers have a wide range of applications along with high versatility.For transverse anisotropic waveguide structures,two full-vectorial meshless FC mode solvers based on magnetic field and electric field components are respectively proposed,which can achieve the free node distribution of clouds with different refractive indexes and effectively reduce the computational burden.Moreover,the obtained global eigenvalue matrix is a spares one,which improves the computational efficiency.In tests of typical waveguides structures show that these two mode solvers have the advantages of high computational accuracy and fast convergence.For full anisotropic waveguide structures,two full-vectorial FC mode solvers based on magnetic field and electric field components are proposed for analysis of liquid crystal waveguide structures with regular and tilted interfaces,respectively.In these two mode solvers,a new boundary treatment scheme is proposed,which can eliminate the computational difficulties caused by complex materials and irregular interfaces,and can accurately simulate the modal fields near the boundaries.Moreover,a simple and efficient iterative scheme is established by using Newton iterative method,and the convergent solutions can be obtained after only four iterations.A simple modification is introduced into the fixed meshless interpolated shape function approximation scheme,which can enforce the Kronecker property.By utilizing the complex coordinate extension,the local coordinate transformation and curve mapping technology,three meshless modified-finite cloud(M-FCM)mode solvers for isotropic complex straight waveguides.These three kinds of mode solvers can accurately calculate the guided modes of complex waveguides and complex devices with different structures,while maintaining superior computational efficiency.For nonlinear dielectric waveguide structures,a full-vectorial meshless M-FCM mode solver is proposed.Based on the full-vectorial nonlinear wave equation,a simple and efficient iterative scheme is established to solve the nonlinear dielectric waveguides with different structures.Several typical numerical tests show that the computational accuracy of this mode solver is superior to the classical finite element method(FEM)and FE-based imaginary-distance beam propagation method(FE-IDBPM).Finally,the conclusion of the whole thesis is drawn and the outlook for future work is given.