The Study On Numerical Simulation Algorithms And Waveguide Characteristic Of Optical Waveguides And Fiber Gratings

In this thesis, optical slab waveguide, optical fiber and fiber grating is simulated with numerical simulation algorithms respectively. To improve the computation efficiency, some modification and innovation were made to the simulation algorithms. The thesis is organized as follows.In Chapter 1, a short introduction about numerical simulation of optical waveguide is presented, and a brief development history of numerical simulation of optical waveguide is outlined.In Chapter 2, a single mode slab waveguide is simulated with the two-dimensional FDBPM. With the simulation, the guided mode of the slab waveguide is calculated and compared with the analytical theory. The Matrix Pencil Method (MPM) is used to calculate the propagation constant of the guided mode. The difference of the guided mode and the propagation constant between the numerical simulation and analytical theory is about 10-4, which clarified the correctness of the numerical simulation. With conformal mapping and FDBPM, bent slab waveguide is also simulated, and the bending loss is calculated. Compared with analytical theory, the error of the bending loss is about 3%.In Chapter 3, three-dimensional ADI-FDBPM is used to simulate light propagation in optical fiber. To improve the computation efficiency, a modified algorithm which is derived by extending the Thomas method is proposed to solve a specific bend linear system during the computation with ADI-FDBPM. With the proposed algorithm, Corning SMF28 optical fiber is simulated, and the guided mode and propagation constant is calculated. The errors between the numerical and analytical result is about 10-4. Bending optical fiber is also simulated with conformal mapping and ADI-FDBPM.In Chapter 4, fiber grating is simulated with three-dimensional FDTD method. As the simulated fiber grating is very short, which contains only 16 periods, the reflected light wave at the fiber grating is quite weak. So, a method that can make the faint reflected wave distinct and legible is proposed. The proposed method is to run two simulations synchronously, one with grating, and the other with no grating; the difference between the electric field of the two simulations shows the reflected light wave at the fiber grating. With this method, light wave reflection and radiation in fiber grating and tilted fiber grating is exhibited respectively, in numerical simulation.