ADI-FDTD+PML Analysis For Planar Lightwave Components

The steadily increasing bit-rates in modern optical communications and other photonic systems needs various photonic integrated circuits (PIC) that can processes directly optical signals in a small chip without using electronic converting way. In the meantime, fabrication methods have been improved and the tolerances required for the fabrication of PIC are beginning to be met. Also, it is necessary to develop theoretical and numerical method to investigate high index-contrast (HIC) passive components that can serve as building blocks at the end-points and nodes of WDM communications systems.In this work, some theories of optical waveguides is introduced in the second chapter, and effective index method is also studied, which may transfer the problem about three dimensional waveguide to a two dimensional problem.In the third chapter, various problems in FDTD is introduced including Yee grid, difference expressions, source excitation, boundary condition, numerical dispersion and numerical stability.In the fourth chapter, FDTD based on alternating direction implicit method (ADI-FDTD) is discussed. Applying general method and matrix method, we deduced the numerical dispersion equation for ADI-FDTD and validated its unconditional stability. Meanwhile, we prove that ADI-FDTD is an O( ?t 2) perturbation of the implicit Crank-Nicolson (CN) formulation for FDTD.In the fifth chapter, we reviewed the physics of a plane wave impinging upon a conventional lossy material. Then, we derived the condition of non-reflection for a one dimensional wave (normal incidence). Lastly, the theory of PML boundary condition was introduced.In the sixth chapter, Total-Field / Scattered-Field technique and connecting boundary condition is introduced. Then normal plane wave, TE mode in slab waveguide and plane wave in a period structure were discussed.Based on the former work, we applied ADI-FDTD+PML to the analysis of various components including guided mode grating, microcavity and single mode waveguide grating in the seventh chapter, which validated the efficiency of this algorithm.