Analysis of Optical Waveguides and Multimodenterference Devices Using the Finite-Differencerequency-Domain Method

In this research, the ?nite-di®erence frequency- domain (FDFD) method is adoptedo analyze optical waveguides with di®erent cross-sections and related multi-modenterference (MMI) devices. The perfectly matched layer (PML) is employed as thebsorbing boundary of the computing window in the FDFD solver. Several opticalaveguides including channel waveguides, rib waveguides, optical ?bers, photonicires, and two kinds of low loss fabricated waveguides are analyzed. The conceptnd phenomena of the MMI are introduced, and we utilize the modal propagationnalysis and the FDFD mode solver to analyze and design the MMI. The MMIhenomena for di®erent input positions are also investigated. Finally, we try toesign simple MMI power splitter devices using the structure of a photonic wire and low loss etchless waveguide, respectively, and discuss the imaging length and theoupling e?ciency versus the width of the multi-mode waveguide.1 Introduction 1.1 Numerical Schemes for the Analysis of Optical Waveguides . . . . . . 1.2 Optical Multi-Mode Interference Devices . . . . . . . . . . . . . . . . 2.3 Chapter Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 The Finite-Di®erence Frequency-Domain Method 5.1 Central Di®erence Scheme . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Mode Solvers for 1-D Waveguide Problem . . . . . . . . . . . . . . . 6.2.1 The TE Polarized Wave . . . . . . . . . . . . . . . . . . . . . 6.2.2 The TM Polarized wave . . . . . . . . . . . . . . . . . . . . . 8.3 Formulae for Two-Dimensional Problems . . . . . . . . . . . . . . . . 9.4 FDFD Method with Perfectly Matched Layers . . . . . . . . . . . . . 12.5 Approximation method for the Dielectric Interfaces . . . . . . . . . . 16.5.1 Stair-Case Approximation . . . . . . . . . . . . . . . . . . . . 16.5.2 Index Average scheme . . . . . . . . . . . . . . . . . . . . . . 16.5.3 Proper Boundary Condition Matching . . . . . . . . . . . . . 17 Analysis of Two-Dimensional Optical Waveguides 25.1 Channel Waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25.2 Optical Fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26.3 Rib Waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28.4 Photonic Wire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28.5 Low Loss Silicon Photonic Wire . . . . . . . . . . . . . . . . . . . . . 30 Analyzing 3-D Multi-Mode Interference Optical Waveguide Sruc-ures 58.1 Introduction to Multi-Mode Interference Based on Self-Imaging . . . 59.1.1 Self-Imaging Principle . . . . . . . . . . . . . . . . . . . . . . 59.1.2 Multi-mode waveguides . . . . . . . . . . . . . . . . . . . . . . 59.1.3 Modal Propagation Analysis . . . . . . . . . . . . . . . . . . . 60.1.4 Multi-Mode Interference . . . . . . . . . . . . . . . . . . . . . 62.2 Procedure of Analyzing Multi-Mode Interference for Channel Waveg-ides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66.3 Numerical Results of Multi-Mode Interference for Silicon-on-Insulatorhotonic Wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69.3.1 Photonic wire . . . . . . . . . . . . . . . . . . . . . . . . . . . 69.3.2 Fabricated etchless photonic waveguide . . . . . . . . . . . . . 71 Conclusion 98ibliography 10