Closed-Form Solutions of Dielectric Waveguides with Micro Bends

• Main Authors: Chien-ming Wang, 王建銘
• Other Authors: Hung-wen Chang
• Format: Others
• Language: zh-TW
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/5g936e

碩士 === 國立中山大學 === 光電工程研究所 === 95 === Analysis of dielectric straight bending waveguides has been a difficult problem in the past. Traditionally the task for computing bending of optical waveguides is carried out by the beam propagation method (BPM). However, due its assumptions on one-way propagation and paraxial approximation, BPM is unable to consider the reflection of dielectric straight-bent waveguides when the bending angles are large. In a straight-bent waveguide, two coordinate systems are needed to fully describe the ongoing complex scattering process in the transition region of the waveguide. It is extremely hard to analyze such an unbounded problems with two incompatible coordinate systems even for those general-purpose methods like the finite-difference, finite-element. In this thesis, we use the analytic continuity method (ACM) to deal with the boundary conditions that both the tangential electromagnetic field components must be continuous across the bending line. This method can handle the mismatch of two coordinate systems and decrease the amount of calculation and error for small bending angles. From the two coupled integral equation we can derive matrix equation via Galerkin least squared error method. The main part of this thesis contains the derivation of the approximate formula of the transmission and reflection matrices (scattering matrices) for a micro-bent waveguide. We show numerical results of various two-corner bends using cascading of these scattering matrices.