Finite-difference time-domain simulation on photonic crystal waveguide - Lai, Chieh Cheng (2008)
Photonic crystals have received much attention lately because they are very interesting candidates for the realization of photonic integrated circuits in view of their ability to confine light, guide it around tight bends and perform a wealth of other optical functionality. In this dissertation, an extensive literature review is presented, including photonic crystal theory, Maxwell’s equation for photonic media, 1 -dimensional photonic band gap, 2-dimensional photonic band gap, 3-dimensional photonic band gap and photonic crystals with defect. For numerical modeling, we adopt the well-known finite-difference time-domain (FDTD) method, which is a full-vectorial model necessary for accurate modeling photonic crystal devices. In this dissertation, the theory of FDTD and associated absorbing boundary conditions are introduced, including FDTD formulation, time stepping algorithm, stability and accuracy criterion, absorbing boundary conditions. FDTD is then implemented in MATLAB code and tested by a series of 2-dimensional examples with either Transverse Magnetic wave propagates along z direction (TMz) or Transverse Electric wave propagates along z direction (TEz). Electromagnetic simulations on photonic band gap by using FDTD with Perfect Electric Conductor (PEC) and Berenger’s Perfect Matched Layer (PML) absorbing boundary condition were presented and discussed. This study is ended by a chapter of discussions and conclusions. A list of references and all the MATLAB source codes are attached at the end of the dissertation.