Three-dimensional alternating direction implicit finite difference time domain for cylindrical structures

In recent years, high index contrast optical waveguides have become of practical interest. Initially, waveguides with large index contrast were so lossy as to be useless. Nanotechnology has spawned new techniques in fabrication of small, pure semiconductor structures. Such guides can be pure enough and have smooth enough boundaries so as to propagate light. When the radius of a semiconductor fiber (silicon nano cylinder) becomes comparable to a wavelength of light, it is necessary to use the wave propagation theory to investigate the guiding properties of the fiber.; Finite-Difference-Time-Domain (FDTD) methods have become popular wave propagation analysis tools due to their simplicity and ease of implementation. FDTD is a powerful full wave simulation tool that is based on finite differencing of Maxwell's curl equations. The spatial and temporal derivatives are implemented using central finite differences resulting in a fully explicit leapfrog scheme that marches the discritized electric and magnetic fields forward in time. A major limitation of the FDTD is that numerical stability is constrained by the Courant-Friedrich-Levy (CFL) condition. The CFL requires a bound on the time step relative to the space increment and the material properties. The limit on the time step leads to longer simulation times when it comes to modeling complex and large structures.; Alternating Direction Implicit Finite Difference Time Domain (ADI-FDTD) technique has been recently introduced to solve electromagnetic problems. The new technique which is based on alternating direction implicit method and conventional FDTD is unconditionally stable. The time step can be arbitrarily chosen which has a potential to reduce the number of time steps by several orders of magnitude.; The thesis investigates the use of the alternating direction implicit technique for modeling cylindrical structures. The ADI-FDTD technique is introduced and compared to the conventional FDTD technique. The ADI-FDTD field update equations have been derived in cylindrical coordinates for lossless and lossy materials.; This thesis also investigates the use of the Alternating Direction Implicit Finite Difference Time Domain (ADI-FDTD) technique for modeling cylindrical structures. The three dimensional ADI-FDTD field equations have been derived in cylindrical coordinates for both lossless and lossy materials. The ADI-FDTD technique was compared to the conventional FDTD.; This thesis also investigates the application of the three dimensional ADI-FDTD technique in cylindrical coordinates to model strongly guiding optical fibers. This thesis reports the effect of time step increase on the accuracy of results.