Finite-Difference Time-Domain Analysis of Periodic Anisotropic Media

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Title: Finite-Difference Time-Domain Analysis of Periodic Anisotropic Media
Author: Oh, Chulwoo
Advisors: Michael J. Escuti, Committee Chair
Gianluca Lazzi, Committee Member
Keith Weninger, Committee Member
Abstract: The Finite-Difference Time-Domain (FDTD) method is a numerical technique for solving electromagnetic propagation and scattering problems. The FDTD method has been one of the most popular numerical tools in the computational electromagnetics since Kane Yee proposed his efficient and stable algorithm, often called the Yee algorithm. Recent rapid development in computer technologies in the last two decades allows us to have more power in computation and memory capacity, which overcomes the computationally intensive nature, the main hindrance of wide use of the FDTD method. Still, emerging new applications need modification to the original FDTD algorithm. For the applications of periodic structures such as gratings and photonic crystals, the FDTD method can be much more efficient and accurate by taking the advantage of the periodicity of structures. The simulation space can be dramatically reduced into only one unit cell by enforcing periodic boundary conditions (PBC). An efficient way of implementing PBCs is the split-field update method. The main advantage of the split-field FDTD method is its capability of wideband simulation at oblique incidence. However, the previous works were limited to materials that are either isotropic or that have diagonal tensors. Here we present a modified FDTD algorithm for periodic structures in more general anisotropic media, which incorporates the nondiagonal permittivity tensor. PBCs are implemented by using the split-field technique. Validation of the new FDTD method is done by applying it for problems of different structures and comparing the results from FDTD simulations with other analytical or numerical solutions. We report a rigorous numerical analysis of the Polarization Grating (PG) at the first time. Diffraction properties such as the diffraction efficiency and the polarization selectivity of each diffraction order are analyzed for all kinds of PGs. We discuss the effect of the grating regimes and the finite grating width on the diffraction properties of PGs. In addition, the minimum number of grating periods within a single pixel to get high diffraction effciency is presented. We apply this FDTD method, as a simulation tool, to analyze three different structures of broadband PGs. The optical performance of each structure is evaluated by the results from FDTD simulations in terms of the bandwidth for the maximum diffraction effciency. The achromatic PG using three gratings shows the best bandwidth and the twist-PG using two gratings with the opposite twist sense is found to be most attractive because of its simple structure and fairly large bandwidth. Preliminary experimental studies are also presented. Here we report a rigorous numerical analysis of polarization gratings for the first time. To this end, we develop the modified FDTD algorithm for periodic anisotropic media. We successfully demonstrate the FDTD method for a number of problems with different structures and the results from FDTD simulations show excellent agreement with other analytical or numerical solutions. Finally, we present the extensive analysis of polarization gratings and novel structures of broadband PG using our FDTD simulation tool. A package of the FDTD code written in the standard C⁄C++ language will be available in public as an open source.
Date: 2007-08-07
Degree: MS
Discipline: Electrical Engineering

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