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Development of A Fast Converging Hybrid Method for Analyzing Three-Dimensional Doubly Periodic Structures
Wang, Feng

2013, Doctor of Philosophy, Ohio State University, Electrical and Computer Engineering.
In this dissertation, we present an efficient hybrid method based on finite element (FE) and rigorous coupled wave analysis (RCWA) to model scattering from 3-D doubly periodic dielectric structures, which has been extensively studied over decades due to its wide applications. Double periodicity RCWA method, which reduces the diffraction problem to an eigenvalue problem, is mostly used for analyzing simple periodic structures. For arbitrary shape, it suffers from slow convergence and soon becomes impractical as its computational cost grows as M^6, where M is related to the Fourier harmonics included in analysis. The 3-D finite element method (FEM) is inherently suitable for modeling arbitrary shape, however, at the cost of increased number of unknowns. Fortunately, the proposed FE/RCWA method is a balanced approach, which provides better flexibility for modeling arbitrary structures over the double periodicity RCWA method, and significantly reduces the number of unknowns compared to 3-D FEM. To further reduce the size of the problem, the mode matching method (MMM) is chosen as boundary truncation scheme among other choices such as perfectly matched layer (PML), absorbing boundary condition (ABC) and boundary integral method (BIE). MMM not only allows the truncation boundaries to be placed very close to the periodic structures, but most importantly, has the property to match evanescent diffraction orders. For comparison, the employment of PML often requires large air regions between periodic structures and truncation boundaries to eliminate reflections. We also investigate the slow convergence behavior of the proposed FE/RCWA method under certain conditions. By incorporating fast Fourier factorization (FFF) method into the FE/RCWA formulation, we significantly improve the convergence rate for TE excitation. In addition, because the FFF method preserves the surface normal vectors of the original geometry, the gap between converged results under different polarizations is order of magnitude smaller than that of original FE/RCWA method. The advantage of FE/RCWA with FFF is demonstrated by a variety of examples.
Robert Lee (Advisor)
Fernando Teixeira (Committee Member)
Robert Burkholder (Committee Member)
160 p.

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Wang, F. (2013). Development of A Fast Converging Hybrid Method for Analyzing Three-Dimensional Doubly Periodic Structures. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Wang, Feng. "Development of A Fast Converging Hybrid Method for Analyzing Three-Dimensional Doubly Periodic Structures." Electronic Thesis or Dissertation. Ohio State University, 2013. OhioLINK Electronic Theses and Dissertations Center. 25 Nov 2017.

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Wang, Feng "Development of A Fast Converging Hybrid Method for Analyzing Three-Dimensional Doubly Periodic Structures." Electronic Thesis or Dissertation. Ohio State University, 2013. https://etd.ohiolink.edu/

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