Analysis of Special Periodic Structures with Differential Method

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Kazemi Jahromi, Ali | 2010

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 40598 (05)
University: Sharif University of Technology
Department: Electrical Engineering
Advisor(s): Mehrany, Khashayar; Rashidian, Bizhan
Abstract:
In this thesis, the Maxwell's equations are transformed into a set of ordinary differential equations and then solved in periodic structures by using the differential method (DM). The periodic structures considered in this thesis are carved in linear anisotropic, nonlinear isotropic and nonlinear anisotropic media. Different numerical issues, e.g. stability and convergence rate, are addressed by following the conventional methods, e.g. S- and R- matrix formalism, and Fourier factorization. In addition, an algorithm is proposed for fast and efficient analysis of periodic structures with identical layers. Binary gratings and photonic crystals are examples of such structures. In this algorithm, the R-matrix of the whole structure is extracted by using the R-matrix of the identical layer. As expected, the computation time becomes almost independent of the total number of identical layers in the structure and a considerable amount of calculation time is saved.
Keywords:
Photonic Crystal ; Anisotropic Media ; Differential Method ; Diffraction Gratings ; Fast Fourier Factorization

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