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Effective Medium Properties of 2D Finite Photonic Crystal

Author: ChenWei
Tutor: ZengMing
School: National University of Defense Science and Technology
Course: Optical Engineering
Keywords: Photonic crystal Scattering matrix Equivalent group velocity refractive index Dispersion curve Cascade structure
CLC: O734
Type: Master's thesis
Year: 2008
Downloads: 38
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Abstract


The concept of photonic crystals since 1987 by E.Yablonovitch and S.John, this special material, has aroused widespread concern, the series also will be carried out for the theoretical study of photonic crystals. In this thesis, the scattering matrix method as a tool focuses on the two-dimensional finite periodic photonic crystal structure of the the equivalent group velocity refractive index of this electromagnetic characteristics. Scattering matrix method is an effective method for the analysis of two-dimensional finite periodic structure. Scattering matrix of the papers from a single media or metal cylinder, the transition to the single-cycle column structure of the scattering matrix, and then expanded to the ideal photonic crystal structure and limited cycle column structure, a more detailed derivation of the relevant scattering matrix. Thereby establishing the scattering matrix algorithm, and use this algorithm to analyze the electromagnetic properties of two-dimensional ideal photonic crystal structure and two-dimensional finite periodic photonic crystal structure. First, the study of the band structure of the two-dimensional ideal photonic crystal structure. Calculated band diagram of the dielectric and the metal ideal two-dimensional photonic crystal structure, results show that: the square lattice photonic crystal structure of the TM mode the direction of the band gap of the complete band gap, TE mode exist; square lattice the metal column photonic crystal structure of TM mode The presence of the cutoff frequency, the TE-mode exists flat belts. TM mode on the square lattice photonic crystal structure, with the the column relative permittivity increase the band gap first increases, reaches a maximum value slightly decreases, the lower edge of the forbidden band downward trend; With column radius increases, the band gap first increases, reaches a maximum and then decreases, the lower edge of the forbidden band also showed a downward trend. Second, the study of the eigenmodes of the two-dimensional finite periodic photonic crystal structure and effective medium characteristics. The class structure of the dispersion curves and transmission spectra calculated results show: the band edge position with the increase of the number of layers, the dispersion curve tends to remain unchanged, an increase in the number of in-band mode, and the band edge ideal photonic crystal structure with Figure some of the energy band is one to one; in the case of large-rise, the structure of the equivalent refractive index of the group velocity is almost not changed with the changes in the number of layers; on different frequency bands and different angles of incident light, the structure of the equivalent The refractive index of the group velocity is significantly different. This suggests that the two-dimensional finite periodic photonic crystal is equivalent to the anisotropy of the dispersion medium. Finally, two-dimensional finite periodic photonic crystal structure analysis of dielectric and metal cascade eigenmodes. The results show: the forbidden band in the frequency range of the photonic crystal, the finite-period photonic crystal cascade structure supports the waveguide mode of the high Q values; and showed an increasing trend as the waveguide width increases, the number of waveguide modes; these waveguide modes Q values ??tended to increase with the increase in the intrinsic frequency or the number of layers of finite periodic structure. This indicates that the light on the frequency range of the band gap, the cascade of two-dimensional finite periodic photonic crystal structure is actually an ideal waveguide.

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CLC: > Mathematical sciences and chemical > Crystallography > Crystal physics > The optical properties of the crystal
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