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Photonic crystals (PhCs) have wavelength scale periodically alternating refractive indexes. Photon in such structures is subject to strong scattering, experiencing distinctive redistribution of energy, yielding interesting properties such as photonic band gaps, field enhancement, strong nonlinear optic effects and photon confinement. The modified fields also alter the propagation of light beams. By proper setup, super collimation could be realized in PhCs where beams can travel long distance without spreading, while no waveguide structure is used. Redirection of light can extend the refraction to negative range, without violating physics rules. This distinguished phenomenon has been envisioned as the core mechanism for super lens to enable sub-wavelength focusing and imaging.
The objective of this work is to theoretically model and analyze both two dimensional and three dimensional photonic crystals, esp. with anisotropic optical materials. Attention has been focused on developing of mathematical treatment for calculating the dispersive relationship and density of states. The plane wave expansion method is employed as an analysis tool.
In two dimensional photonic band gap structures, the tunable character is realized by infiltration of liquid crystal. A uniaxial crystal model is employed in the calculation. The first part deals with the design of a refraction tuning functionality. Choosing of lattice and structure parameters is discussed. The scheme is simulated with frequency difference time domain (FDTD) method. The second part lays more emphasis on the role of anisotropy introduced in the dispersive relationship and local density of states, by in-plane directional tuning.
The complicacy of three dimensional photonic crystals poses large barrier for straightforward appreciation. An analytical method is demonstrated for identification of refraction. The tool is implemented in the following investigation of three dimensional tunable structures. The effective refractive index is thereby obtained. The tuning of dispersion relationship is visualized.