We investigate defect modes of cholesteric liquid crystals as photonic band gap materials. For normal incidence of light, cholesteric liquid crystals exhibit total reflection for the circular polarization with the same handedness as that of cholesteric helix. However, the other orthogonal component is completely transmitted. When we replace a thin layer of liquid crystal by an isotropic material as a defect, defect modes are induced for both polarizations of incident light. We analyze the wavelength and reflectivity of the defect modes in terms of the refractive index of defect layer.

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We show that line defects can give rise to the bending and splitting of self-collimated beams in two-dimensional photonic crystals from the equifrequency contour calculations and the finite-difference time-domain simulations. The power ratio between two split self-collimated beams can be controlled systematically by varying the radii of rods or holes in the line defect. We also show that the bending and controllable splitting of self-collimated beams can be useful in steering the flow of light in photonic crystal integrated light circuits.

We propose a method to design antireflection structures to minimize the reflection of light beams at the interfaces between a two-dimensional photonic crystal and a homogeneous dielectric. The design parameters of the optimal structure to give zero reflection can be obtained from the one-dimensional antireflection coating theory and the finite-difference time-domain simulations. We examine the performance of a Mach-Zehnder interferometer utilizing the self-collimated beams in two-dimensional photonic crystals with and without the optimal antireflection structure introduced. It is shown that the optimal antireflection structure significantly improves the performance of the device.