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.

We experimentally and theoretically demonstrate subwavelength scale localization of spoof surface plasmon polaritons at a point defect in a two-dimensional groove metal array. An analytical expression for dispersion relation of spoof surface plasmon polaritons substantiates the existence of a band gap where a defect mode can be introduced. A waveguide coupling method allows us to excite localized spoof surface plasmon polariton modes and measure their resonance frequencies. Numerical calculations confirm that localized modes can have a very small modal volume and a high Q factor both of which are essential in enhancing light-matter interactions. Interestingly, we find that the localized spoof surface plasmon polariton has a significant toroidal dipole moment, which is responsible for the high Q factor, as well as an electric quadrupole moment. In addition, the dispersion properties of spoof surface plasmon polaritons are analyzed using a modal expansion method and numerical calculations.

A two-dimensional photonic crystal asymmetric Mach-Zehnder filter (AMZF) based on the self-collimation effect is studied by numerical simulations and experimental measurements in microwave region. A self-collimated beam is effectively controlled by employing line-defect beam splitters and mirrors. The measured transmission spectra at the two output ports of the AMZF sinusoidally oscillate with the phase difference of pi in the self-collimation frequency range. Position of the transmission peaks and dips can be controlled by varying the size of the defect rod of perfect mirrors, and therefore this AMZF can be used as a tunable power filter.

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We study the transmission of water waves propagating in finite-size two-dimensional periodic structures which consist of bottom-mounted cylinders using the multiple-scattering method. Complete band gaps exist between the first and the second bands in square and triangular periodic structures, as well as one modeled on a graphite atomic lattice. We investigate the dependence of the band edges on the filling fraction. The graphite-type structure shows the band gap at a lower filling fraction than the others. Therefore, the graphite-type structure may be more suitable for practical coastal protection. We also calculate the first-order force on cylinders located along the symmetry direction.