We investigate the properties of surface modes generated at the surfaces of photonic crystals, and especially the coupling between these modes by using a plane wave expansion method. We show that the coupling behavior between defect modes in photonic crystals is quite different from that between defect modes of electrons confined in atoms. Parities of defect modes which are split due to coupling are not conserved as the interdefect distance changes. This parity nonconservation is attributed to the oscillatory nature of evanescent waves of localized photons at defects. The same is true for the surface modes of photonic crystals. Coupling of surface modes results in two kinds of modes; i.e. odd modes and even modes. Odd modes have one node in the space between two adjacent surfaces of photonic crystals, while even modes do not have any. Thus, odd modes are in higher energy state than even modes. But, as the distance between two surfaces increases, the energies of odd modes become lower than those of even modes. This shows that the energy state is determined by the energy stored in the electric fields as well as by the number of nodes which exist in the interdefect region. Also it is observed that frequency splitting of coupled modes depends not on the shape of the trucated surface but on the distance between two surfaces.
Generally, waveguides are made by removing a line of air holes in photonic crystals. In this thesis, the structure for the study of the surface-mode-coupled waveguide(SMCW) is made by cutting out some part of the two-dimensional photonic crystal. Coupled modes between localized photons at these truncated surfaces are obtained to understand the transmission phenomena of waves in this SMCW.
We get high transmittance at the even mode frequency by using finite-difference time-domain method because incident Gaussian beam has even parity, which is the same as general photonic crystal waveguide. We get high transmittance at the even mode frequency by using the finite-difference time-domain method because incident Gaussian beam has even parity, which is the same as general photonic crystal waveguides. The longer distance between two surfaces, the wider the guided frequency range of SMCW. This SMCW can have guided mode for the whole band gap which is a strong point compared with general photonic crystal wave guides. The waveguides which have smooth surfaces show higher transmittance than those have rough surfaces through the whole guided region, which means that the shape of truncated surface plays a role in the waveguide band.
