Study on the coupling of defect modes in triangular lattice photonic crystals

Abstract

Defect modes in a triangular lattice photonic crystal (PC) and the coupling characteristics of them have been investigated. As a PC of triangular lattice of air holes has large transverse electric (TE) band gap, the triangular lattice PC slab of air holes with in-plane photonic band gap and index-confinement in the third dimension is expected to serve as a good platform for compact optical devices. A point defect in the triangular lattice PC slab of air holes act as a micro-cavity and a line-defect as a waveguide because the defect modes are strongly localized about the local defects. The coupling between defect modes causes the splitting of energy bands and the power transfer between the modes. The field of localized photons in defects of PC``s oscillates with an exponentially decaying envelope because the localization in a PC is due to the strong multiple scattering. Due to the oscillatory nature of the evanescent waves of localized photons in PC``s, the symmetries of the defect modes split by coupling are not conserved, and the coupling strength is significantly influenced by not only the distance between the defects but also the field profiles of the individual mode and the relative locations of two defects. The oscillatory nature of the evanescent waves of localized photons distinguishes the coupling between defect modes in a PC from that of electronic states in a solid crystal. We have investigated channel drop tunneling processes in triangular lattice PC``s based on the coupling between defect modes. For channel drop tunneling processes, the resonant cavity system must have a mirror symmetry plane perpendicular to the bus and drop waveguides, and support even and odd resonant modes with respect to the plane. Accidental degeneracy must be forced between the two resonant modes so that the frequency and width of the resonant modes must be equal. The energy transfer rates of channel drop tunneling processes in PC slabs have been theoretically analyzed b...