Wavelength-scale photonic crystal cavities toward high-efficiency unidirectional photon sources

Abstract

In Chapter 1, we review the basic background of photonic crystals including conservation laws originating from various structural symmetries. Then, we present an overview of this thesis. In Chapter 2, we derive the Purcell factor which accounts for the spontaneous emission modification by a microcavity whose dimension is comparable with the emission wavelength. Although the spontaneous emission itself can only be justified by a rigorous quantum theory where both the atom and the radiation field are quantized, the well-known Fermi\`s Golden Rule can be applied to the calculation of the spontaneous emission rate. In Chapter 3, we explain how the finite-difference time-domain (FDTD) method works. Begining with the discretization of the one-dimensional scalar wave equation, underlying principles including `numerical dispersion\` and `numerical stability\` will be discussed. Then, we show how the original Maxwell equations are expressed in terms of the finite-differences. We present very useful conversion rules which relate the FDTD results to the values in real world. As applications of the FDTD method, we give detailed explanations on the `contour FDTD\` and the far-field simulation. In Chapter 4, degeneracy of resonant modes in two-dimensional photonic crystal cavities are investigated using the symmetry relations. The two-dimensional photonic crystal cavity tends to have either a pair of doubly degenerate modes or nondegenerate modes. We derive simple relations between degenerate modes without using a rigorous group theory. These relations are useful for classifying the resonant modes into degenerate pairs and nondegenerate ones. In Chapter 5, hexagonal ring-type resonators defined by two-dimensional photonic crystal waveguides are proposed and demonstrated. Lasing actions are observed from the photonic crystal ring resonator patterned on a free-standing slab with InGaAsP active layers emitting near 1.55 $\\mu{\\rm m}$. For a ...