No Arabic abstract
The asymptotic analysis of the radiation pattern of a classical dipole in a photonic crystal possessing an incomplete photonic bandgap is presented. The far-field radiation pattern demonstrates a strong modification with respect to the dipole radiation pattern in vacuum. Radiated power is suppressed in the direction of the spatial stopband and strongly enhanced in the direction of the group velocity, which is stationary with respect to a small variation of the wave vector. An effect of radiated power enhancement is explained in terms of emph{photon focusing}. Numerical example is given for a square-lattice two-dimensional photonic crystal. Predictions of asymptotic analysis are substantiated with finite-difference time-domain calculations, revealing a reasonable agreement.
A novel polarizer made from two-dimensional photonic bandgap materials was demonstrated theoretically. This polarizer is fundamentally different from the conventinal ones. It can function in a wide frequency range with high performance and the size can be made very compact, which renders it useful as a micropolarizer in microoptics.
According to a recent proposal [S. Takayama et al., Appl. Phys. Lett. 87, 061107 (2005)], the triangular lattice of triangular air holes may allow to achieve a complete photonic band gap in two-dimensional photonic crystal slabs. In this work we present a systematic theoretical study of this photonic lattice in a high-index membrane, and a comparison with the conventional triangular lattice of circular holes, by means of the guided-mode expansion method whose detailed formulation is described here. Photonic mode dispersion below and above the light line, gap maps, and intrinsic diffraction losses of quasi-guided modes are calculated for the periodic lattice as well as for line- and point-defects defined therein. The main results are summarized as follows: (i) the triangular lattice of triangular holes does indeed have a complete photonic band gap for the fundamental guided mode, but the useful region is generally limited by the presence of second-order waveguide modes; (ii) the lattice may support the usual photonic band gap for even modes (quasi-TE polarization) and several band gaps for odd modes (quasi-TM polarization), which could be tuned in order to achieve doubly-resonant frequency conversion between an even mode at the fundamental frequency and an odd mode at the second-harmonic frequency; (iii) diffraction losses of quasi-guided modes in the triangular lattices with circular and triangular holes, and in line-defect waveguides or point-defect cavities based on these geometries, are comparable. The results point to the interest of the triangular lattice of triangular holes for nonlinear optics, and show the usefulness of the guided-mode expansion method for calculating photonic band dispersion and diffraction losses, especially for higher-lying photonic modes.
A theoretical study of photonic bands for one-dimensional (1D) lattices embedded in planar waveguides with strong refractive index contrast is presented. The approach relies on expanding the electromagnetic field on the basis of guided modes of an effective waveguide, and on treating the coupling to radiative modes by perturbation theory. Photonic mode dispersion, gap maps, and intrinsic diffraction losses of quasi-guided modes are calculated for the case of self-standing membranes as well as for Silicon-on-Insulator structures. Photonic band gaps in a waveguide are found to depend strongly on the core thickness and on polarization, so that the gaps for transverse electric and transverse magnetic modes most often do not overlap. Radiative losses of quasi-guided modes above the light line depend in a nontrivial way on structure parameters, mode index and wavevector. The results of this study may be useful for the design of integrated 1D photonic structures with low radiative losses.
Dipole-dipole interaction between two two-level `atoms in photonic crystal nanocavity is investigated based on finite-difference time domain algorithm. This method includes both real and virtual photon effects and can be applied for dipoles with different transition frequencies in both weak and strong coupling regimes. Numerical validations have been made for dipoles in vacuum and in an ideal planar microcavity. For dipoles located in photonic crystal nanocavity, it is found that the cooperative decay parameters and the dipole-dipole interaction potential strongly depend on the following four factors: the atomic position, the atomic transition frequency, the resonance frequency, and the cavity quality factor. Properly arranging the positions of the two atoms, we can acquire equal value of the cooperative decay parameters and the local coupling strength. Large cooperative decay parameters can be achieved when transition frequency is equal to the resonance frequency. For transition frequency varying in a domain of the cavity linewidth around the resonance frequency, dipole-dipole interaction potential changes continuously from attractive to repulsive case. Larger value and sharper change of cooperative parameters and dipole-dipole interaction can be obtained for higher quality factor. Our results provide some manipulative approaches for dipole-dipole interaction with potential application in various fields such as quantum computation and quantum information processing based on solid state nanocavity and quantum dot system.
Experimental results on the dislocation dynamics in a two-dimensional plasma crystal are presented. Edge dislocations were created in pairs in lattice locations where the internal shear stress exceeded a threshold and then moved apart in the glide plane at a speed higher than the sound speed of shear waves, $C_T$. The experimental system, a plasma crystal, allowed observation of this process at an atomistic (kinetic) level. The early stage of this process is identified as a stacking fault. At a later stage, supersonically moving dislocations generated shear-wave Mach cones.