A Novel Photonic Material for Designing Arbitrarily Shaped Waveguides in Two Dimensions

We investigate numerically optical properties of novel two-dimensional photonic materials where parallel dielectric rods are randomly placed with the restriction that the distance between rods is larger than a certain value. A large complete photonic gap (PG) is found when rods have sufficient density and dielectric contrast. Our result shows that neither long-range nor short-range order is an essential prerequisite to the formation of PGs. A universal principle is proposed for designing arbitrarily shaped waveguides, where waveguides are fenced with side walls of periodic rods and surrounded by the novel photonic materials. We observe highly efficient transmission of light for various waveguides. Due to structural uniformity, the novel photonic materials are best suited for filling up the outer region of waveguides of arbitrary shape and dimension comparable with the wavelength.Comment: 4 figure

How to construct a coordinate representation of a Hamiltonian operator on a torus

The dynamical system of a point particle constrained on a torus is quantized \`a la Dirac with two kinds of coordinate systems respectively; the Cartesian and toric coordinate systems. In the Cartesian coordinate system, it is difficult to express momentum operators in coordinate representation owing to the complication in structure of the commutation relations between canonical variables. In the toric coordinate system, the commutation relations have a simple form and their solutions in coordinate representation are easily obtained with, furthermore, two quantum Hamiltonians turning up. A problem comes out when the coordinate system is transformed, after quantization, from the Cartesian to the toric coordinate system.Comment: 17 pages, LaTeX, 1 Figure included as a compressed uuencoded postscript fil

First-Principles Study of Electronic Structure in α\alpha-(BEDT-TTF)2_2I3_3 at Ambient Pressure and with Uniaxial Strain

Within the framework of the density functional theory, we calculate the electronic structure of $\alpha$-(BEDT-TTF)$_2$I$_3$ at 8K and room temperature at ambient pressure and with uniaxial strain along the $a$- and $b$-axes. We confirm the existence of anisotropic Dirac cone dispersion near the chemical potential. We also extract the orthogonal tight-binding parameters to analyze physical properties. An investigation of the electronic structure near the chemical potential clarifies that effects of uniaxial strain along the a-axis is different from that along the b-axis. The carrier densities show $T^2$ dependence at low temperatures, which may explain the experimental findings not only qualitatively but also quantitatively.Comment: 10 pages, 7 figure

Inverse versus Normal NiAs Structure as High-Pressure Phase of FeO and MnO

The high-pressure phases of FeO and MnO were studied by the first principles calculations. The present theoretical study predicts that the high-pressure phase of MnO is a metallic normal B8 structure (nB8), while that of FeO should take the inverse B8 structure (iB8). The novel feature of the unique high-pressure phase of stoichiometric FeO is that the system should be a band insulator in the ordered antiferromagnetic (AF) state and that the existence of a band gap leads to special stability of the phase. The observed metallicity of the high-pressure and high-temperature phase of FeO may be caused by the loss of AF order and also by the itinerant carriers created by non-stoichiometry. Analysis of x-ray diffraction experiments provides a further support to the present theoretical prediction for both FeO and MnO. Strong stability of the high-pressure phase of FeO will imply possible important roles in Earth's core.Comment: 7 pages, 3 figures and 1 table; submitted to "Nature