Symmetry characterization of eigenstates in opal-based photonic crystals

The complete symmetry characterization of eigenstates in bare opal systems is obtained by means of group theory. This symmetry assignment has allowed us to identify several bands that cannot couple with an incident external plane wave. Our prediction is supported by layer-KKR calculations, which are also performed: the coupling coefficients between bulk modes and externally excited field tend to zero when symmetry properties mismatch.Comment: 7 pages, 5 figures, submitted to Physical Review

Strong Resonance of Light in a Cantor Set

The propagation of an electromagnetic wave in a one-dimensional fractal object, the Cantor set, is studied. The transfer matrix of the wave amplitude is formulated and its renormalization transformation is analyzed. The focus is on resonant states in the Cantor set. In Cantor sets of higher generations, some of the resonant states closely approach the real axis of the wave number, leaving between them a wide region free of resonant states. As a result, wide regions of nearly total reflection appear with sharp peaks of the transmission coefficient beside them. It is also revealed that the electromagnetic wave is strongly enhanced and localized in the cavity of the Cantor set near the resonant frequency. The enhancement factor of the wave amplitude at the resonant frequency is approximately $6/|\eta_\mathrm{r}|$, where $\eta_\mathrm{r}$ is the imaginary part of the corresponding resonant eigenvalue. For example, a resonant state of the lifetime $\tau_\mathrm{r}=4.3$ms and of the enhancement factor $M=7.8\times10^7$ is found at the resonant frequency $\omega_\mathrm{r}=367$GHz for the Cantor set of the fourth generation of length L=10cm made of a medium of the dielectric constant $\epsilon=10$.Comment: 20 pages, 11 figures, to be published in Journal of the Physical Society of Japa

Photonic Band Gaps of Three-Dimensional Face-Centered Cubic Lattices

We show that the photonic analogue of the Korringa-Kohn-Rostocker method is a viable alternative to the plane-wave method to analyze the spectrum of electromagnetic waves in a three-dimensional periodic dielectric lattice. Firstly, in the case of an fcc lattice of homogeneous dielectric spheres, we reproduce the main features of the spectrum obtained by the plane wave method, namely that for a sufficiently high dielectric contrast a full gap opens in the spectrum between the eights and ninth bands if the dielectric constant $\epsilon_s$ of spheres is lower than the dielectric constant $\epsilon_b$ of the background medium. If $\epsilon_s> \epsilon_b$, no gap is found in the spectrum. The maximal value of the relative band-gap width approaches 14% in the close-packed case and decreases monotonically as the filling fraction decreases. The lowest dielectric contrast $\epsilon_b/\epsilon_s$ for which a full gap opens in the spectrum is determined to be 8.13. Eventually, in the case of an fcc lattice of coated spheres, we demonstrate that a suitable coating can enhance gap widths by as much as 50%.Comment: 19 pages, 6 figs., plain latex - a section on coated spheres, two figures, and a few references adde

Poles and zeros of the scattering matrix associated to defect modes

We analyze electromagnetic waves propagation in one-dimensional periodic media with single or periodic defects. The study is made both from the point of view of the modes and of the diffraction problem. We provide an explicit dispersion equation for the numerical calculation of the modes, and we establish a connection between modes and poles and zeros of the scattering matrix.Comment: 6 pages (Revtex), no figure

Path-decomposition expansion and edge effects in a confined magnetized free-electron gas

Path-integral methods can be used to derive a `path-decomposition expansion' for the temperature Green function of a magnetized free-electron gas confined by a hard wall. With the help of this expansion the asymptotic behaviour of the profiles for the excess particle density and the electric current density far from the edge is determined for arbitrary values of the magnetic field strength. The asymptotics are found to depend sensitively on the degree of degeneracy. For a non-degenerate electron gas the asymptotic profiles are essentially Gaussian (albeit modulated by a Bessel function), on a length scale that is a function of the magnetic field strength and the temperature. For a completely degenerate electron gas the asymptotic behaviour is again proportional to a Gaussian, with a scale that is the magnetic length in this case. The prefactors are polynomial and logarithmic functions of the distance from the wall, that depend on the number of filled Landau levels $n$. As a consequence, the Gaussian asymptotic decay sets in at distances that are large compared to the magnetic length multiplied by $\sqrt{n}$.Comment: 16 pages, 2 figures, submitted to J. Phys. A: Math. Gen; corrected small typ

Fermi Edge Singularities and Backscattering in a Weakly Interacting 1D Electron Gas

The photon-absorption edge in a weakly interacting one-dimensional electron gas is studied, treating backscattering of conduction electrons from the core hole exactly. Close to threshold, there is a power-law singularity in the absorption, $I(\epsilon) \propto \epsilon^{-\alpha}$, with $\alpha = 3/8 + \delta_+/\pi - \delta_+^2/2\pi^2$ where $\delta_+$ is the forward scattering phase shift of the core hole. In contrast to previous theories, $\alpha$ is finite (and universal) in the limit of weak core hole potential. In the case of weak backscattering $U(2k_F)$, the exponent in the power-law dependence of absorption on energy crosses over to a value $\alpha = \delta_+/\pi - \delta_+^2/2\pi^2$ above an energy scale $\epsilon^* \sim [U(2k_F)]^{1/\gamma}$, where $\gamma$ is a dimensionless measure of the electron-electron interactions.Comment: 8 pages + 1 postscript figure, preprint TPI-MINN-93/40-

Metallo-dielectric diamond and zinc-blende photonic crystals

It is shown that small inclusions of a low absorbing metal can have a dramatic effect on the photonic band structure. In the case of diamond and zinc-blende photonic crystals, several complete photonic band gaps (CPBG's) can open in the spectrum, between the 2nd-3rd, 5th-6th, and 8th-9th bands. Unlike in the purely dielectric case, in the presence of small inclusions of a low absorbing metal the largest CPBG for a moderate dielectric constant (epsilon<=10) turns out to be the 2nd-3rd CPBG. The 2nd-3rd CPBG is the most important CPBG, because it is the most stable against disorder. For a diamond and zinc-blende structure of nonoverlapping dielectric and metallo-dielectric spheres, a CPBG begins to decrease with an increasing dielectric contrast roughly at the point where another CPBG starts to open--a kind of gap competition. A CPBG can even shrink to zero when the dielectric contrast increases further. Metal inclusions have the biggest effect for the dielectric constant 2<=epsilon<=12, which is a typical dielectric constant at near infrared and in the visible for many materials, including semiconductors and polymers. It is shown that one can create a sizeable and robust 2nd-3rd CPBG at near infrared and visible wavelengths even for a photonic crystal which is composed of more than 97% low refractive index materials (n<=1.45, i.e., that of silica glass or a polymer). These findings open the door for any semiconductor and polymer material to be used as genuine building blocks for the creation of photonic crystals with a CPBG and significantly increase the possibilities for experimentalists to realize a sizeable and robust CPBG in the near infrared and in the visible. One possibility is a construction method using optical tweezers, which is analyzed here.Comment: 25 pp, 23 figs, RevTex, to appear in Phys Rev B. For more information look at http://www.amolf.nl/research/photonic_materials_theory/moroz/moroz.htm

Comparison of flow angle variations of E-region echo characteristics at VHF and HF

In this study, characteristics of the auroral E-region echoes at two significantly different radar frequencies of 12 and 50 MHz are compared. Considered observations were performed at the Syowa Antarctic station in March of 1997 using two HF and one VHF radars at various angles with respect to the magnetic L shells. The diurnal variation of echo occurrence was found to be similar at two frequencies and consistent with previous studies. On the other hand, variation of echo occurrence with L-shell angle φ was shown to be significantly different at two frequencies. 50-MHz echoes were detected preferentially along the L shell (dominating direction of the electrojet flow) while 12-MHz echoes were detected in a broad range of azimuths with the maximum in echo occurrence at φ=40-50°. By plotting the Doppler velocity versus L-shell angle, we demonstrate that 12-MHz echoes can be divided into two populations, the high- and low-velocity echoes. The high-velocity echoes were observed mostly along the L shells while the low-velocity echoes were observed at all directions. We also show that the echo populations exhibit different variation of the Doppler velocity with the L-shell angle. We argue that while the 50-MHz echoes are related to the Farley-Buneman and gradient drift plasma instabilities, the 12-MHz echoes can have additional sources, such as the thermo-diffusion instability and/or neutral wind-related plasma instabilities

Relative energetics and structural properties of zirconia using a self-consistent tight-binding model

We describe an empirical, self-consistent, orthogonal tight-binding model for zirconia, which allows for the polarizability of the anions at dipole and quadrupole levels and for crystal field splitting of the cation d orbitals. This is achieved by mixing the orbitals of different symmetry on a site with coupling coefficients driven by the Coulomb potentials up to octapole level. The additional forces on atoms due to the self-consistency and polarizabilities are exactly obtained by straightforward electrostatics, by analogy with the Hellmann-Feynman theorem as applied in first-principles calculations. The model correctly orders the zero temperature energies of all zirconia polymorphs. The Zr-O matrix elements of the Hamiltonian, which measure covalency, make a greater contribution than the polarizability to the energy differences between phases. Results for elastic constants of the cubic and tetragonal phases and phonon frequencies of the cubic phase are also presented and compared with some experimental data and first-principles calculations. We suggest that the model will be useful for studying finite temperature effects by means of molecular dynamics.Comment: to be published in Physical Review B (1 march 2000