372 research outputs found
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
Exotic radiation from a photonic crystal excited by an ultra-relativistic electron beam
We report the observation of an exotic radiation (unconventional
Smith-Purcell radiation) from a one-dimensional photonic crystal. The physical
origin of the exotic radiation is direct excitation of the photonic bands by an
ultra-relativistic electron beam. The spectrum of the exotic radiation follows
photonic bands of a certain parity, in striking contrast to the conventional
Smith-Purcell radiation, which shows solely a linear dispersion. Key
ingredients for the observation are the facts that the electron beam is in an
ultra-relativistic region and that the photonic crystal is finite. The origin
of the radiation was identified by comparison of experimental and theoretical
results.Comment: 4 pages, 5 figure
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 , where
is the imaginary part of the corresponding resonant
eigenvalue. For example, a resonant state of the lifetime
ms and of the enhancement factor is
found at the resonant frequency GHz for the Cantor set
of the fourth generation of length L=10cm made of a medium of the dielectric
constant .Comment: 20 pages, 11 figures, to be published in Journal of the Physical
Society of Japa
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, , with where is the forward scattering
phase shift of the core hole. In contrast to previous theories, is
finite (and universal) in the limit of weak core hole potential. In the case of
weak backscattering , the exponent in the power-law dependence of
absorption on energy crosses over to a value above an energy scale , where is a dimensionless measure of the
electron-electron interactions.Comment: 8 pages + 1 postscript figure, preprint TPI-MINN-93/40-
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
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
of spheres is lower than the dielectric constant of
the background medium. If , 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 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
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 . As a
consequence, the Gaussian asymptotic decay sets in at distances that are large
compared to the magnetic length multiplied by .Comment: 16 pages, 2 figures, submitted to J. Phys. A: Math. Gen; corrected
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