92 research outputs found
Singularities in Speckled Speckle
Speckle patterns produced by random optical fields with two (or more) widely
different correlation lengths exhibit speckle spots that are themselves highly
speckled. Using computer simulations and analytic theory we present results for
the point singularities of speckled speckle fields: optical vortices in scalar
(one polarization component) fields; C points in vector (two polarization
component) fields. In single correlation length fields both types of
singularities tend to be more{}-or{}-less uniformly distributed. In contrast,
the singularity structure of speckled speckle is anomalous: for some sets of
source parameters vortices and C points tend to form widely separated giant
clusters, for other parameter sets these singularities tend to form chains that
surround large empty regions. The critical point statistics of speckled speckle
is also anomalous. In scalar (vector) single correlation length fields phase
(azimuthal) extrema are always outnumbered by vortices (C points). In contrast,
in speckled speckle fields, phase extrema can outnumber vortices, and azimuthal
extrema can outnumber C points, by factors that can easily exceed for
experimentally realistic source parameters
Optical Mobius Strips in Three Dimensional Ellipse Fields: Lines of Circular Polarization
The major and minor axes of the polarization ellipses that surround singular
lines of circular polarization in three dimensional optical ellipse fields are
shown to be organized into Mobius strips. These strips can have either one or
three half-twists, and can be either right- or left-handed. The normals to the
surrounding ellipses generate cone-like structures. Two special projections,
one new geometrical, and seven new topological indices are developed to
characterize the rather complex structures of the Mobius strips and cones.
These eight indices, together with the two well-known indices used until now to
characterize singular lines of circular polarization, could, if independent,
generate 16,384 geometrically and topologically distinct lines. Geometric
constraints and 13 selection rules are discussed that reduce the number of
lines to 2,104, some 1,150 of which have been observed in practice; this number
of different C lines is ~ 350 times greater than the three types of lines
recognized previously. Statistical probabilities are presented for the most
important index combinations in random fields. It is argued that it is
presently feasible to perform experimental measurements of the Mobius strips
and cones described here theoretically
Optical M0bius Strips in Three Dimensional Ellipse Fields: Lines of Linear Polarization
The minor axes of, and the normals to, the polarization ellipses that
surround singular lines of linear polarization in three dimensional optical
ellipse fields are shown to be organized into Mobius strips and into structures
we call rippled rings (r-rings). The Mobius strips have two full twists, and
can be either right- or left-handed. The major axes of the surrounding ellipses
generate cone-like structures. Three orthogonal projections that give rise to
15 indices are used to characterize the different structures. These indices, if
independent, could generate 839,808 geometrically and topologically distinct
lines; selection rules are presented that reduce the number of lines to 8,248,
some 5,562 of which have been observed in a computer simulation. Statistical
probabilities are presented for the most important index combinations in random
fields. It is argued that it is presently feasible to perform experimental
measurements of the Mobius strips, r-rings, and cones described here
theoretically
Short and Long Range Screening of Optical Singularities
Screening of topological charges (singularities) is discussed for paraxial
optical fields with short and with long range correlations. For short range
screening the charge variance in a circular region with radius grows
linearly with , instead of with as expected in the absence of
screening; for long range screening it grows faster than : for a field whose
autocorrelation function is the zero order Bessel function J_{0}, the charge
variance grows as R ln R$. A J_{0} correlation function is not attainable in
practice, but we show how to generate an optical field whose correlation
function closely approximates this form. The charge variance can be measured by
counting positive and negative singularities inside the region A, or more
easily by counting signed zero crossings on the perimeter of A. \For the first
method the charge variance is calculated by integration over the charge
correlation function C(r), for the second by integration over the zero crossing
correlation function Gamma(r). Using the explicit forms of C(r) and of Gamma(r)
we show that both methods of calculation yield the same result. We show that
for short range screening the zero crossings can be counted along a straight
line whose length equals P, but that for long range screening this
simplification no longer holds. We also show that for realizable optical
fields, for sufficiently small R, the charge variance goes as R^2, whereas for
sufficiently large R, it grows as R. These universal laws are applicable to
both short and pseudo-long range correlation functions
Singularities in Speckled Speckle: Screening
We study screening of optical singularities in random optical fields with two
widely different length scales. We call the speckle patterns generated by such
fields speckled speckle, because the major speckle spots in the pattern are
themselves highly speckled. We study combinations of fields whose components
exhibit short- and long-range correlations, and find unusual forms of
screening
Signed zeros of Gaussian vector fields-density, correlation functions and curvature
We calculate correlation functions of the (signed) density of zeros of
Gaussian distributed vector fields. We are able to express correlation
functions of arbitrary order through the curvature tensor of a certain abstract
Riemann-Cartan or Riemannian manifold. As an application, we discuss one- and
two-point functions. The zeros of a two-dimensional Gaussian vector field model
the distribution of topological defects in the high-temperature phase of
two-dimensional systems with orientational degrees of freedom, such as
superfluid films, thin superconductors and liquid crystals.Comment: 14 pages, 1 figure, uses iopart.cls, improved presentation, to appear
in J. Phys.
Large-scale Graphitic Thin Films Synthesized on Ni and Transferred to Insulators: Structural and Electronic Properties
We present a comprehensive study of the structural and electronic properties
of ultrathin films containing graphene layers synthesized by chemical vapor
deposition (CVD) based surface segregation on polycrystalline Ni foils then
transferred onto insulating SiO2/Si substrates. Films of size up to several
mm's have been synthesized. Structural characterizations by atomic force
microscopy (AFM), scanning tunneling microscopy (STM), cross-sectional
transmission electron microscopy (XTEM) and Raman spectroscopy confirm that
such large scale graphitic thin films (GTF) contain both thick graphite regions
and thin regions of few layer graphene. The films also contain many wrinkles,
with sharply-bent tips and dislocations revealed by XTEM, yielding insights on
the growth and buckling processes of the GTF. Measurements on mm-scale
back-gated transistor devices fabricated from the transferred GTF show
ambipolar field effect with resistance modulation ~50% and carrier mobilities
reaching ~2000 cm^2/Vs. We also demonstrate quantum transport of carriers with
phase coherence length over 0.2 m from the observation of 2D weak
localization in low temperature magneto-transport measurements. Our results
show that despite the non-uniformity and surface roughness, such large-scale,
flexible thin films can have electronic properties promising for device
applications.Comment: This version (as published) contains additional data, such as cross
sectional TEM image
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