421 research outputs found
Smectic Phases with Cubic Symmetry: The Splay Analog of the Blue Phase
We report on a construction for smectic blue phases, which have quasi-long
range smectic translational order as well as long range cubic or hexagonal
order. Our proposed structures fill space with a combination of minimal surface
patches and cylindrical tubes. We find that for the right range of material
parameters, the favorable saddle-splay energy of these structures can stabilize
them against uniform layered structures.Comment: 4 pages, 4 eps figures, RevTe
The dynamics of thin vibrated granular layers
We describe a series of experiments and computer simulations on vibrated
granular media in a geometry chosen to eliminate gravitationally induced
settling. The system consists of a collection of identical spherical particles
on a horizontal plate vibrating vertically, with or without a confining lid.
Previously reported results are reviewed, including the observation of
homogeneous, disordered liquid-like states, an instability to a `collapse' of
motionless spheres on a perfect hexagonal lattice, and a fluctuating,
hexagonally ordered state. In the presence of a confining lid we see a variety
of solid phases at high densities and relatively high vibration amplitudes,
several of which are reported for the first time in this article. The phase
behavior of the system is closely related to that observed in confined
hard-sphere colloidal suspensions in equilibrium, but with modifications due to
the effects of the forcing and dissipation. We also review measurements of
velocity distributions, which range from Maxwellian to strongly non-Maxwellian
depending on the experimental parameter values. We describe measurements of
spatial velocity correlations that show a clear dependence on the mechanism of
energy injection. We also report new measurements of the velocity
autocorrelation function in the granular layer and show that increased
inelasticity leads to enhanced particle self-diffusion.Comment: 11 pages, 7 figure
Gain properties of dye-doped polymer thin films
Hybrid pumping appears as a promising compromise in order to reach the much
coveted goal of an electrically pumped organic laser. In such configuration the
organic material is optically pumped by an electrically pumped inorganic device
on chip. This engineering solution requires therefore an optimization of the
organic gain medium under optical pumping. Here, we report a detailed study of
the gain features of dye-doped polymer thin films. In particular we introduce
the gain efficiency , in order to facilitate comparison between different
materials and experimental conditions. The gain efficiency was measured with
various setups (pump-probe amplification, variable stripe length method, laser
thresholds) in order to study several factors which modify the actual gain of a
layer, namely the confinement factor, the pump polarization, the molecular
anisotropy, and the re-absorption. For instance, for a 600 nm thick 5 wt\% DCM
doped PMMA layer, the different experimental approaches give a consistent value
80 cm.MW. On the contrary, the usual model predicting the gain
from the characteristics of the material leads to an overestimation by two
orders of magnitude, which raises a serious problem in the design of actual
devices. In this context, we demonstrate the feasibility to infer the gain
efficiency from the laser threshold of well-calibrated devices. Besides,
temporal measurements at the picosecond scale were carried out to support the
analysis.Comment: 15 pages, 17 figure
Monge's transport problem in the Heisenberg group
We prove the existence of solutions to Monge transport problem between two
compactly supported Borel probability measures in the Heisenberg group equipped
with its Carnot-Caratheodory distance assuming that the initial measure is
absolutely continuous with respect to the Haar measure of the group
An insight into polarization states of solid-state organic lasers
The polarization states of lasers are crucial issues both for practical
applications and fundamental research. In general, they depend in a combined
manner on the properties of the gain material and on the structure of the
electromagnetic modes. In this paper, we address this issue in the case of
solid-state organic lasers, a technology which enables to vary independently
gain and mode properties. Different kinds of resonators are investigated:
in-plane micro-resonators with Fabry-Perot, square, pentagon, stadium, disk,
and kite shapes, and external vertical resonators. The degree of polarization P
is measured in each case. It is shown that although TE modes prevail generally
(P>0), kite-shaped micro-laser generates negative values for P, i.e. a flip of
the dominant polarization which becomes mostly TM polarized. We at last
investigated two degrees of freedom that are available to tailor the
polarization of organic lasers, in addition to the pump polarization and the
resonator geometry: upon using resonant energy transfer (RET) or upon pumping
the laser dye to an higher excited state. We then demonstrate that
significantly lower P factors can be obtained.Comment: 12 pages, 12 figure
Buckling Instabilities of a Confined Colloid Crystal Layer
A model predicting the structure of repulsive, spherically symmetric,
monodisperse particles confined between two walls is presented. We study the
buckling transition of a single flat layer as the double layer state develops.
Experimental realizations of this model are suspensions of stabilized colloidal
particles squeezed between glass plates. By expanding the thermodynamic
potential about a flat state of confined colloidal particles, we derive
a free energy as a functional of in-plane and out-of-plane displacements. The
wavevectors of these first buckling instabilities correspond to three different
ordered structures. Landau theory predicts that the symmetry of these phases
allows for second order phase transitions. This possibility exists even in the
presence of gravity or plate asymmetry. These transitions lead to critical
behavior and phases with the symmetry of the three-state and four-state Potts
models, the X-Y model with 6-fold anisotropy, and the Heisenberg model with
cubic interactions. Experimental detection of these structures is discussed.Comment: 24 pages, 8 figures on request. EF508
Lasing in a cholesteric liquid crystal doped with derivative of triphenylamine and 1,8-naphthalimide, and optical characterization of the materials
Conformal dimension and random groups
We give a lower and an upper bound for the conformal dimension of the
boundaries of certain small cancellation groups. We apply these bounds to the
few relator and density models for random groups. This gives generic bounds of
the following form, where is the relator length, going to infinity.
(a) 1 + 1/C < \Cdim(\bdry G) < C l / \log(l), for the few relator model,
and
(b) 1 + l / (C\log(l)) < \Cdim(\bdry G) < C l, for the density model, at
densities .
In particular, for the density model at densities , as the relator
length goes to infinity, the random groups will pass through infinitely
many different quasi-isometry classes.Comment: 32 pages, 4 figures. v2: Final version. Main result improved to
density < 1/16. Many minor improvements. To appear in GAF
Order and Frustration in Chiral Liquid Crystals
This paper reviews the complex ordered structures induced by chirality in
liquid crystals. In general, chirality favors a twist in the orientation of
liquid-crystal molecules. In some cases, as in the cholesteric phase, this
favored twist can be achieved without any defects. More often, the favored
twist competes with applied electric or magnetic fields or with geometric
constraints, leading to frustration. In response to this frustration, the
system develops ordered structures with periodic arrays of defects. The
simplest example of such a structure is the lattice of domains and domain walls
in a cholesteric phase under a magnetic field. More complex examples include
defect structures formed in two-dimensional films of chiral liquid crystals.
The same considerations of chirality and defects apply to three-dimensional
structures, such as the twist-grain-boundary and moire phases.Comment: 39 pages, RevTeX, 14 included eps figure
Effective index of refraction, optical rotation, and circular dichroism in isotropic chiral liquid crystals
This paper concerns optical properties of the isotropic phase above the
isotropic-cholesteric transition and of the blue phase BP III. We introduce an
effective index, which describes spatial dispersion effects such as optical
rotation, circular dichroism, and the modification of the average index due to
the fluctuations. We derive the wavelength dependance of these spatial
dispersion effects quite generally without relying on an expansion in powers of
the chirality and without assuming that the pitch of the cholesteric is
much shorter than the wavelength of the light , an approximation which
has been made in previous studies of this problem. The theoretical predictions
are supported by comparing them with experimental spectra of the optical
activity in the BP III phase.Comment: 15 pages and 7 figures. Submitted to PR
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