7,996 research outputs found
Short-Pulsed Wavepacket Propagation in Ray-Chaotic Enclosures
Wave propagation in ray-chaotic scenarios, characterized by exponential
sensitivity to ray-launching conditions, is a topic of significant interest,
with deep phenomenological implications and important applications, ranging
from optical components and devices to time-reversal focusing/sensing schemes.
Against a background of available results that are largely focused on the
time-harmonic regime, we deal here with short-pulsed wavepacket propagation in
a ray-chaotic enclosure. For this regime, we propose a rigorous analytical
framework based on a short-pulsed random-plane-wave statistical representation,
and check its predictions against the results from
finite-difference-time-domain numerical simulations.Comment: 11 pages, 11 figures; minor modifications in the tex
Electromagnetic tunneling through a single-negative slab paired with a double-positive bi-layer
We show that resonant tunneling of electromagnetic fields can occur through a
three-layer structure composed of a single-negative (i.e., either
negative-permittivity or negative-permeability) slab paired with bi-layer made
of double-positive (i.e., positive permittivity and permeability) media. In
particular, one of the two double-positive media can be chosen arbitrarily
(even vacuum), while the other may exhibit extreme (either near-zero or very
high) permittivity/permeability values. Our results on this counterintuitive
tunneling phenomenon also demonstrate the possibility of synthesizing
double-positive slabs that effectively exhibit single-negative-like
wave-impedance properties within a moderately wide frequency range.Comment: 5 pages, 5 figures (minor revisions
Parameterizing Quasiperiodicity: Generalized Poisson Summation and Its Application to Modified-Fibonacci Antenna Arrays
The fairly recent discovery of "quasicrystals", whose X-ray diffraction
patterns reveal certain peculiar features which do not conform with spatial
periodicity, has motivated studies of the wave-dynamical implications of
"aperiodic order". Within the context of the radiation properties of antenna
arrays, an instructive novel (canonical) example of wave interactions with
quasiperiodic order is illustrated here for one-dimensional (1-D) array
configurations based on the "modified-Fibonacci" sequence, with utilization of
a two-scale generalization of the standard Poisson summation formula for
periodic arrays. This allows for a "quasi-Floquet" analytic parameterization of
the radiated field, which provides instructive insights into some of the basic
wave mechanisms associated with quasiperiodic order, highlighting similarities
and differences with the periodic case. Examples are shown for quasiperiodic
infinite and spatially-truncated arrays, with brief discussion of computational
issues and potential applications.Comment: 29 pages, 10 figures. To be published in IEEE Trans. Antennas
Propagat., vol. 53, No. 6, June 200
Perspectives on Beam-Shaping Optimization for Thermal-Noise Reduction in Advanced Gravitational-Wave Interferometric Detectors: Bounds, Profiles, and Critical Parameters
Suitable shaping (in particular, flattening and broadening) of the laser beam
has recently been proposed as an effective device to reduce internal (mirror)
thermal noise in advanced gravitational wave interferometric detectors. Based
on some recently published analytic approximations (valid in the
infinite-test-mass limit) for the Brownian and thermoelastic mirror noises in
the presence of arbitrary-shaped beams, this paper addresses certain
preliminary issues related to the optimal beam-shaping problem. In particular,
with specific reference to the Laser Interferometer Gravitational-wave
Observatory (LIGO) experiment, absolute and realistic lower-bounds for the
various thermal noise constituents are obtained and compared with the current
status (Gaussian beams) and trends ("mesa" beams), indicating fairly ample
margins for further reduction. In this framework, the effective dimension of
the related optimization problem, and its relationship to the critical design
parameters are identified, physical-feasibility and model-consistency issues
are considered, and possible additional requirements and/or prior information
exploitable to drive the subsequent optimization process are highlighted.Comment: 12 pages, 9 figures, 2 table
On the Analytic Structure of a Family of Hyperboloidal Beams of Potential Interest for Advanced LIGO
For the baseline design of the advanced Laser Interferometer
Gravitational-wave Observatory (LIGO), use of optical cavities with
non-spherical mirrors supporting flat-top ("mesa") beams, potentially capable
of mitigating the thermal noise of the mirrors, has recently drawn a
considerable attention. To reduce the severe tilt-instability problems
affecting the originally conceived nearly-flat, "Mexican-hat-shaped" mirror
configuration, K. S. Thorne proposed a nearly-concentric mirror configuration
capable of producing the same mesa beam profile on the mirror surfaces.
Subsequently, Bondarescu and Thorne introduced a generalized construction that
leads to a one-parameter family of "hyperboloidal" beams which allows
continuous spanning from the nearly-flat to the nearly-concentric mesa beam
configurations. This paper is concerned with a study of the analytic structure
of the above family of hyperboloidal beams. Capitalizing on certain results
from the applied optics literature on flat-top beams, a physically-insightful
and computationally-effective representation is derived in terms of
rapidly-converging Gauss-Laguerre expansions. Moreover, the functional relation
between two generic hyperboloidal beams is investigated. This leads to a
generalization (involving fractional Fourier transform operators of complex
order) of some recently discovered duality relations between the nearly-flat
and nearly-concentric mesa configurations. Possible implications and
perspectives for the advanced LIGO optical cavity design are discussed.Comment: 9 pages, 6 figures, typos corrected, Eqs. (24) and (26) change
Mode Confinement in Photonic Quasi-Crystal Point-Defect Cavities for Particle Accelerators
In this Letter, we present a study of the confinement properties of
point-defect resonators in finite-size photonic-bandgap structures composed of
aperiodic arrangements of dielectric rods, with special emphasis on their use
for the design of cavities for particle accelerators. Specifically, for
representative geometries, we study the properties of the fundamental mode (as
a function of the filling fraction, structure size, and losses) via 2-D and 3-D
full-wave numerical simulations, as well as microwave measurements at room
temperature. Results indicate that, for reduced-size structures, aperiodic
geometries exhibit superior confinement properties by comparison with periodic
ones.Comment: 4 pages, 4 figures, accepted for publication in Applied Physics
Letter
Resources Underlying Visuo-Spatial Working Memory Enable Veridical Large Numerosity Perception
Humans can quickly approximate how many objects are in a visual image, but no clear consensus has been achieved on the cognitive resources underlying this ability. Previous work has lent support to the notion that mechanisms which explicitly represent the locations of multiple objects in the visual scene within a mental map are critical for both visuo-spatial working memory and enumeration (at least for relatively small numbers of items). Regarding the cognitive underpinnings of large numerosity perception, an issue currently subject to much controversy is why numerosity estimates are often non-veridical (i.e., susceptible to biases from non-numerical quantities). Such biases have been found to be particularly pronounced in individuals with developmental dyscalculia (DD), a learning disability affecting the acquisition of arithmetic skills. Motivated by findings showing that DD individuals are also often impaired in visuo-spatial working memory, we hypothesized that resources supporting this type of working memory, which allow for the simultaneous identification of multiple objects, might also be critical for precise and unbiased perception of larger numerosities. We therefore tested whether loading working memory of healthy adult participants during discrimination of large numerosities would lead to increased interference from non-numerical quantities. Participants performed a numerosity discrimination task on multi-item arrays in which numerical and non-numerical stimulus dimensions varied congruently or incongruently relative to each other, either in isolation or in the context of a concurrent visuo-spatial or verbal working memory task. During performance of the visuo-spatial, but not verbal, working memory task, precision in numerosity discrimination decreased, participants’ choices became strongly biased by item size, and the strength of this bias correlated with measures of arithmetical skills. Moreover, the interference between numerosity and working memory tasks was bidirectional, with number discrimination impacting visuo-spatial (but not verbal) performance. Overall, these results suggest that representing visual numerosity in a way that is unbiased by non-numerical quantities relies on processes which explicitly segregate/identify the locations of multiple objects that are shared with visuo-spatial (but not verbal) working memory. This shared resource may potentially be impaired in DD, explaining the observed co-occurrence of working memory and numerosity discrimination deficits in this clinical population
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