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

Neural Network Aided Glitch-Burst Discrimination and Glitch Classification

We investigate the potential of neural-network based classifiers for discriminating gravitational wave bursts (GWBs) of a given canonical family (e.g. core-collapse supernova waveforms) from typical transient instrumental artifacts (glitches), in the data of a single detector. The further classification of glitches into typical sets is explored.In order to provide a proof of concept,we use the core-collapse supernova waveform catalog produced by H. Dimmelmeier and co-Workers, and the data base of glitches observed in laser interferometer gravitational wave observatory (LIGO) data maintained by P. Saulson and co-Workers to construct datasets of (windowed) transient waveforms (glitches and bursts) in additive (Gaussian and compound-Gaussian) noise with different signal-tonoise ratios (SNR). Principal component analysis (PCA) is next implemented for reducing data dimensionality, yielding results consistent with, and extending those in the literature. Then, a multilayer perceptron is trained by a backpropagation algorithm (MLP-BP) on a data subset, and used to classify the transients as glitch or burst. A Self-Organizing Map (SOM) architecture is finally used to classify the glitches. The glitch/burst discrimination and glitch classification abilities are gauged in terms of the related truth tables. Preliminary results suggest that the approach is effective and robust throughout the SNR range of practical interest. Perspective applications pertain both to distributed (network, multisensor) detection of GWBs, where someintelligenceat the single node level can be introduced, and instrument diagnostics/optimization, where spurious transients can be identified, classified and hopefully traced back to their entry point

Free-Space Antenna Field/Pattern Retrieval in Reverberation Environments

Simple algorithms for retrieving free-space antenna field or directivity patterns from complex (field) or real (intensity) measurements taken in ideal reverberation environments are introduced and discussed.Comment: 6 pages, 2 figures, submitted to IEEE Antennas and Wireless Propagation Letter

Modeling the Impulsive Noise Component and its Effect on the Operation of a Simple Coherent Network Algorithm for Unmodeled Gravitational Wave Bursts Detection

An analytic model a la Middleton of the impulsive noise component in the data of interferometric gravitational wave detectors is proposed, based on an atomic representation of glitches. A fully analytic characterization of the coherent network data analysis algorithm proposed by Rakhmanov and Klimenko is obtained, for the simplest relevant case of triggered detection of unmodeled gravitational wave bursts, using the above noise model. The detector's performance is evaluated under a suitable central-limit hypothesis, and the effects of both the noisiness of the pseudo-templates, and the presence of the impulsive noise component are highlighted.Comment: 15 pages, 8 figure

Robust Gravitational Wave Burst Detection and Source Localization in a Network of Interferometers Using Cross Wigner Spectra

We discuss a fast cross-Wigner transform based technique for detecting gravitational wave bursts, and estimating the direction of arrival, using a network of (three) non co-located interferometric detectors. The performances of the detector as a function of signal strength and source location, and the accuracy of the direction of arrival estimation are investigated by numerical simulations.Comment: accepted in Class. Quantum Gravit

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