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

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