Related papers: On Gaussian Beams Described by Jacobi's Equation
The mutual information between a complex-valued channel input and its complex-valued output is decomposed into four parts based on polar coordinates: an amplitude term, a phase term, and two mixed terms. Numerical results for the additive…
The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…
Explicit and compact expressions describing the reflection and the transmission of a Gaussian beam by anisotropic parallel plates are given. Multiple reflections inside the plate are taken into account as well as arbitrary optical axis…
Paraxial diffraction of monochromatic Gaussian beams by arbitrarily shaped polygonal apertures is analytically explored within the boundary diffraction wave theory framework. Exact closed-form expressions of the diffracted wavefield are…
Gaussian distribution is commonly used as a good approximation to study the trapped one-component Bose-condensed atoms with relatively small nonlinear effect. It is not adequate in dealing with the one-component system of large nonlinear…
We consider a generalised Webster's equation for describing wave propagation in curved tubular structures such as variable diameter acoustic wave guides. Webster's equation in generalised form has been rigorously derived in a previous…
Most of the modern literature on robust mean estimation focuses on designing estimators which obtain optimal sub-Gaussian concentration bounds under minimal moment assumptions and sometimes also assuming contamination. This work looks at…
Relationships that exist between the classical, Shannon-type, and geometric-based approaches to sampling are investigated. Some aspects of coding and communication through a Gaussian channel are considered. In particular, a constructive…
We provide several diagrams for the graphical determination of certain elements of a Gaussian beam based on prior knowledge of other elements. For example, these diagrams allow us to determine the plane of the beam waist and the Rayleigh…
The point symmetry group is studied for the generalized Webster-type equation describing non-linear acoustic waves in lossy channels with variable cross sections. It is shown that, for certain types of cross section profiles, the admitted…
In next-generation wireless networks, the combination of electrically large radiating apertures and high-frequency transmission extends the radiating near-field region around the transmitter. In this region, unlike in the far field, the…
We investigate, theoretically and experimentally, the evolution of a paraxial beam propagating in free space when its initial transverse structure is characterized by an asymmetric Gaussian modulation combined with an entire function.…
This paper concerns the propagation of high frequency wave-beams in highly turbulent atmospheres. Using a paraxial model of wave propagation, we show in the long-distance weak-coupling regime that the wavefields are approximately described…
In a previous paper (gr-qc/0105100) we derived a set of near-optimal signal detection techniques for gravitational wave detectors whose noise probability distributions contain non-Gaussian tails. The methods modify standard methods by…
The Covariant Canonical Gauge theory of Gravity is generalized by including at the Lagrangian level all possible quadratic curvature invariants. In this approach, the covariant Hamiltonian principle and the canonical transformation…
Geometric perturbation theory is universal. A typical example is provided by the 3D wave equation, widely used in acoustics. We face vibrating eardrums as a binaural auditory input stemming from an external sound source. In the setup of…
Phase estimation plays a central role in communications, sensing, and information processing. Quantum correlated states, such as squeezed states, enable phase estimation beyond the shot-noise limit, and in principle approach the ultimate…
We analyze the equilibrium statistical mechanics of canonical, non-canonical and non-Hamiltonian equations of motion by throwing light into the peculiar geometric structure of phase space. Some fundamental issues regarding time translation…
We consider a model nondispersive nonlinear optical fiber channel with additive white Gaussian noise at large $\mathrm{SNR}$ (signal-to-noise ratio) in the intermediate power region. Using Feynman path-integral technique we for the first…
In high-dimensional time series analysis, Gaussian approximation (GA) schemes under various distance measures or on various collections of subsets of the Euclidean space play a fundamental role in a wide range of statistical inference…