Related papers: Uniform approximation of paraxial flat-topped beam…
A purely analytical extension of the flattened Gaussian beams [Opt. Commun. \textbf{107,} 335 (1994)] to any values of the beam order, is here proposed. Due to it, the paraxial propagation problem of axially symmetric, coherent flat-top…
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.…
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…
In this paper, we develop a theoretical analysis to efficiently handle superpositions of waves with concentrated wavevector and frequency spectra, allowing an easy analytical description of fields with interesting transverse profiles.…
A hidden symmetry of the nonlinear wave equation is exploited to analyse the propagation of paraxial and uniform atom-laser beams in time-independent, quadratic and cylindrical potentials varying smoothly along the propagation axis. The…
We propose the frozen Gaussian approximation for computation of high frequency wave propagation. This method approximates the solution to the wave equation by an integral representation. It provides a highly efficient computational tool…
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…
Gaussian beams are asymptotically valid high frequency solutions concentrated on a single curve through the physical domain, and superposition of Gaussian beams provides a powerful tool to generate more general high frequency solutions to…
We consider the propagation of Gaussian beams in a waveguide with gain and loss in the paraxial approximation governed by the Schr\"odinger equation. We derive equations of motion for the beam in the semiclassical limit that are valid when…
We obtain uniform asymptotics for polynomials orthogonal on a fixed and varying arc of the unit circle with a positive analytic weight function. We also complete the proof of the large $s$ asymptotic expansion for the Fredholm determinant…
Complete bases that are useful for beam propagation problems and that present the distinct property of being spatially confined at the initial plane are proposed. These bases are constructed in terms of polynomials of Gaussians, in contrast…
The Gaussian theory of errors has been generalized to situations, where the Gaussian distribution and, hence, the Gaussian rules of error propagation are inadequate. The generalizations are based on Bayes' theorem and a suitable measure.…
New results on uniform convergence in probability for expansions of Gaussian random processes using compactly supported wavelets are given. The main result is valid for general classes of nonstationary processes. An application of the…
Analytic expressions of the spatial coherence of partially coherent fields propagating in the Fresnel regime in all but the simplest of scenarios are largely lacking and calculation of the Fresnel transform typically entails tedious…
We show that an analog of the physics at the Planck scale can be found in the propagation of tightly focused laser beams. Various equations that occur in generalized quantum mechanics are formally identical to those describing the nonlinear…
A new class of nonparaxial accelerating optical waves is introduced. These are beams with a Bessel-like profile that are capable of shifting laterally along fairly arbitrary trajectories as the wave propagates in free space. The concept…
New results on uniform convergence in probability for the most general classes of wavelet expansions of stationary Gaussian random processes are given.
In this work, we extend the analytic treatment of Bessel functions of large order and/or argument. We examine uniform asymptotic Bessel function expansions and show their accuracy and range of validity. Such situations arise in a variety of…
Propagation of sound beam diffracted from a circular aperture in far-field region has been studied in this paper by the method of angular spectrum representation and stationary phase method. This nonparaxial theory is useful when beam angle…
Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions…