For many industrial and scientific laser applications, such as materials processing, fiber coupling, beam collimation, and beam focusing, it is necessary to have a good laser beam quality. In general, propagating laser beams deviate from an ideal Gaussian intensity distribution. The degree of deviation can be conveniently quantified by a quality factor M (called the “M-squared” factor or the “t...

Asymptotic techniques have been successfully applied to compute electromagnetic wave radiation in various high-frequency engineering domains. Recent approaches based on Gaussian beams for tracking fields may overcome some problems inherent to the ray methods such as caustics. The efficiency of these methods is based on the ability to expand surface fields into a superposition of Gaussian beams....

A new numerical method for approximating highly oscillatory wave fields as a superposition of Gaussian beams is presented. The method estimates the number of beams and their parameters automatically. This is achieved by an expectation-maximization algorithm that fits real, positive Gaussians to the energy of the highly oscillatory wave fields and its Fourier transform. Beam parameters are furth...

We present a novel wavefront method based on Gaussian beams for computing high frequency wave propagation problems. Unlike standard geometrical optics, Gaussian beams compute the correct solution of the wave field also at caustics. The method tracks a front of two canonical beams with two particular initial values for width and curvature. In a fast postprocessing step, from the canonical soluti...

In this paper, we propose a hybrid method coupling a Schrödinger solver and the Gaussian beam method for the numerical simulation of quantum tunneling through potential barriers or surface hopping across electronic potential energy surfaces. The idea is to use a Schrödinger solver near potential barriers or zones where potential energy surfaces cross, and the Gaussian beam method–which is much ...

LETER A R IC LE Abstract A method is proposed for nonlinear beam shaping, employing a non-collinear quasi phase-matched interaction in a crystal whose nonlinear coefficient is encoded by a computer generated hologram pattern. In this method the same axis is used for both satisfying the phase-matching requirements and encoding the holographic information, the result is a single shaped beam in th...

Computation of high frequency solutions to wave equations is important in many applications, and notoriously difficult in resolving wave oscillations. 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 PDEs. A...

Using the delta-P(1) approximation to the Boltzmann transport equation we develop analytic solutions for the fluence rate produced by planar (1-D) and Gaussian beam (2-D) irradiation of a homogeneous, turbid, semi-infinite medium. To assess the performance of these solutions we compare the predictions for the fluence rate and two metrics of the optical penetration depth with Monte Carlo simulat...

The Gaussian beam superposition method is an asymptotic method for computing high frequency wave fields in smoothly varying inhomogeneous media. In this paper we study the accuracy of the Gaussian beam superposition method and derive error estimates related to the discretization of the superposition integral and the Taylor expansion of the phase and amplitude off the center of the beam. We show...

The effect on the Stokes parameters of a Gaussian Schell model beam on propagation in free space is studied experimentally and results are matched with the theory [X. H. Zhao, et al. Opt. Express 17, 17888 (2009)] that in general the degree of polarization of a Gaussian Schell model beam doesn't change on propagation if the three spectral correlation widths δ xx, δ yy, δ xy are equal and the be...