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...

Symmetric hyperbolic systems include many physically relevant systems of partial differential equations (PDEs) such as Maxwell’s equations, the elastic wave equations and the acoustic equations [28]. In this paper we extend the Gaussian beam method to efficiently compute the high frequency solutions to such systems with polarized waves, in which the dispersion matrix of the hyperbolic system ha...

We study the maximum temperature rise induced by a rotating or dithering Gaussian laser beam on a semi-infinite body. An analytical solution is obtained by solving the transient three-dimensional heat equation in a semi-infinite domain with insulating surface. The effect of rotating or dithering frequency on maximum temperature rise is quantitatively investigated for stainless steel and carbon ...