We present an ab initio account of the paraxial complex geometrical optics (CGO) in application to scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic expansion of the complex eikonal and reduces the wave problem to the solution of ordinary differential equations of the Riccati type. This substantially simplifies the desc...

We design an Eulerian Gaussian beam summation method for solving Helmholtz equations in the high-frequency regime. The traditional Gaussian beam summation method is based on Lagrangian ray tracing and local ray-centered coordinates. We propose a new Eulerian formulation of Gaussian beam theory which adopts global Cartesian coordinates, level sets, and Liouville equations, yielding uniformly dis...

A non-Gaussian, flat-top laser beam profile, also called Mesa Beam Profile, supported by non spherical mirrors known as Mexican Hat (MH) mirrors, has been proposed as a way to depress the mirror thermal noise and thus improve the sensitivity of future interferometric Gravitational Wave detectors, including Advanced LIGO [1]. Non-Gaussian beam configurations have never been tested before [2] hen...

As an important model in quantum semiconductor devices, the Schrödinger-Poisson equations have generated widespread interests in both analysis and numerical simulations in recent years. In this paper, we present Gaussian beam methods for the numerical simulation of the one-dimensional Schrodinger-Poisson equations. The Gaussian beam methods for high frequency waves outperform the geometrical op...

To apply annular output beams emitted from an unstable resonator to a multiple-pass cell (MPC) for Raman conversion, we studied the mode-matching condition of non-Gaussian beams to a MPC using beam propagation analysis based on Laguerre-Gaussian functions. During transits of the MPC, the radial profile of an annular beam changes between annular and Airy patterns. Although such behavior indicate...

In this paper we investigate the self-focusing of a Gaussian beam in a saturable nonlinear medium. We show that the dynamics of the incident Gaussian beam become progressively more complicated as the ratio of the Gaussian spot size to that of the ground-state solution is increased for a fixed energy flux. As this ratio is increased (or decreased) from unity, recurrence of the field is observed ...