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 based on the asymptotic analysis on phase plane. Compared to geometric optics, it provides a valid solution around caustics. Compared to the Gaussian beam metho...

A packet of light rays is defined that is equivalent to a Gaussian beam of light. The transformation of the Gaussian beam as it passes through any combination of perfect lenses and flat dielectric interfaces can be found by applying geometric optics to the equivalent ray packet.. The envelope of the ray packet gives the Gaussian beam spot size and the curves perpendicular to the average ray slo...

Laser forming is a modern process which is mainly used for forming metals. Different Lasers are used in this regard that includes Nd: YAG and CO2. In this study, forming bi-layer sheets of Aluminum/Ceramic by Laser was investigated. Furthermore, effect of Uniform and Gaussian heat flux distribution in different power, velocity, and beam diameters on bending angle was studied. FEM simulation ind...

We investigate the propagation of one-dimensional and two-dimensional (1D, 2D) Gaussian beams in the fractional Schrödinger equation (FSE) without a potential, analytically and numerically. Without chirp, a 1D Gaussian beam splits into two nondiffracting Gaussian beams during propagation, while a 2D Gaussian beam undergoes conical diffraction. When a Gaussian beam carries linear chirp, the 1D b...

Motivated by fast multiscale Gaussian wavepacket transforms and multiscale Gaussian beam methods which were originally designed for pure initial-value problems of wave equations, we develop fast multiscale Gaussian beam methods for initial boundary value problems of wave equations in bounded convex domains in the high frequency regime. To compute the wave propagation in bounded convex domains, ...

We show how to decouple a coherent Gaussian beam having general astigmatism (to transform it into a beam having only simple astigmatism, or orthogonal symmetry) by using a single rotated thin cylindrical lens. The resulting coherent orthogonal Gaussian beam may be further transformed into a stigmatic (rotationally symmetric) Gaussian beam by an orthogonal telescopic magnifier. The initial beam ...

The dynamical properties of cos-Gaussian beams in strongly nonlocal nonlinear (SNN) media are theoretically investigated. Based on the moments method, the analytical expression for the rootmean-square (RMS) of the cos-Gaussian beam propagating in a SNN medium is derived. The critical powers that keep the RMS beam widths invariant during propagation in a SNN medium are discussed. The RMS beam wi...

We present a new, compact, and practical optical mode converter that efficiently transforms a high-order Hermite-Gaussian (HG) laser beam into a nearly Gaussian beam. The mode converter is based on coherently adding different transverse parts of the high-order mode beam by use of a single planar interferometric element. The method, configuration, and experimental results obtained with a pulsed ...

A beam shaping method is presented where a diffractive optical element (DOE) is designed by optimizing the complex mode coefficient weights of a set of Gaussian beam modes. This method is compared with the more standard unidirectional approach. Differential evolution is used for the optimization in both the unidirectional and Gaussian beam mode optimization methods. For the particular transform...