Tomography of Atom Beams

Abstract

We investigate the accuracy of an experimental reconstruction of the Wigner function of the transverse motion in an atom beam using numerical wave packet simulations. For the example of a superposition of two Gaussians (the outcome of a double slit, for example) we study in detail the influence of experimental restraints on the quality of the reconstruction. For the potential candidate, metastable helium, we demonstrate that an accurate reconstruction of the Wigner function, especially of its negative parts, is well within experimental reach.     

Twisted Gaussian Schell-model Beams: A Superposition Model

Abstract

We present a simple model in which a twisted Gaussian Schell-model beam is produced by an incoherent superposition of ordinary Gaussian beams. The meaning and some direct consequences of the model are given.     

Non-diffractive Vector Bessel Beams

Abstract

The non-diffractive vector Bessel beams of an arbitrary order are examined as both the solution to the vector Helmholtz wave equation and the superposition of vector components of the angular spectrum. The transverse and longitudinal intensity components of the vector Bessel beams are analysed for the radial, azimuthal, circular and linear polarizations. The radially and azimuthally polarized beams are assumed to be formed by the axicon polarizers used with the initially unpolarized or linearly polarized light. Conditions in which the linearly polarized Bessel beams can be approximated by the scalar solutions to the wave equation are also discussed.     

Fresnel Diffraction of Gaussian Beams by a Circular Aperture in Gradient-index Media

Abstract

This work presents a method of evaluating the intensity distribution of a Gaussian beam in a weakly inhomogeneous medium when it has been truncated by a circular aperture. An analytical expression for the diffracted field is obtained in terms of Bessel functions.     

Augmented ABCD Matrix for Non-specular Diffraction of Gaussian Beams

Abstract

Optical beams reflected or transmitted by a dielectric interface undergo several non-specular deformations: changes in the beam amplitude, lateral, focal and angular shifts of the beam axis and a magnification of the beam width. In this communication the non-specular interaction of the beam with, in general, multilayered, planar dielectric structure is described in terms of the ray transfer matrix formalism. A relationship between the beam deformations and a 3 × 3 ray transfer matrix of the structure is built. Transfer matrix elements are shown in a simple form dependent on the real deformations.     

Thermal Blooming of Laser Beams in the Framework of Spinor Formalism

Abstract

In this paper, we first give a survey of the spinor formalism applied to the propagation of laser beams through the atmosphere, then we discuss a numerical algorithm to solve the spinor equations. Finally, this algorithm is applied to numerical computations of thermal blooming for a Gaussian collimated beam in the steady-state regime.     

Cross-spectral Density of Partially Coherent Gaussian Beams for Arbitrary Space Distances

Abstract

A formula for partially coherent Gaussian beams is presented, for which both of the arguments of the cross-spectral density are arbitrary points. Numerical discussions show ‘internal’ diffraction inside the beam.     

Lamellar Gratings as Polarization Components for Specularly Reflected Beams

Abstract

High spatial frequency lamellar gratings are shown to function as phase compensators, quarter-wave and half-wave retarders, and polarization rotators that operate on specularly reflected (zeroth-order) beams. These gratings are designed using rigorous coupled-wave and modal grating diffraction theories. Controlling the geometrical parameters of these gratings allows for engineering the phase retardation and polarization conversion introduced to a reflected beam. Fabrication and operational tolerances for these elements are discussed. Wavelength and polar angle of incidence variation affect the performance of these elements more strongly than variations in other geometrical and operational parameters.     

The Theory of Spiral Laser Beams in Nonlinear Media

Abstract

The analytical theory governing the propagation of spiral laser beams in nonlinear media is developed. It is shown that, taking into account the saturation effect in a Kerr medium, spiral beams have a tube-like structure with a periodicity along the axis of a nonlinear autoguide. In the case of the absence of saturation mechanism the collapse of spiral beams is described. It is found that critical autoguide power depends on the topological charge of the spiral beam. The stability of a circular symmetry structure of the beam is investigated. The analytical results are in good agreement with the numerical experiment.     

Examination of Focal Shifts of Modified Gaussian Beams Under External Lensing

Abstract

Beam profiles, belonging to a class of modified Gaussians, are subjected to external lensing, and the focal shifts are computed. The results are verified using a numerical technique based on a Fourier transform approach to diffraction. The method can be readily extended to the study of the external characteristics of other classes of non-Gaussians, including the flat-top and super-Gaussian profiles.     

Self-action of Counterpropagating Axially Symmetric Light Beams in a Transparent Cubic-nonlinearity Medium

Abstract

The stationary effect of self-action of counterpropagating axially symmetric light beams in a medium with cubic nonlinearity is discussed. Self-similar solutions for initial radiation parameters and nonlinear medium characteristics in the case of slowly varying amplitudes of beams are found. The analysis of approximate solutions obtained on the basis of motion constants is carried out and results are compared with numerical experimental data.     

Propagation of Gaussian Schell-model Beams in Dispersive and Absorbing Media

Abstract

The spectral properties and the coherence properties of Gaussian Schell-model beams, propagating in dispersive and absorbing media, are discussed. Unlike in free space, the ratio of the transverse spectral correlation length to the beam width is found to increase on propagation. Consequently upon propagation the beam becomes spatially more coherent at each frequency. Numerical results for the spectrum and for the degrees of spectral and of temporal coherence of the field are presented for some selected values of the beam parameters and for several values of the propagation distance. Propagation in a gain medium is also briefly discussed.     

Optical Particle Trapping with Higher-order Doughnut Beams Produced Using High Efficiency Computer Generated Holograms

Abstract

Laser beams containing higher-order phase singularities can be produced with high efficiency computer generated holograms made with very simple equipment. Using such holograms in an optical tweezers experiment we have successfully trapped reflective and absorptive particles in the dark central spot of a focused charge 3 singularity beam. Angular momentum absorbed from the beam can set particles into rotation.     

A Simple Interferometric Method for Measuring the Fidelity of Phase Conjugated Beams

Abstract

One of the most interesting properties of the process of nonlinear optical phase conjugation is the capability of compensating for aberrations. The quality of compensation can be determined by investigation of the wavefront. A simple interferometric method for measuring fidelity of phase conjugated beams which allows a quantitative evaluation with respect to the phase distribution is described. This method was used to investigate the quality of phase conjugation by four-wave mixing in saturable absorbers. Illustrative examples are presented for the case of a phase conjugating and an ordinary mirror.     

Deflection of Atoms by Circularly Polarized Light Beams in Triple Laue Configuration

Abstract

A new type of atomic interferometer is discussed, in which atoms with two ground-state Zeeman sub-levels m = ± 1, and an excited state with m = 0, pass through three laser interaction zones—each comprising two counter-propagating waves of opposite circular polarization with a large detuning from resonance. By means of Raman-type transitions between the two ground-state levels, which convey a recoil of two photon momenta, the atomic wave function is split up into two coherent spatially separated branches, and subsequently recombined. In this system, conservation of energy and momentum leads to a strong correlation between the external centre of mass motion and internal magnetic degrees of freedom. As a consequence, the paths within the interferometer are tagged by the internal quantum number m. As an example, we calculate the position and momentum distribution function of a helium atom on its way through the interferometer.     

Optics for Neutral Atomic Beams: Reflection and Diffraction of Sodium Atoms by Evanescent Laser Light Fields

Abstract

Realization of the analogues of optical components for the manipulation of atomic de Broglie waves has recently become possible through the use of laser-based techniques. The strong fields generated by laser light have already been used to reflect atoms using travelling evanescent waves, and to diffract atomic beams through small angles using transmission gratings formed by a standing laser light wave in vacuo. Present experiments aim to combine these techniques to produce a reflection diffraction grating formed by a standing evanescent laser-light field, and to exploit the larger diffraction angles made possible theoretically by such a scheme.     

Self-deflection of Three-dimensional Optical Beams by a Thin Nonlinear Layer with Saturable Dispersive and Absorptive Nonlinearity

Abstract

This paper describes self-deflection effects arising from the propagation of symmetric and asymmetric three-dimensional scalar optical beams through thin nonlinear layers. The model of nonlinearity used includes both saturation and absorption. In several cases, significant differences are observed between the present three-dimensional results and previous two-dimensional results based on the Kerr model of nonlinearity. Also, the existence of a large axial component of the self-deflected beam for a three-dimensional geometry against the absence of this component for a two-dimensional geometry is discussed.     

Equivalent Homogeneous Variable Depth Beams for Cracked FGM Beams; Compliance Approach

We explore the compliance approach for K _I evaluation of a cracked three point beam (TPB) of functionally graded material (FGM). We suggest an equivalent beam of variable height for cracked FGM beams which includes the homogeneous beam for the linear, quadratic and cubic variations in elastic modulus along the beam span. The efficacy of equivalent beams is demonstrated numerically on a 250 × 41 × 6 mm FGM beam with modulus varying from 210 – 315 GPa under 5000 N load.     

Narrow-Angle Beams of Strongly Interacting Phonons

We demonstrate that narrow-angle phonon pulses of low energy phonons in liquid ⁴ He are strongly interacting and rapidly come into equilibrium within a narrow cone in momentum space. The effect of collimation on such a system is to strongly reduce the axial phonon flux. This gives a method of separating high and low energy phonons.