Exact ray-trace beam for an off-axis paraboloid surface

When an off-axis paraboloidal mirror focuses a parallel beam, the image is formed on one side of the optical axis. For a tilted beam focused by an off-axis paraboloidal mirror, the focus is no longer pointlike (not considering the diffraction effect); rather, it is a distorted spot. This is due to the inherent aberrations of the surface. In addition, there is a change in the focus position. We calculate by exact ray-trace equations the modified wave-front aberration and express it in power series. Our formulation uses the optical path variation along a defined principal ray that we relate to the parameter that describe the surface and the beam angle of incidence. We designate this ray as that reflected by the center of the entrance pupil and field of view. We employ the direction cosines of the principal ray to compute the wave-front aberration function of a beam reflected by an off-axis paraboloid.     

Far-field scattering of a non-Gaussian off-axis axisymmetric laser beam by a spherical particle

Experimental laser beam profiles often deviate somewhat from the ideal Gaussian shape of the axisymmetric TEM(00) laser mode. To take these deviations into account when calculating light scattering of an off-axis beam by a spherical particle, we use our phase-modeling method to approximate the beam-shape coefficients in the partial wave expansion of an experimental laser beam. We then use these beam-shape coefficients to compute the near-forward direction scattering of the off-axis beam by the particle. Our results are compared with laboratory data, and we give a physical interpretation of the various features observed in the angular scattering patterns.     

Analyses of vector Gaussian beam propagation and the validity of paraxial and spherical approximations

The analysis of many systems in optical communications and metrology utilizing Gaussian beams, such as free-space propagation from single-mode fibers, point diffraction interferometers, and interference lithography, would benefit from an accurate analytical model of Gaussian beam propagation. We present a full vector analysis of Gaussian beam propagation by using the well-known method of the angular spectrum of plane waves. A Gaussian beam is assumed to traverse a charge-free, homogeneous, isotropic, linear, and nonmagnetic dielectric medium. The angular spectrum representation, in its vector form, is applied to a problem with a Gaussian intensity boundary condition. After some mathematical manipulation, each nonzero propagating electric field component is expressed in terms of a power-series expansion. Previous analytical work derived a power series for the transverse field, where the first term (zero order) in the expansion corresponds to the usual scalar paraxial approximation. We confirm this result and derive a corresponding longitudinal power series. We show that the leading longitudinal term is comparable in magnitude with the first transverse term above the scalar paraxial term, thus indicating that a full vector theory is required when going beyond the scalar paraxial approximation. In spite of the advantages of a compact analytical formalism, enabling rapid and accurate modeling of Gaussian beam systems, this approach has a notable drawback. The higher-order terms diverge at locations that are sufficiently far from the initial boundary, yielding unphysical results. Hence any meaningful use of the expansion approach calls for a careful study of its range of applicability. By considering the transition of a Gaussian wave from the paraxial to the spherical regime, we are able to derive a simple expression for the range within which the series produce numerically satisfying answers.     

Light intensity distributions of the Gaussian laser beam through an aperture team

Based on the propagating theory of the laser beam, the propagating characteristics of the Gaussian beam through an aperture team that comprises two apertures and a convergent lens, are studied. The approximate expressions for the field distribution are derived by the diffracted integral equation in detail under the condition of approximations. In comparison with the approximate expression and the precise expression, we know that there are the approximate same results for the two expressions if the radius of the second aperture is not too large. The numerical examples are given to confirm the correctness of our calculated results.     

Evanescent wave coupling in light scattering of an off-axis normally incident Gaussian beam by two parallel nonabsorbing cylinders

A theoretical and numerical investigation is devised for resonant light scattering of an off-axis normally incident Gaussian beam by two parallel nonabsorbing cylinders based on the related beam theory developed in J. Opt. Soc. Am. A 14, 640 (1997). By varying the half-beam width, we show that the multireflection process between the two scatterers can be minimized. Moreover, the study is an attempt to understand the underlying physics present in the process of resonance excitation by evanescent wave coupling.     

Procedures for reducing large datasets of crystal orientations using generalized spherical harmonics

We present a rigorous methodology for the compaction of crystallographic texture data associated with a given material volume and show that a statistical orientation distribution function (ODF) containing any number of orientations can be compacted to a significantly smaller but representative set of orientations. This methodology is based on the spectral representation of ODFs through the use of generalized spherical harmonic functions. The Fourier coefficients of an initial full-size ODF can be matched with those of a more compact but equivalent ODF. The reduced-size ODF contains a predetermined set of representative orientations whose weights are adjusted using an algorithm for finding the closest reduced-size ODF to a given full-size ODF. To demonstrate the accuracy of the methodology, we consider three measured ODFs of two cubic metals (pure Cu and an Al alloy) and a hexagonal metal (pure Zr) and then subsequently perform plane strain and simple compression simulations with both the initial ODFs and the reduced-size ODFs. We quantitatively demonstrate that texture evolution and stress–strain response simulated with reduced-size ODFs are in excellent agreement with those simulated with initial full-size ODFs.     

Far-field scattering of an axisymmetric laser beam of arbitrary profile by an on-axis spherical particle

Experimental laser beam profiles often deviate somewhat from the ideal Gaussian shape of the TEM(00) laser mode. In order to take these deviations into account when calculating light scattering, we propose a method for approximating the beam shape coefficients in the partial wave expansion of an experimental laser beam. We then compute scattering by a single dielectric spherical particle placed on the beam's axis using this method and compare our results to laboratory data. Our model calculations fit the laboratory data well.     

Acousto-optic interaction of a Gaussian laser beam with an ultrasonic wave of cylindrical symmetry

We present experimental studies of the interaction between a narrow Gaussian laser beam and a standing cylindrical ultrasonic wave. As a theoretical approach, a Fourier-optics-based successive diffraction model is used. Depending on the ratio of the Gaussian laser beam diameter to the first nodal diameter of the cylindrical ultrasound, light refraction or diffraction is observed. We experimentally investigate the time-averaged light intensity as well as the modulation of light in the far field of light refraction-diffraction by a cylindrical ultrasound. It is revealed that significant focusing appears if the phase front of the incident light is curved. The focusing effects of the acousto-optic system depend on the width of the laser beam and curvature of the phase front. Finally, possible applications are discussed.     

Optimization of the Gaussian beam flattening using a phase-plate

Abstract

We consider the conversion of a Gaussian beam into a flat-top profile by using a phase-plate which consists of a single-zone binary optic. The near- and far-field distributions are studied. We deduce the conditions required to produce super-Gaussian profiles of order 6 at the focal plane of a converging lens.     

Investigation in the propagation of non-paraxial TE vector Gaussian beam from vectorial structure

Based on the vectorial structure of non-paraxial electromagnetic beam and the non-paraxial vectorial moment theory of light beam propagation, the beam waists, the divergence angles and the beam propagation factors of TE and TM terms have been presented for non-paraxial TE vector Gaussian beam. The formulae obtained are further discussed at the highly non-paraxial and paraxial cases. Their respective maximum divergence angles are given at the highly non-paraxial case. When reducing to the paraxial case, the beam propagation factors of TE and TM terms are smaller than unity, which results from their special energy flux distribution. As TE and TM terms can be detached in the far field, they can be applied in the optical storage and collimation domains.     

Transformation of the multimode terahertz quantum cascade laser beam into a Gaussian, using a hollow dielectric waveguide

We demonstrate that a short hollow dielectric tube can act as a dielectric waveguide and transform the multimode, highly diverging terahertz quantum cascade laser beam into the lowest order dielectric waveguide hybrid mode, EH(11), which then couples efficiently to the free-space Gaussian mode, TEM(00). This simple approach should enable terahertz quantum cascade lasers to be employed in applications where a spatially coherent beam is required.     

Determination of the true airspeed vector for aircraft using an airborne laser doppler measuring system

We consider the fundamental aspects of airborne laser Doppler measurements of the true airspeed vector for aircraft, the principles of the theory of the measurement process, analysis of the accuracy characteristics and questions concerning performance of the measurements.Translated from Izmeritel'naya Tekhnika, No. 8, pp. 27–31, August, 1994.     

Different models for a hard-aperture function and corresponding approximate analytical propagation equations of a Gaussian beam through an apertured optical system

Beam profiles that consist of a sum of complex-Gaussian functions, a sum of polynomial-Gaussian functions and a sum of multi-Gaussian functions offset by some fixed amount are proposed as three types of model for a hard-aperture function. By expanding an aperture function into these models, approximate analytical propagation equations for a Gaussian beam through an apertured ABCD optical system are obtained. Comparison among these models themselves and among propagation characteristics of a Gaussian beam through these models are made. It is shown that the first and third types of model for a hard-aperture function are more suitable than the second type, in terms of calculation efficiency and simulation results, for application to such diffraction problems. Moreover, there are some differences in the applicability of the first and the third models.     

A frame-invariant scheme for the geometrically exact beam using rotation vector parametrization

While frame-invariant solutions for arbitrarily large rotational deformations have been reported through the orthogonal matrix parametrization, derivation of such solutions purely through a rotation vector parametrization, which uses only three parameters and provides a parsimonious storage of rotations, is novel and constitutes the subject of this paper. In particular, we employ interpolations of relative rotations and a new rotation vector update for a strain-objective finite element formulation in the material framework. We show that the update provides either the desired rotation vector or its complement. This rules out an additive interpolation of total rotation vectors at the nodes. Hence, interpolations of relative rotation vectors are used. Through numerical examples, we show that combining the proposed update with interpolations of relative rotations yields frame-invariant and path-independent numerical solutions. Advantages of the present approach vis-a-vis the updated Lagrangian formulation are also analyzed.     

Optical investigations of short-lived processes using an electron beam pumped semiconductor laser

Translated from Izmeritel'naya Tekhnika, No. 6, pp. 22–23, June, 1994.     

On the use of Somigliana's formulae and series of surface spherical harmonics for elasticity problems with spherical boundaries

This paper discusses applications of Somiglina's identities to the solutions of elasticity problems with spherical boundaries. The components of the boundary displacements and tractions involved in the identities are represented as truncated series of surface spherical harmonics, and all of the integrals involved in the formulae are evaluated analytically. The classical problems of a solid sphere, a spherical cavity, and a perfectly bonded spherical inhomogeneity (an inclusion with the elastic properties different from those of the surrounding material) are solved with the use of Somiglina's identities. Extensions of the new solutions to more complicated three-dimensional problems with spherical boundaries are discussed.     

Accelerating the annihilation of an optical vortex dipole in a Gaussian beam

When a Gaussian beam with two oppositely charged vortices propagates in free space, these two vortices will move around on the transverse beam plane. They may either move toward each other and annihilate each other spontaneously or survive all the way depending on the conditions. Here, we investigate how to force vortex dipoles to annihilate. We find that the background phase function created by two oppositely charged vortices during beam propagation can cause the vortices to move together and annihilate each other. The background phase function on a transverse plane just beyond the point where a dipole annihilated is continuous and retains the potential that forces a dipole to annihilate. We use this background phase function to accelerate the annihilation of vortex dipoles. Numerical results are provided to show the acceleration of dipole annihilation in a Gaussian beam, using such a background phase function.     

Optimal control of high harmonics for the generation of double attosecond pulses by using a chirped laser pulse

An efficient scheme for the optimization of ultrashort femtosecond pulse shapes interacting with an atom to control high harmonics spectrum and double attosecond pulse generation is presented. The time-dependent Schrödinger equation of one-dimensional hydrogen atom is solved numerically to obtain electric field emission. The genetic algorithm optimization method is used to control the phase and amplitude of ultrashort excitation laser pulses to generate the desired attosecond-shaped pulses. An appropriate cost function is introduced for genetic algorithm optimization of double attosecond pulse generation. It is shown that the relative intensity of two generated pulses, their delay time and duration can be controlled in this approach. Finally, the parameters of the optimized emitted attosecond pulse are compared with those of desired pulses, and the underlying physical mechanisms are discussed in detail.