Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. I. By a spherical particle

The geometrical-optics approximation of light scattering by a transparent or absorbing spherical particle is extended from plane wave to Gaussian beam incidence. The formulas for the calculation of the phase of each ray and the divergence factor are revised, and the interference of all the emerging rays is taken into account. The extended geometrical-optics approximation (EGOA) permits one to calculate the scattering diagram in all directions from 0 degrees to 180 degrees. The intensities of the scattered field calculated by the EGOA are compared with those calculated by the generalized Lorenz-Mie theory, and good agreement is found. The surface wave effect in Gaussian beam scattering is also qualitatively analyzed by introducing a flux ratio factor. The approach proposed is particularly important to the further extension of the geometrical-optics approximation to the scattering of large spheroidal particles.     

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.     

Scattering of a spheroidal particle illuminated by a gaussian beam

An approach to expanding a Gaussian beam in terms of the spheroidal wave functions in spheroidal coordinates is presented. The beam-shape coefficients of the Gaussian beam in spheroidal coordinates can be computed conveniently by use of the known expression for beam-shape coefficients, g(n), in spherical coordinates. The unknown expansion coefficients of scattered and internal electromagnetic fields are determined by a system of equations derived from the boundary conditions for continuity of the tangential components of the electric and magnetic vectors across the surface of the spheroid. A solution to the problem of scattering of a Gaussian beam by a homogeneous prolate (or oblate) spheroidal particle is obtained. The numerical values of the expansion coefficients and the scattered intensity distribution for incidence of an on-axis Gaussian beam are given.     

Electromagnetic field calculations for a sphere illuminated by a higher-order Gaussian beam. II. Far-field scattering

A previously developed theoretical procedure for determination of electromagnetic fields associated with the interaction of a higher-order Gaussian beam with a homogeneous spherical particle is used to investigate the effects of incident beam type on far-field scattering. Far-field scattering patterns are calculated for (0,0), (0,1), and (1,1) mode Hermite-Gaussian beams and for the helix doughnut mode beam. The effects of incident beam type on the angular distribution of far-field scattering, for both on-sphere-center and off-sphere-center focusing, are examined.     

Computation of the internal field of a large spherical particle by use of the geometrical-optics approximation

We obtain the internal electric field of an illuminated liquid droplet using geometrical optics. The approximation includes the phase effects of various components. We compare the geometrical-optics solution with the Mie theory solution for a nonabsorbing particle with a size parameter of alpha = 500 and an index of refraction of n = 1.332.     

Light scattering by a coated sphere illuminated with a Gaussian beam

The intensity of light scattered by a coated sphere illuminated with an off-axis Gaussian beam is calculated. Results are shown for different beam positions with respect to the sphere. As the beam is shifted further away from the surface of the sphere, the higher-Q morphology-dependent resonances become increasingly important in the backscatter spectra, and the angular scattering intensity becomes smoother.

The scattered intensity depends on the beam position, the refractive indices of the core and coat, the radius of the core, and the thickness of the coat. As the beam is moved further away from the sphere, the effect of the core on the scattering intensity decreases. When the incident Gaussian beam is focused outside of a particle with a relatively small core, the scattering spectra and angular scattering patterns become similar to those of a homogeneous sphere having the refractive index of the coat. These calculated results suggest that measurements of spectral scattering and angular scattering patterns for several Gaussian beam positions could be useful for the characterization of coated spheres.

     

Forward scattering of a Gaussian beam by a nonabsorbing sphere

The forward scattering of a Gaussian laser beam by a spherical particle located along the beam axis is analyzed with the generalized Lorenz-Mie theory (GLMT) and with diffraction theory. Forwardscattering and near-forward-scattering profiles from electrodynamically levitated droplets, 51.6 μm in diameter, are also presented and compared with GLMT-based predictions. The total intensity in the forward direction, formed by the superposition of the incident and the scattered fields, is found to correlate with the particle-extinction cross section, the particle diameter, and the beam width. Based on comparison with the GLMT, the diffraction solution is accurate when beam widths that are approximately greater than or equal to the particle diameter are considered and when large particles that have an extinction efficiency near the asymptotic value of 2 are considered. However, diffraction fails to describe the forward intensity for more tightly focused beams. The experimental observations, which are in good agreement with GLMT-based predictions, reveal that the total intensity profile about the forward direction is quite sensitive to particle axial position within a Gaussian beam. These finite beam effects are significant when the ratio of the beam to the particle diameter is less than approximately 5:1. For larger beam-to-particle-diameter ratios, the total field in the forward direction is dominated by the incident beam.     

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.     

Efficient analysis of temporal broadening of a pulsed focused Gaussian beam in scattering media

We show that the temporal broadening of a pulsed, tightly focused TEM(00) beam propagating in a scattering medium can be accurately modeled as a convolution between the initial pulse profile and an effective impulse response that is given by the propagation behavior of an infinitely thin pulse in the said medium. The impulse response is obtained with a Monte Carlo (MC) analysis of the propagating photons in the impulse. Our algorithm is 2 orders of magnitude less complex than the full MC solution of the pulse propagation problem. The accuracies, however, are comparable even for scattering path lengths that are 20 times the mean free path.     

Use of a laser beam with an oblique angle of incidence to measure the reduced scattering coefficient of a turbid medium

A simple and quick approach is used to measure the reduced scattering coefficient (μ(s)') of a semi-infinite turbid medium having a much smaller absorption coefficient than μ(s)'. A laser beam with an oblique angle of incidence to the medium causes the center of the diffuse reflectance that is several transport mean-free paths away from the incident point to shift away from the point of incidence by an amount Δx. This amount is used to compute μ(s)' by μ(s)' = sin(α(i))/(nΔx) where n is the refractive index of the turbid medium divided by that of the incident medium and α(i) is the angle of incidence measured from the surface normal. For a turbid medium having an absorption coefficient comparable with μ(s)', a revision to the above formula is made. This method is tested theoretically by Monte Carlo simulations and experimentally by a video reflectometer.     

Estimation of scattering from a moist rough surface with spheroidal dust particles

The scattering from moisture rough surface with spheroidal dust particles having surface with spheroidal dust particles has recently received much attention. In part due to the recent prediction and observation of the spheroidal dust particles in rough surfaces under elastic wave by the Kirchhoff scattering model and scalar approximation with slope. Our analysis shows that the scattering depends on the moisture (2–4·5%) with spheroidal dust particles. At slightly moisture rough surface the dielectric properties increase with change in field amplitude in a rough surface with spheroidal dust particles.     

Transmission of a Gaussian beam into a biaxial crystal.

We derive integral representations that are suitable for studying the transmission of an electromagnetic Gaussian beam through a plane interface that lies between an isotropic medium and a biaxially anisotropic crystal for the case in which the interface normal is along one of the principal axes of the crystal. To that end, we use recently developed exact solutions for the transmitted fields to derive explicit expressions for the corresponding dyadic Green's functions as well as integral representations that are suitable for asymptotic analysis and efficient numerical evaluation.     

Transmission of a two-dimensional Gaussian beam into a uniaxial crystal.

We study the transmission of a two-dimensional (2-D) TM Gaussian beam through a plane interface between an isotropic medium (e.g., air) and a uniaxially anisotropic crystal. The optic axis of the crystal is taken to be in the plane of incidence but is arbitrarily oriented relative to the interface normal. We show that, in the paraxial approximation, a nontruncated transmitted 2-D TM Gaussian beam inside a uniaxial crystal can be expressed in a form similar to that of a scalar Gaussian beam that propagates in a homogeneous medium. We also show that the transmitted beam corresponding to an incident 2-D TM Gaussian beam with its main propagation direction along the interface normal is tilted inside the crystal by the same angle as is the transmitted axial ray that corresponds to a normally incident ray.     

Shape-invariance properties of a quartic-aberrated TEM00 Gaussian beam.

The concepts of shape-invariance error (SIE) and shape-invariance range (SIR) have recently been introduced to specify in a quantitative way the shape changes suffered by a beam on propagation. Here such parameters are evaluated for the case of a fundamental Gaussian beam in the presence of a quartic aberration of its wave front. Numerical results are presented for the case of a collimated aberrated beam. Generalization to the case of noncollimated beams is also given.     

Generation of flattened Gaussian beam profiles in a Nd:YAG laser with a Gaussian mirror resonator

We report the experimental generation of a family of flattened Gaussian beams with bell-shaped, flattened, and annular intensity profiles in an electro-optically Q-switched Nd:YAG laser with a variable reflectivity mirror of a Gaussian reflectivity profile as an output coupler. The laser beams of different profiles were generated by modifying the resonator magnification. The propagation characteristics of the experimentally generated flat Gaussian beams were found to be in agreement with theory. To the best of our knowledge this is the first time such a family of flattened Gaussian beams is experimentally generated intracavity using a single variable reflectivity mirror.     

Role of multiple scattering in cross-correlated light scattering with a single laser beam

Previous systems for measuring cross-correlated light scattering by small particles suspended in a liquid with multiple-scattering suppression have illuminated the particles with two laser beams. It is shown that multiple-scattering suppression should also occur in cross correlation for a system that employs a single laser beam and two closely spaced detectors with wide fields of view. The single-scattering, double-scattering, and single-double-scattering cross-term contributions to the intensity cross-correlation function are calculated. It is found that the two cross terms, when added together, are unimportant for both autocorrelation and cross correlation. The amplitude of the double-scattering term can be greatly diminished by judicious detector spacing because the spatial coherence area in the detector plane for double scattering is much smaller than that for single scattering.     

Kinetics of heat transfer to a spherical particle from a rarefied plasma. 3. Maxwellian ion approximation

A. A. Baikov Metallurgical Institute, Russian Academy of Sciences, Moscow. Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 62, No. 2, pp. 254–260, February, 1992.     

Provision of exact formulations for the "forward scattering of a Gaussian beam by a nonabsorbing sphere": comment

The purpose of an earlier publication [Appl. Opt. 34, 2120 (1995)], to provide an exact formulation of the scattering of beamlike radiation fields from spheres, is clarified and its relation to the treatment of this subject in two more recent publications is described. Also, an error in the reference list in the earlier publication is rectified.     

First operation with a crystal septum to replace a magnet in a charged particle beam

Particle channeling in a bent crystal at Fermilab has been used to replace a magnet in a secondary charged particle beam. The maximum momentum of particles that could be transmitted to an experimental location was raised from the magnetic septum limit of 225 GeV/c to the full primary beam momentum of 400 GeV/c.