G. Gouesbet

Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation

We present a theoretical description of the scattering of a Gaussian beam by a spherical, homogeneous, and isotropic particle. This theory handles particles with arbitrary size and nature having any location relative to the Gaussian beam. The formulation is based on the Bromwich method and closely follows Kerker’s formulation for plane-wave scattering. It provides expressions for the scattered intensities, the phase angle, the cross sections, and the radiation pressure.

Particle lagrangian simulation in turbulent flows

Abstract A Lagrangian approach is used to describe particle dispersion in turbulent flows. Fluid particle trajectories are simulated with the aid of a correlation matrix evolving along the particle trajectory. Discrete particles are tracked in a given turbulent field taking into account crossing-trajectory effects, and the influence of the particles on the flow characteristics is deduced from momentum and energy exchanges between both phases. Comparisons of the simulations are given for both experimental and theoretical results for fluid particle diffusion problems. Particle dispersion predictions are presented for grid turbulence experiments, and for three two-phase turbulent round jets, from different authors. Predictions compared favourably with experimental results.

Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz–Mie theory. I. On-axis beams

Generalized Lorenz–Mie theory describes electromagnetic scattering of an arbitrary light beam by a spherical particle. The computationally most expensive feature of the theory is the evaluation of the beam-shape coefficients, which give the decomposition of the incident light beam into partial waves. The so-called localized approximation to these coefficients for a focused Gaussian beam is an analytical function whose use greatly simplifies Gaussian-beam scattering calculations. A mathematical justification and physical interpretation of the localized approximation is presented for on-axis beams.

Four-flux models to solve the scattering transfer equation in terms of Lorenz-Mie parameters.

The radiative transfer equation in nonemitting media is solved using a four-flux model in the case of Lorenz-Mie scatter centers embedded in a slab. The various coefficients of absorption and scattering appearing in the theory are nonphenomenological but expressed in terms of quantities available from the Lorenz-Mie framework. Formulas for the various transmittances and reflectances are established. Special cases are then discussed, and (potential or actual) applications reported.

Generalized Lorenz-Mie theories

Background in Maxwells Electromagnetism and Maxwells Equations.- Resolution of Special Maxwells Equations.- Generalized Lorenz-Mie Theories in the Strict Sense, and other GLMTs.- Gaussian Beams, and Other Beams.- Finite Series.- Special Cases of Axisymmetric and Gaussian Beams.- The Localized Approximation and Localized Beam Models.- Applications, and Miscellaneous Issues.- Conclusion.

Localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory

Numerical computations in the framework of the generalized Lorenz–Mie theory require the evaluation of a new double set of coefficients gn,TMm and gn,TEm (n = 1, …, ∞; m = − n, … +n). A localized interpretation of these coefficients is designed to permit fast and accurate computations, even on microcomputers. When the scatter center is located on the axis of the beam, a previously published localized approximation for a simpler set of coefficients gn is recovered as a special case. The subscript n in coefficients gn and gnm is associated with ray localization and discretization of space in directions perpendicular to the beam axis, while superscript m in coefficients gnm is associated with azimuthal wave modes.

Improved algorithm for electromagnetic scattering of plane waves and shaped beams by multilayered spheres

An efficient numerical procedure for computing the scattering coefficients of a multilayered sphere is discussed. The stability of the numerical scheme allows us to extend the feasible range of computations, both in size parameter and in number of layers for a given size, by several orders of magnitude with respect to previously published algorithms. Exemplifying results, such as scattering diagrams and cross-sectional curves, including the case of Gaussian beam illumination, are provided. Particular attention is paid to scattering at the rainbow angle for which approaches based on geometrical optics might fail to provide accurate enough results.

Electromagnetic scattering from a multilayered sphere located in an arbitrary beam

A solution is given for the problem of scattering of an arbitrary shaped beam by a multilayered sphere. Starting from Bromwich potentials and using the appropriate boundary conditions, we give expressions for the external and the internal fields. It is shown that the scattering coefficients can be generated from those established for a plane-wave illumination. Some numerical results that describe the scattering patterns and the radiation-pressure behavior when an incident Gaussian beam or a plane wave impinges on a multilayered sphere are presented.

A concise presentation of the generalized Lorenz-Mie theory for arbitrary location of the scatterer in an arbitrary incident profile

The authors present a synthetic formulation of the generalized Lorenz-Mie theory. With this very general fofmulation, they can describe scattering of arbitrary incident profiles by arbitrarily located spherical scatterers. The physical basis of the GLMT is highlighted and formulae are given for the physical quantities characterizing the scattered wave. The present state of numerical computations is discussed, as well as their further extension.

Scattering of laser beams by Mie scatter centers: numerical results using a localized approximation

Relying on van de Hulst’s localization principle, a localized approximation to the generalized Lorenz-Mie theory is introduced. The validation of this simple approximation is obtained from numerical comparisons the Rayleigh-Gans theory. Other comparisons concerning scattering profiles are carried out first with theoretical data published in the literature and later with experimental measurements. Original results are given for coal particles as an example of the versatility of the method.