Gérard Gréhan

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.

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.

Prediction of reverse radiation pressure by generalized Lorenz-Mie theory.

Radiation pressure exerted on a spherical particle by one extremely focused Gaussian beam is investigated by the use of generalized Lorenz-Mie theory (GLMT). Particular attention is devoted to reverse radiation pressure. GLMT predictions for different descriptions of the incident beam are compared with electrostriction predictions when the particle size is smaller than the wavelength and with geometric-optics predictions when the particle size is larger than the wavelength.

Computations of the gn coefficients in the generalized Lorenz-Mie theory using three different methods

Three different methods can be used to numerically compute the g(n) coefficients in the generalized Lorenz-Mie theory. Two of them are rigorous and involve (i) numerical evaluation of quadratures and (ii) numerical evaluation of finite series. The third way relies on the so-called localized interpretation that we discussed in previous papers. These three methods are discussed and compared.

Integral localized approximation in generalized Lorenz–Mie theory

The generalized Lorenz-Mie theory deals with the interaction between spheres and arbitrarily shaped illuminating beams. An efficient use of the theory requires efficient evaluation of the so-called beam-shape coefficients involved in the description of the illuminating beam. A less time-consuming method of evaluation relies on the localized approximation. However, it lacks flexibility when the description of the illuminating beam is modified. We present a new version of this method, called the integral localized approximation, that exhibits the desired property of flexibility.