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In this paper we investigate the integral version of the localized approximation (ILA)—a powerful technique for evaluating the beam shape coefficients in the framework of the generalized Lorenz–Mie theory—as applied to ideal scalar Bessel beams (BBs). Originally conceived for arbitrary shaped beams with a propagating factor exp(±ikz), it has recently been shown that care must be taken when applying the ILA for the case of ideal scalar BBs, since they carry a propagating factor exp(±ikz cos α), with α being the axicon angle, which cannot be smoothly accommodated into its mathematical formalism. Comparisons are established between the beam shape coefficients calculated from both ILA and exact approaches, assuming paraxial approximation and both on- and off-axis beams. Particular simulations of radiation pressure forces are provided based on the existing data in the literature. This work helps us in elucidating that ILA provides adequate beam shape coefficients and descriptions of ideal scalar BBs up to certain limits and, even when it fails to do so, reliable information on the physical optical properties of interest can still be inferred, depending on specific geometric and electromagnetic aspects of the scatterer.

The use of the generalized Lorenz–Mie theory (GLMT) requires knowledge of beam-shape coefficients (BSC’s) that describe the beam illuminating a spherical scatterer. We theoretically demonstrated that these BSC’s can be determined from an actual beam in the laboratory. We demonstrate the effectiveness of our theoretical proposal by determining BSC’s for a He–Ne laser beam focused to a diameter of a few micrometers. Once these BSC’s are determined, the electromagnetic fields of the illuminating beam may be evaluated. By relying on the GLMT, we can also determine all properties of the interaction between beam and scatterer, including mechanical effects (radiation pressures and torques).

Our aim is to present the application of the hybrid method presented in part I to an inverse procedure to determine particle size and concentration under multiple-scattering conditions. The hybrid method is introduced as a combination of the four-flux method with coefficients obtained from Monte Carlo statistical simulations to take into account the actual three-dimensional geometry. Then an inversion scheme is expanded to enable the application of the hybrid method to particle size and concentration determination. We present the inversion method as well as exemplifying results of spectrum inversions.

Our aim is to present a method of predicting light transmittances through dense three-dimensional layered media. A hybrid method is introduced as a combination of the four-flux method with coefficients predicted from a Monte Carlo statistical model to take into account the actual three-dimensional geometry of the problem under study. We present the principles of the hybrid method, some exemplifying results of numerical simulations, and their comparison with results obtained from Bouguer–Lambert–Beer law and from Monte Carlo simulations.

We establish a localized approximation to evaluate the beam-shape coefficients of a Gaussian beam in elliptical cylinder coordinates. As for the case of spherical coordinates and of circular cylinder coordinates, this approximation provides an efficient way to speed up computations within the framework of a generalized Lorenz–Mie theory for elliptical cylinders.

The development of initial disturbances is relevant to the understanding of atomization processes in which droplets are generated by the breakup of a liquid jet. We theoretically and experimentally demonstrate that such disturbances can be characterized by rainbow sizing. More specifically, for a liquid jet with a diameter of 600 μm, disturbances in the range from 10 nm to 0.2 μm are accessible.

A cylindrical localized approximation to speed up numerical computations in generalized Lorenz–Mie theory for cylinders, in a special case of perpendicular illumination, was recently introduced and rigorously justified. We generalize this approximation to the case when the cylinder is arbitrarily located and arbitrarily oriented in a Gaussian beam.

We present numerical results concerning the properties of the electromagnetic field scattered by an infinite circular cylinder illuminated by a circular Gaussian beam. The cylinder is arbitrarily located and arbitrarily oriented with respect to the illuminating Gaussian beam. Numerical evaluations are provided within the framework of a rigorous electromagnetic theory, the generalized Lorenz–Mie theory, for infinite cylinders. This theory provides new insights that could not be obtained from older formulations, i.e., geometrical optics and plane-wave scattering. In particular, some emphasis is laid on the waveguiding effect and on the rainbow phenomenon whose fine structure is hardly predictable by use of geometrical optics.

Recently a so-called standard beam description of Gaussian beams was introduced [J. Opt. Soc. Am. A11, 2503 (1994)]. However, it was afterward observed [Appl. Opt.35, 2702 (1996)] that this description exhibits a finite radius of convergence, limiting its range of applicability. We introduce an improved standard beam description with an infinite radius of convergence. The utility of this improved description is illustrated by evaluation of radiation pressure forces under severe focusing conditions.

The use of the generalized Lorenz–Mie theory that describes the interaction between a spherical particle and an arbitrarily shaped beam requires knowledge of the beam-shape coefficients (BSC’s) that describe the illuminating beam. Classically, these BSC’s are evaluated from an a priori mathematical description of the illuminating beam. We propose a method that relies on intensity measurements along the beam axis that permits one to measure directly the BSC’s of an actual beam in the laboratory.

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.

In the framework of generalized Lorenz–Mie theory, laser beams are described by sets of beam-shape coefficients. The modified localized approximation to evaluate these coefficients for a focused Gaussian beam is presented. A new description of Gaussian beams, called standard beams, is introduced. A comparison is made between the values of the beam-shape coefficients in the framework of the localized approximation and the beam-shape coefficients of standard beams. This comparison leads to new insights concerning the electromagnetic description of laser beams. The relevance of our discussion is enhanced by a demonstration that the localized approximation provides a very satisfactory description of top-hat beams as well.

The theory of scattering of arbitrary-shaped beams by an infinite cylinder with arbitrary location and arbitrary orientation is presented. The theory relies on the use of distributions that provide the most general framework, which allows the use of any description of the incident beam. Apart from this peculiarity, the theory relies on the use of scalar potentials, and the resulting framework is rather similar to that of the generalized Lorenz–Mie theory for 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.

Scattered light patterns from a spherical particle located on the axis of a Gaussian beam are computed with localized interpretation of the generalized Lorenz-Mie theory and compared with diffraction theory results as well as experimental results.