Wave-amplitude synthesis applied to Gaussian-beam scattering by an off-axis sphere.

Electromagnetic scattering of a Gaussian beam by an off-axis dielectric sphere is treated by the sum-of-waves formulation, which is inherent in Lorenz-Mie theory. Each "wave" is a spherical eigenvector, defined in the natural frame of the scatterer, and the coefficient of that wave is the "wave amplitude." Decomposition of the beam into homogeneous plane waves lays the ground for a synthesis of the wave amplitudes, which is done by an integration over the polar angle that defines the direction of propagation of the plane-wave constituents of the beam.

Dyadic Green's function of an eccentrically stratified sphere.

The electric dyadic Green's function (dGf) of an eccentrically stratified sphere is built by use of the superposition principle, dyadic algebra, and the addition theorem of vector spherical harmonics. The end result of the analytical formulation is a set of linear equations for the unknown vector wave amplitudes of the dGf. The unknowns are calculated by truncation of the infinite sums and matrix inversion.

Dyadic Green's function of a cluster of spheres.

The electric dyadic Green's function (dGf) of a cluster of spheres is obtained by application of the superposition principle, dyadic algebra, and the indirect mode-matching method. The analysis results in a set of linear equations for the unknown, vector, wave amplitudes of the dGf; that set is solved by truncation and matrix inversion. The theory is exact in the sense that no simplifying assumptions are made in the analytical steps leading to the dGf, and it is general in the sense that any number, position, size and electrical properties can be considered for the spheres that cluster together.

Dyadic Green's function of a sphere with an eccentric spherical inclusion.

An exact, analytical solution to the problem of point-source radiation in the presence of a sphere with an eccentric spherical inclusion has been obtained by combined use of the dyadic Green's function formalism and the indirect mode-matching technique. The end result of the analysis is a set of linear equations for the vector wave amplitudes of the electric Green's dyad. The point source can be anywhere, even within the aforesaid nonspherical body, and there is no restriction with regard to the electrical properties in any part of space.

On the accuracy of perturbative solutions to wave scattering from rough closed surfaces.

The method of small perturbations is applied to the problem of plane-wave scattering from a soft circular surface with sinusoidal roughness. Rayleigh-theory and extinction-theorem perturbative solutions of arbitrary order are developed, and they are compared to each other as well as to an exact solution. A numerical study yields quantitative information about effects associated with the use of the Rayleigh hypothesis, about the merit of higher-order solutions, and about the reliability of the error criteria that measure a posteriori the conformity of perturbative solutions to the boundary condition.

Interactive resonant scattering by a cluster of air bubbles in water.

An exact, analytical solution is developed for the problem of acoustic-wave scattering from a cluster of ideal, gaseous, spherical bubbles in an unbounded, homogeneous, host fluid. This solution takes into account all modes of oscillation of the bubbles as well as all interactions between them; it is applicable to a wide range of bubble sizes and excitation frequencies. In the low frequency regime, the theory of this paper is shown to reduce to the "monopole" approximation, the effect of higher-order modes being non-negligible only for very small bubble-to-bubble separations.

Electromagnetic-wave scattering by a sphere with multiple spherical inclusions.

An exact solution to the problem of electromagnetic-wave scattering from a sphere with an arbitrary number of nonoverlapping spherical inclusions is obtained by use of the indirect mode-matching technique. A set of linear equations for the wave amplitudes of the electric field intensity throughout the inhomogeneous sphere and in the surrounding empty space is determined. Numerical results are calculated by truncation and matrix inversion of that set of equations.