Optical Cross-section Theorem Research Articles

A Tutorial on the Classical Theories of Electromagnetic Scattering and Diffraction

AbstractStarting with Maxwell’s equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering. These results are then extended to cover the case of vector electromagnetic fields. The famous Sommerfeld solution to the problem of diffraction from a perfectly conducting half-plane is elaborated. Far-field scattering of plane waves from obstacles is treated in some detail, and the well-known optical cross-section theorem, which relates the scattering cross-section of an obstacle to its forward scattering amplitude, is derived. Also examined is the case of scattering from mild inhomogeneities within an otherwise homogeneous medium, where, in the first Born approximation, a fairly simple formula is found to relate the far-field scattering amplitude to the host medium’s optical properties. The related problem of neutron scattering from ferromagnetic materials is treated in the final section of the paper.

Analysis of forward scattering of an acoustical zeroth-order Bessel beam from rigid complicated (aspherical) structures

The forward scattering from rigid spheroids and endcapped cylinders with finite length (even with a large aspect ratio) immersed in a non-viscous fluid under the illumination of an idealized zeroth-order acoustical Bessel beam (ABB) with arbitrary angles of incidence is calculated and analyzed in the implementation of the T-matrix method (TTM). Based on the present method, the incident coefficients of expansion for the incident ABB are derived and simplifying methods are proposed for the numerical accuracy and computational efficiency according to the geometrical symmetries. A home-made MATLAB software package is constructed accordingly, and then verified and validated for the ABB scattering from rigid aspherical obstacles. Several numerical examples are computed for the forward scattering from both rigid spheroids and finite cylinder, with particular emphasis on the aspect ratios, the half-cone angles of ABBs, the incident angles and the dimensionless frequencies. The rectangular patterns of target strength in the (β, θs) domain (where β is the half-cone angle of the ABB and θs is the scattered polar angle) and local/total forward scattering versus dimensionless frequency are exhibited, which could provide new insights into the physical mechanisms of Bessel beam scattering by rigid spheroids and finite cylinders. The ray diagrams in geometrical models for the scattering in the forward half-space and the optical cross-section theorem help to interpret the scattering mechanisms of ABBs. This research work may provide an alternative for the partial wave series solution under certain circumstances interacting with ABBs for complicated obstacles and benefit some related works in optics and electromagnetics.

A New Theory of the Generalized Optical Theorem in Anisotropic Media

A new general approach for the generalized optical cross-section theorem and its particular manifestation, the ordinary optical theorem, is developed for electromagnetic scattering in anisotropic media (corresponding to the scatterer and the background medium where the scatterer is embedded). The derived results are based on cross-flux concepts, and interaction and reciprocity relations, and apply under arbitrary incident fields, hence they apply in arbitrary representational domains for the data or scattering matrix. This generalization is demonstrated for arbitrary anisotropic scatterers embedded in lossless anisotropic background media by means of the so-called modified reciprocity theorem plus duality. A new reactive optical theorem is also derived which clarifies the possibilities and limitations of the extraction of reactive energy storage information of an scatterer from scattering field data. Fundamental and practical imaging implications of the derived optical theorems are discussed. The developed theory is elaborated for general anisotropic scatterers embedded in free space via the multipole expansion of the electromagnetic field.

New perspective on the optical theorem of classical electrodynamics

A proof of the optical theorem (also known as the optical cross-section theorem) is presented, which reveals the intimate connection between the forward scattering amplitude and the absorption-plus-scattering of the incident wave within the scatterer. The oscillating charges and currents as well as the electric and magnetic dipoles of the scatterer, driven by an incident plane wave, extract energy from the incident beam. The same oscillators radiate electromagnetic energy into the far field, thus giving rise to well-defined scattering amplitudes along various directions. The essence of the proof presented here is that the extinction cross-section of an object can be related to its forward scattering amplitude using the induced oscillations within the object without knowledge of the form assumed by these oscillations.

The optical cross-section theorem with incident fields containing evanescent components

Abstract The optical cross-section theorem is extended to cases in which the incident field contains evanescent waves. Physical interpretations are discussed. Some explicit examples are given and possible applications are proposed.

The optical cross-section theorem with incident fields containing evanescent components

The optical cross-section theorem is extended to cases in which the incident field contains evanescent waves. Physical interpretations are discussed. Some explicit examples are given and possible applications are proposed.

An energy theorem for scattering of partially coherent beams

A recent generalization of the optical cross-section theorem is applied to obtain an expression for the rate at which energy is removed by scattering and absorption from a wide class of partially coherent beams. The class of beams considered includes the outputs of many lasers.

Statistical generalizations of the optical cross-section theorem with application to inverse scattering

A fundamental result of scattering theory, the so-called optical theorem, applies to situations where the field incident on the scatterer is a monochromatic plane wave and the scatterer is deterministic. We present generalizations of the theorem to situations where either the incident field or the scatterer or both are spatially random. By using these generalizations we demonstrate the possibility of determining the structure of some random scatterers from the knowledge of the power absorbed from two plane waves incident on it.