The eikonal approximation revisited

Abstract

Certain problems in optical scattering are best understood when the more complicated exact scattering theory is replaced by an approximation. The Fraunhofer approximation is a well-known example. In the past ten years a considerable amount of work has been done in various disciplines towards assessing the usefulness of a new approximation referred to in the literature either as the eikonal approximation or as the high-energy approximation. The purpose of this paper is to provide a much needed review of this work and in addition to examine the historical evolution of this approximation which essentially started in optics when Bruns introduced the term eikonal in 1895.PACS 42.10.Dy -Wave, fronts and ray tracing. PACS 42.10.Hc -Diffraction and scattering from extended bodies.

On the Validity of Soft-particle Approximations for the Scattering of Light by Infinitely Long Homogeneous Cylinders

“…The resulting expressions (1) and (2) can be summed using the addition theorem (9). One then obtains for the scattering function…”

“…In addition to giving simple analytic expressions for quick and easy use, these also provide a deeper physical and mathematical insight into the general scattering problem so that one is aware of the important factors to guide the necessary approximations in intractable situations . This is indeed the reason why so much time and effort is being put into studies of approximation methods even now (for example [2,5,6]) . This paper has been organized as follows .…”

“…Among the approximations developed for the analysis of light scattered by soft particles, the most extensively studied are the Rayleigh-Gans-Debye approximation (RGDA) [1], the anomalous diffraction approximation (ADA) [1] and the eikonal approximation (EA) [2] . If we denote by a and m respectively the `radius' and the relative refractive index of the scatterer and by A the wavelength of the incident radiation, then the softness requirement for the validity of these approximations is Im-1 I << 1 .…”

Diffraction of light by the gravitational field of the Sun and the solar corona

“…The region of scattering of high frequency EM waves on the plasma-induced potential V p is bounded by the heliocentric distance to the heliopause, R ⋆ from (3). We implement the eikonal approximation [54][55][56][57][58][59]. In this approximation, the short-range plasma potential contributes only a phase shift to the EM wave which can be directly calculated.…”

On the validity of soft particle approximations for the light scattering by a homogeneous dielectric sphere

“…This is essentially due to the fact that the errors introduced in ignoring the vector nature of light are indeed small for large particles. In fact the errors so introduced have been noted to be less than 3 per cent for x >> 10.0 [2]. Therefore, it seems worthwhile to obtain and study a scalar analogue of the S-approximation.…”