Diffraction Theory

Abstract

A critical review is presented of recent progress in classical diffraction theory.Both scalar and electromagnetic problems are discussed. The report may serve as an introduction to general diffraction theory although the main emphasis is on diffraction by plane obstacles. Various modifications of the Kirchhoff and Kottler theories are presented. Diffraction by obstacles small compared with the wavelength is discussed in some detail. Other topics included are : variational formulation of diffraction problems, the Wiener-Hopf technique of solving integral equations of diffraction theory, the rigorous formulation of Babinet's principle, the nature of field singularities at sharp edges, the application of Mathieu functions and spheroidal wave functions to diffraction theory. Reference is made to more than 500 papers published since 1940. Q 1. INTRODUCTION, SCOPE AND LIMITATION OF THE REPORT G L A N C E through the scientific literature of the last decade reveals an increasing interest in diffraction theory. Undoubtedly the impetus to

Near-field microscopy with a single-photon point-like emitter: Resolution versus the aperture tip?

“…This is qualitatively different from the Bethe-Bouwkamp model [51,52] which predicts an electric dipole along the axis normal to the aperture plane. This difference is justified on a symmetry ground due to the conical nature of the NSOM metal coating [45,46] which contrasts with the planar geometry used in the work of Bethe and Bouwkamp.…”

“…However, there was to our knowledge no use of such a model for describing the NSOM tip emission prior to our own work. Additionally, it should be observed that in complete analogy with the old work by Stratton and Chu (reviewed by Bouwkamp [52]) we can also include in the present description a fictitious density of "magnetic charge" γ and magnetic current K along the rim in order to introduce a net magnetic dipole in the formalism. The formulas for the dipole and fields generated by such magnetic distributions are obtained by analogy with the electric ones (i.e., Eqs.…”

“…Therefore, another approach must be developed. Historically the first model used for describing an aperture near-field probe is the one given by Rayleigh, Bethe, and Bouwkamp for the transmission by a subwavelength circular aperture in a infinitely thin and perfectly conducting flat screen [51,52]. However, because of important differences between the geometry considered for the aperture-NSOM tip on the one hand and the ideal flat and thin metal screen of the "Bethe" model on the other hand [45,46] we developed some time ago a different approach [7,49], which takes into account the conical geometry of the optical tip and also the various field symmetries.…”

Finite element study of ultrasonic imaging

“…It does not, however, predict several key aspects of coupled wave phenomena. For high frequencyproblems, or equivalently, the situation with large crack size in comparison with wavelength, the KirchhofF approximation [12,13] is applicable if the incident angle is in a restricted range. The basic assumptions involved in the approximation are that the incident field reflects at each point on the defect as though the defect were an infinite plane and the wavefield is zero on the dark side of the crack.…”

Single photon transport by a moving atom through sub-wavelength hole

“…Unfortunately as was shown by Bethe [1] and Bouwkamp [2] the efficiency of such transport is low in the case of subwavelength holes. A remarkable discovery about the transmission of light through a subwavelength hole in a metal screen of a finite thickness and a finite conductivity that has been made by Ebbesen et al [3] has shown that the standard theory of diffraction by small holes is invalid, and, in this case, the transmission of light through the subwavelength hole can be strongly enhanced.…”