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Proceedings Paper

A General Diffraction Theory: A New Approach
Author(s): Orestes N. Stavroudis
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Paper Abstract

Several years ago we published some results concerning the structure of geometrical wavefronts in a homogeneous medium. A description of a wavefront was obtained as a general solution of the eikonal equation. By means of some standard techniques in differential geometry this led to the description of the general caustic. This in turn led us to the study of the geometric aberrations of an optical system from a completely different point of view. These results also suggest an approach to the physics of. the Propagation of light in a homogeneous medium which ought to lead to a proper vector diffraction theory. Recall Hertz' approach to the problem of the spherical wavefront in which he transformed the Maxwell equations into wave equations for the vector and scalar potential functions. To apply these to the spherical wavefront he transformed the arguments of the aradient, divergence and curl operators to a spherical coordinate system. The near-field solution of the wave equation predicted the existence of the dipole oscillator. The farfield solution yielded the now well-known description of the polarization and energy distribution on a spherical wavefront. Present work involves applying these same techniques to the general wavefront obtained as a solution of the eikonal equation. The vector differential operators have been transformed to an appropriate generalized coordinate system. The wave equation for the Potential functions have been obtained and an intermediate integral has been found. As is stands at the present time the electric and magnetic vectors can be expressed in terms of this intermediate integral.

Paper Details

Date Published: 26 February 1982
PDF: 7 pages
Proc. SPIE 0294, New Methods for Optical, Quasi-Optical, Acoustic, and Electromagnetic Synthesis, (26 February 1982); doi: 10.1117/12.932347
Show Author Affiliations
Orestes N. Stavroudis, University of Arizona (United States)

Published in SPIE Proceedings Vol. 0294:
New Methods for Optical, Quasi-Optical, Acoustic, and Electromagnetic Synthesis
W. Ross Stone, Editor(s)

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