A General Diffraction Theory: A New Approach

Orestes N. Stavroudis

doi:10.1117/12.932347

26 February 1982 A General Diffraction Theory: A New Approach

Orestes N. Stavroudis

Proceedings Volume 0294, New Methods for Optical, Quasi-Optical, Acoustic, and Electromagnetic Synthesis; (1982) https://doi.org/10.1117/12.932347
Event: 25th Annual Technical Symposium, 1981, San Diego, United States

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.

Citation Download Citation

Orestes N. Stavroudis "A General Diffraction Theory: A New Approach", Proc. SPIE 0294, New Methods for Optical, Quasi-Optical, Acoustic, and Electromagnetic Synthesis, (26 February 1982); https://doi.org/10.1117/12.932347

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available