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International Journal of Antennas and Propagation
Volume 2015, Article ID 478580, 10 pages
Research Article

A Simple Proof of Damien’s Theorem and Duality in Theory of the Zero-Distance Phase Front

Institut für Optik und Atomare Physik, Technische Universität Berlin, Sekretariat ER 1-1, Strasse des 17. Juni 135, 10623 Berlin, Germany

Received 9 April 2015; Accepted 31 May 2015

Academic Editor: Giuseppe Castaldi

Copyright © 2015 Andrey Valerievich Gitin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Duality plays the main role in all mathematical theories. In wave optics based on the concept of “the zero-distance phase front,” duality takes the form of Damien’s theorem and the mirror symmetry between the conic refracting surfaces with the plane zero-distance phase front and the plane refracting surfaces with the conic zero-distance phase front. A systematic study of these dualities has been performed.