Abstract

The practice of using complex-valued notation in classical electromagnetic theory is shown to have a more fundamental basis than that of simplifying mathematical manipulations. In the algebraic formulation, the positive and negative time-frequency components of the real-valued field quantities are propagated by two different diffraction operators, each of which is the dual (adjoint) of the other. In addition to the basic distinguishability of these positive and negative time-frequency components, other features distinguish them in general, owing to the constraint of Maxwell’s equations. In the monochromatic case, there are boundary fields for which these other features vanish. For some of these fields, a pseudoscopic image can be propagated. The appearance and location of the pseudoscopic image in holography is shown to be a direct consequence of the unitary property of the diffraction operator in the absence of evanescent waves.

© 1969 Optical Society of America

Distribution Formulation of Diffraction. The Monochromatic Case

W. Duane Montgomery
J. Opt. Soc. Am. 59(2) 136-141 (1969)

Algebraic Formulation of Diffraction Applied to Self Imaging

W. Duane Montgomery
J. Opt. Soc. Am. 58(8) 1112-1124 (1968)

Diffracted Wave Fields Expressible by Plane-Wave Expansions Containing only Homogeneous Waves*

George C. Sherman
J. Opt. Soc. Am. 59(6) 697-711 (1969)

Propagation of the Fourth-Order Coherence Function in a Random Medium (a Nonperturbative Formulation)*

M. J. Beran and T. L. Ho
J. Opt. Soc. Am. 59(9) 1134-1138 (1969)

Relativistic Correlation Theory of the Electromagnetic Field in the Presence of Random Sources*

D. Dialetis
J. Opt. Soc. Am. 59(1) 74-78 (1969)