## Abstract

Several theorems are formulated, regarding symmetry relations between two monochromatic fields that propagate either into the same half-space (<i>z</i> > 0) or into two complementary half-spaces (<i>z</i> > 0 and <i>z</i> < 0) and that satisfy one of two simple phase-conjugacy conditions in a cross sectional plane <i>z</i> = constant. The theorems are rigorously valid for fields whose two-dimensional spatial-frequency spectrum in the cross sectional plane is bandlimited to a circle of radius equal to the wave number of the field. One of the theorems elucidates some recently predicted symmetry properties of focused fields.

© 1980 Optical Society of America

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