Phase conjugacy and symmetries in spatially bandlimited wavefields containing no evanescent components

Abstract

Several theorems are formulated, regarding symmetry relations between two monochromatic fields that propagate either into the same half-space (z > 0) or into two complementary half-spaces (z > 0 and z < 0) and that satisfy one of two simple phase-conjugacy conditions in a cross sectional plane z = 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.