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

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.