Phase conjugation and symmetries with wave fields in free space containing evanescent components

Several theorems are known concerning symmetry relations between monochromatic wave fields that propagate either into the same half-space (z > 0) or into complementary half-spaces (z > 0 and z < 0) and that are complex conjugates of each other in some cross-sectional plane z = constant. The theorems derived up to now apply only to wave fields that do not contain inhomogeneous (evanescent) components. In the present paper two of the main theorems are generalized to a wider class of fields. It is found that homogeneous and inhomogeneous components of a wave field have quite different symmetry properties under phase conjugation. The results are illustrated by a discussion of the behavior of plane waves, both homogeneous and evanescent ones, which undergo phase conjugation followed by transmission or by reflection.