Reciprocity theorems for electromagnetic or acoustic one‐way wave fields in dissipative inhomogeneous media

Abstract

Reciprocity theorems have proven their usefulness in the study of forward and inverse scattering problems. Most reciprocity theorems in the literature apply to the total wave field and are thus not compatible with one‐way wave theory, which is often applied in situations in which there is a clear preferred direction of propagation, like in electromagnetic or acoustic wave guides and in seismic exploration. In this paper we review the theory for one‐way wave fields (or bidirectional beams), and we extensively discuss the symmetry properties of the square root operator appearing in the one‐way wave equation. Using these symmetry properties, it appears to be possible to derive reciprocity theorems of the convolution type and of the correlation type for electromagnetic or acoustic one‐way wave fields in dissipative inhomogeneous media along the same lines as the usual derivation of the reciprocity theorems for the total wave field. The one‐way reciprocity theorem of the convolution type provides a basis for representations of scattered one‐way wave fields in terms of generalized Bremmer series expansions or generalized primaries. The one‐way reciprocity theorem of the correlation type finds its application in reflection imaging based on inverse one‐way wave field propagators.