Time reversal and reciprocity

Abstract

A number of phenomena discussed in earlier chapters indicated a close relationship between Lorentz adjointness and time reversal. In Sees. 2.4.1-3, Sees. 6.2.2-3 and also in Sees. 4.4.1, 4.4.3 and 4.5.3 (Figs. 4.2, 4.4 and 4.6) we noted that spatially transformed time-reversed gyrotropic media were ‘conjugate’ or ‘reciprocal’ to the given medium. The spatial transformation needed to be no more than an identity transformation, so that it was the time reversal (specifically, the reversal in direction of the external magnetic field) that rendered the medium ‘reciprocal’. Furthermore, the Lorentz-adjoint fields and currents that obeyed Maxwell’s equations in this reciprocal medium were found to be related to the fields and currents in the given medium by a Lorentz reciprocity relationship, one of the consequences of which was the interchange of roles of receiving and transmitting antennas. This too could be seen as an expression of time reversal of the transmitting-receiving process.