Figure 7. Signal output vs control output.

(a) Planar metamaterials: Starting from the signal output for phase α, for an arbitrary planar metamaterial and an arbitrary choice of polarization, the control output corresponds to the mirror image experiment (reversed azimuth rotation and ellipticity) with reversed roles of signal and control beams (phase −α). (b) The simplest case for intrinsic 3D chirality: Starting from the signal output for phase α, for normally incident y-polarization onto a pair of mutually twisted crosses in parallel planes, the control output corresponds to the same experiment (same azimuth rotation and ellipticity) with reversed roles of signal and control beams (phase −α). This relationship can be generalized to any choice of linear polarization for metamaterials with polarization azimuth-independent optical properties (e.g. 3-fold or higher rotational symmetry) that are identical for opposite directions of illumination. (a, b) The metamaterial is represented by a unit cell, the plane of incidence is shown by a gray sheet and the polarization state is indicated by a double arrow. The control beam polarization is chosen so that it has the same projection onto the metamaterial plane as the signal beam polarization.