Light-induced nonreciprocity: Directional optical bistability; spectroscopy of induced anisotropy; nonlinear Sagnac effect

It is shown that the effect of nonlinear nonreciprocity is directly related to the anisotropic properties of the third order nonlinear susceptibility. Therefore, it must be extremely sensitive to the mutual arrangement of polarization of both of the counter propagating waves. In the case of abitrary third order nonlinear tensor, the induced anisotropic response of the matter can be expressed as equations that, based on Maxwell equations and Eq(3), have four invariants which allow for some mutual eigen polarizations to propagate without distortion of their initial directions of polarization. Both of the beams are linearly polarized, with their electric vectors either (1) parallel to each other or (2) orthogonal to each other; both of the beams are circularly polarized being either (3) corotating or (4) counterrotating. All of those eigen polarizations have different respective magnitudes of nonlinear nonreciprocity. For instance, the ratio of pertinent nonlinear nonreciprocities for these configurations in the case of pure Kerr-effect is 1:(3/4):(1/4):(1/4):(3/2). Therefore, the proposed effect can be used as a novel experimental tool for the spectroscopy of the anisotropic components of the third order nonlinear tensor of matter.