Directionally asymmetrical bistability in a symmetrically pumped nonlinear ring interferometer

We consider a nonlinear ring resonator pumped symmetrically by two beams of equal intensities and opposite directions. We show that this system is characterized by a new directionally asymmetrical regime of multistability. This is due to the non-reciprocity of propagation of the counterpropagating waves in the resonator produced by a nonlinear index grating.