Nonreciprocal magnetic-field-induced second harmonic generation of exciton polaritons in ZnSe

We report on the optical second harmonic generation (SHG) on the 1S exciton-polariton resonance in bulk ZnSe that is subject to an external magnetic field applied perpendicular to the light wave vector $\mathbf k$ (Voigt geometry). For the symmetry allowed geometry with the $\mathbf{k}\parallel[111]$ crystal axes, the nonreciprocal dependence of the SHG intensity on the magnetic field direction is found. It is explained by an interference of the crystallographic and magnetic-field-induced SHG signals. Relative phases of these signals are evaluated from the rotational anisotropy diagrams. Phenomenological and microscopic models of the effect are developed. To the best of our knowledge, this is the first experimental observation of the nonreciprocal SHG in semiconductor crystals, and the first one for exciton-polaritons.