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We study evolution equations and stationary homogeneous solutions forelectric and magnetic field amplitudes in a ring cavity with flat mirrors. Thecavity is filled with a positive or negative refraction index material withthird order Kerr-like electric nonlinearities and also magnetic nonlinearities,which can be relevant in metamaterials. We consider the degree of freedom ofpolarization in the incident beam. It is found that considering a magneticnonlinearity increases the variety of possible qualitatively differentsolutions. A classification of solutions is proposed in terms of the number ofbifurcations. The analysis can be useful for the implementation of opticalswitching or memory storage using ring cavities with non linear materials.

Homogeneous solutions for elliptically polarized light in a cavity containing materials with electric and magnetic nonlinearities