Cavity equations for a positive or negative refraction index material   with electric and magnetic non-linearities
  We study evolution equations for electric and magnetic field amplitudes in a ring cavity with plane mirrors. The cavity is filled with a positive or negative refraction index material with third order effective electric and magnetic non-linearities. Two coupled non-linear equations for the electric and magnetic amplitudes are obtained. We prove that the description can be reduced to one Lugiato Lefever equation with generalized coefficients. A stability analysis of the homogeneous solution, complemented with numerical integration, shows that any combination of the parameters should correspond to one of three characteristic behaviors. 
Daniel A. M\'artin and Miguel Hoyuelos
physics.optics nlin.PS