%0 Journal Article
%T Cavity equations for a positive or negative refraction index material with electric and magnetic non-linearities
%A Daniel A. M¨¢rtin
%A Miguel Hoyuelos
%J Physics
%D 2012
%I arXiv
%R 10.1103/PhysRevE.80.056601
%X 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.
%U http://arxiv.org/abs/1212.3974v1