title: Cavity equations for a positive- or negative-refraction-index material with electric and magnetic nonlinearities.
abstract: 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 nonlinearities. Two coupled nonlinear 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.
authors.affiliation: Departamento de Física, Universidad Nacional de Mar del Plata, Funes 3350, 7600 Mar del Plata, Argentina.
authors.forename: Daniel A
authors.initials: DA
authors.lastname: Mártin
authors.forename: Miguel
authors.initials: M
authors.lastname: Hoyuelos