Cavity equations for a positive or negative refraction index material with electric and magnetic non-linearities

D.A. MÁRTIN; M. HOYUELOS

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

APS

Año: 2009 vol. 80 p. 56601 - 56609

1063-651X

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 andmagnetic 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.