Cavity Equations For a Negative Index Material with Electric and Magnetic Non-Linearities

D.A. MÁRTIN; M. HOYUELOS

Piriapolis, Uruguay

Workshop; 4TH RIO DE LA PLATA WORKSHOP ON LASER DYNAMICS AND NONLINEAR PHOTONICS; 2009

We present the equations for the evolution of the electric and magnetic field amplitudes, in a plane perpendicular to light propagation, in a ring cavity with plane mirrors containing a material with positive or negative refraction index and with electric and magnetic non-linearities. We prove that the description can be reduced to one Lugiato Lefever equation with generalized coefficients. A stability analysis shows that any combination of the parameters should correspond to one of three typical cases, as the input field intensity is increased: the homogeneous solution is always stable, the homogeneous solutions becomes unstable and gives rise to another homogeneous solution, or, when the homogeneous solution becomes unstable, the system evolves to a non-homogeneous solution.