Abstract
We study a system composed by a cavity with plane mirrors containing a positive or negative refraction index material with third order effective electric and magnetic non-linearities. The aim of the work is to present a general picture of possible non-linear states in terms of the relevant parameters of the system. The parameters are the ones that appear in a reduced description that has the form of the Lugiato-Lefever equation. This equation is obtained from two coupled non-linear Schrodinger equations for the electric and magnetic field amplitudes.
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