Elliptically polarized transverse patterns in a cavity with electric and magnetic nonlinearities

D.A. MÁRTIN; M. HOYUELOS

Workshop; Fifth Rio de la Plata Workshop on laser dynamics and nonlinear photonics; 2011

We analyze the evolution equations of electric and magnetic field amplitudes in a ring cavity with flat mirrors, where the degree of freedom of light polarization is taken into account. The cavity is filled with a positive or negative refraction index material (NRM) with third order Kerr-like electric and magnetic nonlinearities (magnetic nonlinearities can be relevant for NRM). We present an overview of the possible patterns and instabilities for different values of the parameters (detuning, nonlinear parameter, light polarization and sign of diffraction). We also present a method for the analysis of eigenvalues that allows the derivation of some exact and general results. The method allows us to find Turing-Turing codimension 2 (where two different wavenumbers destabilize simultaneously) and a Turing-Hopf-Turing codimension 3 instability. It is shown that for a given input intensity there can not be more than three unstable tongues.