Combined effects of polarization and non-paraxial propagation on pattern formation

We show analytically that the presence of a hard diffracting object inside an optical cavity, for example an aperture or a waveguide, reduces the symmetry of the system from cylindrical to rectangular. As a consequence, patterns with concentric rings of bright or dark spots made up by modes whose azimuthal indexes are not multiples of one another, appear when the zero field solution becomes unstable. This type of bifurcations are anomalous if the symmetry is cylindrical and therefore indicate the presence of polarization effects induced by diffraction. As an example of this type of systems, we investigate numerically the bifurcations of a ring laser with a metallic duct and a polarizer inside the optical cavity. PACS: 42.65.Sf, 42.55.-f, 42.25.Bs, 42.25.Gy