Combined effects of polarization and nonparaxial propagation on pattern formation

Abstract

We show analytically that the presence inside an optical cavity of a polarizer and a hard diffracting object, for example, a circular aperture or 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. These types 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 system, we investigate numerically the bifurcations of a ring laser with a metallic duct and a polarizer inside the optical cavity.

Explicit centre manifold reduction and full bifurcation analysis for an astigmatic Maxwell–Bloch laser

“…In this paper we have analysed in detail the case of an astigmatic laser, but the same normal forms could be used to study the symmetry breaking induced for example by the interaction of a metallic wave guide and an aperture, the case studied in [6,7].…”

“…A final point worth remarking is that our derivation of the normal forms takes place in a broad context of breaking rotational symmetry. In this paper we have analysed in detail the case of an astigmatic laser, but the same normal forms could be used to study the symmetry breaking induced for example by the interaction of a metallic wave guide and an aperture, the case studied in [6,7].…”

“…These ideas have been fruitfully used in optics either to classify the patterns produced by experiments [5] or by models [6][7][8], and to infer from these the symmetry of the systems under investigation. They have also been used to study in great detail the structure of the bifurcations of normal form equations with the same symmetry as the experiments [9][10][11].…”

“…This section contributes to these studies by highlighting the fact that the two interacting modes need not be standard Gauss-Hermite modes but can be any cavity mode: for example they could be the modes of a waveguide cavity as studied in [6][7][8]. Moreover, we include in our analysis a bifurcation scenario with unexpected additional symmetry that is excluded from the generic studies in [14] and which arises when the frequency ω C of the unperturbed cavity mode and the frequency ω A of atomic transmission coincide.…”

“…Symmetries pose considerable constraints on the configuration of stationary solutions and on the time evolution of dynamical systems as well as on their bifurcation behaviour [1][2][3][4], to the extent that the presence of symmetries can often dictate the existence of certain solution branches independently of the specific model under consideration. These ideas have been fruitfully used in optics either to classify the patterns produced by experiments [5] or by models [6][7][8], and to infer from these the symmetry of the systems under investigation. They have also been used to study in great detail the structure of the bifurcations of normal form equations with the same symmetry as the experiments [9][10][11].…”