Codimension-two bifurcations and interactions between differently polarised fields for the laser with saturable absorber

Abstract

The equations for the laser with a saturable absorber in the mean-field limit and exact resonance are considered. For critical values of the number of active atoms in the laser and the absorber the equations exhibit a codimension-two degeneracy of the Takens-Bogdanov type, where a stationary bifurcation and a Hopf bifurcation with infinite period coalesce. The envelopes of the electric field and the atomic polarisations are treated as complex variables. This allows one to take differently polarised laser fields into account. The authors compute the relevant normal form coefficients and divide the space of the physical parameters into a number of regions that give rise to qualitatively different bifurcation scenarios. These include hysteretic and continuous stability exchanges between circularly polarised and modulated linearly polarised laser fields.