Codimension Two Bifurcation in a Laser with Injected Signal

Abstract

The equations of a laser with injected signal have attracted interest not only in optics but also from the community of nonlinear dynamics physicists. After the pioneering works of Ref. [1] and [2] where the proper set of Maxwell-Bloch equations has been derived and integrated numerically, interesting dynamical effects ranging from the coexistence of conservative and dissipative behaviours [3] to the existence of codimension two bifurcations (CTB) [4] have been analysed. In Ref. [4], for example, a CTB was recognised to be responsible of the appearance of frequency pushed solutions which are counter-intuitive in a problem majorly related to locking phenomena. Recently, partial attempts of characterizing the degenerate nature of the CTB have been published [5]. However a complete unfolding of the CTB capable of showing analytically all the dynamical behaviours of the solutions is presently lacking.