Quasi Vertical Hopf Bifurcation for the Multimode Class B Laser

Abstract

Using the rotating wave approximation, Risken and Nummedal [1] have simplified the Maxwell-Bloch laser equations for homogeneously broadened two-level atoms and have analyzed the linear stability of the uniform steady states. They have determined bifurcation points to periodic traveling wave solutions. If I denotes the intensity of the non-zero steady state and a is the spatial wave number of the traveling wave, the first bifurcation occurs at or near (I,a) = (Im,am). See Figure 1. The nonlinear problem has been first investigated by Haken and Ohno [2].