ABSTRACT
Complex pattern formation is commonly observed in spatially extended, continuous, dissipative systems which are driven far from equilibrium by an external stress. Under the influence of this stress, the system can undergo a series of symmetry breaking bifurcations or phase transitions and the resulting patterns become more and more complicated, both temporally and spatially, as the stress is increased. This chapter illustrates the rich variety of pattern forming instability mechanisms in wide aperture lasers, using the two-level and Raman single longitudinal mode lasers as prototype systems. It shows that the Maxwell-Bloch laser equations admit an exact finite amplitude traveling wave solution for positive detuning of the laser and also admit a transverse spatially homogeneous solution for negative detuning. The chapter introduces the laser models, compare and contrast their physical characteristics and briefly review their bifurcation behavior. 1D wide aperture lasers are expected to exhibit fundamentally different spatio-temporal behavior.
