Dynamical systems in nonlinear optics: Maxwell-Bloch models

The types of integrable Maxwell-Bloch models appropriate to a wide class of nonlinear coherent optical phenomena near resonance in a polarisable medium are presented and reviewed. With the attention on 1-dimensional unidirectional propagation, several classes of reduced Maxwell-Bloch models are identified, these models being good approximations in certain circumstances to the much more complex system of full Maxwell’s equations coupled to a quantum-mechanical model for the electrons in the dielectric medium.