Laser threshold and nonlinear Landau fluctuation theory of phase transitions

The threshold region for a single mode laser is treated by Landau's theory of order parameter fluctuations. Taking into account a kinetic energy in the Landau functional, approximate equations of motion for the laser field are derived which include coupling of phase and amplitude. From these it is easy to get the correlation functions and linewidths for intensity and field as well as the transient behaviour of intensity throughout the nonlinear transition region. In addition, a dynamical decoupling scheme of noise theory is applied to calculate the same quantities. Although these methods are very simple the results agree fairly well with those of the much more involved Fokker-Planck theory.