Phase Transition Analogy for a Laser with an Injected Signal

Abstract

The question of the nature of the phase transition for a laser with an injected signal, which is a coherent field with a well-defined phase, has been discussed a number of times in the literature.^1,2,3,4 For a laser in the absence of an injected signal there is general agreement that in the mean field approximation, there is an analogy between the laser transition at threshold and the Landau theory of the equilibrium second order phase transition. A typical example of the Landau theory is the Curie-Weiss theory, which is an approximate model of ferromagnetism where the order parameter is taken as a scalar magnetization which can point up or down, i.e. the order parameter is real and takes on positive and negative values. The second order phase transition is the symmetry breaking spontaneous magnetization that occurs when the temperature T is lowered below the critical temperature T_c. In the mean field treatment of the laser, the usual procedure is to reduce the two component complex order parameter, the electric field, to the one component order parameter, the real part of the electric field which takes on positive and negative values.