Nonperturbative theory of inhomogeneous effects in gas lasers

The self-consistent field approximation (SCFA)[1]-[4] is used to calculate the steady-state mode energies and frequency shifts for a gas laser. The SCFA is a statistical approximation which was shown[3] to be accurate for small values of a parameter (
\gamma^{2}N
), which is always small for gas lasers. The SCFA is simpler and more convenient for studying the complicated dynamical effects that occur in gas lasers than the more recent[5]-[8] quantum theoretical models. It does not, of course, give any new description of the laser photon statistics, since the approximation treats the field as a pure coherent state[9] and is, therefore, equivalent to the semiclassical theory. The main results of this paper are to show how dynamical effects can be calculated nonperturbatively for arbitrary values of the field strength, and to analyze the different roles played by different kinds of inhomogeneous effects in gas lasers. These inhomogeneous effects are due to the dependence of the atomic inversion density on the atomic positions and velocities. Some numerical results are given which show that the nonperturbative theory can explain some effects not previously explained by perturbation theories. [1], [2].