On the Theory of Spectral Line Widths of Coupled Many Wave Systems in Non-Thermal Equilibrium

The problem of the natural spectral line width Aco oi individual waves of a coupled many wave system in non-thermal equilibrium is discussed within the Fokker Planck approach to fluctuation phenomena. Edwards' method in turbulence theory is reinterpreted to relate AOJ via a modified energy balance equation to the spectrum of the mean wave intensities. This equation is solved for a model of the non-resonant feedback laser. AOJ is found to consist of two contributions: The first one is associated with the usual internal noise of a "free" Gaussian wave due to spontaneous emissions. Its contribution to the line width is twice that of a single mode laser far above threshold as found earlier by Brunner and Paul. The second and new contribution stems from the wave-wave coupling. It is similar to half the effective intensity fluctuation line width of the single mode laser and thus dominates above threshold.