Effect of cross relaxation on the spectral flux and population inversion distributions in a CW laser oscillator

The spectral distribution of the output from a CW laser oscillator employing an inhomogeneously broadened transition with a finite cross-relaxatian rate is discussed. A theory is presented that describes the spectral broadening and the inversion distribution variations introduced by the finite cross-relaxation rate. It is found that the criterion that must be satisfied by the ratio of the cross-relaxation rate to the stimulated emission rate, in order that the spectrum reduce to its homogeneously broadened limit, is much more stringent than the amplifier "no hole-burning" condition. The average spectral envelope is described analytically. However, it is found that the self-consistent solution for the spectral distribution exhibits important structure within these average bounds. Computer solutions of the model equations are given for the Nd: glass and the 3.51-μ xenon lasers. These solutions are compared with experimentally observed spectral distributions and it is found that the dominant structure patterns are correctly described. For example, the solution for Nd:glass is composed of a series of sharp intense bands separated by weaker broad bands. This banding is observed in the time resolved spectra of the laser output. The width of these sharp bands is determined by higher order effects and may be the limiting width in producing the 3 ps pulses occurring during mode-locked operation. The xenon laser spectrum is composed of a very sharp central peak and several broader lobes.