SOLUTION BY MEANS OF LIE-SERIES TO LASER RATE EQUATIONS FOR A GIANT PULSE INCLUDING SPONTANEOUS EMISSION

An exact solution of the rate equations for the time evolution of a giant pulse including spontaneous emission, but neglecting pumping, is derived by the technique of Lieseries. It turns out that for normal optically pumped solid-state lasers the influence of spontaneous emission on the properties of the pulse is negligible; however, for materials with very short life time for the excited state involved in the laser transition, the pulse will be reduced or even suppressed by the effect of spontaneous emission. One important consequence of this investigation is that the Lie-series technique proves to be a very powerful means of solving systems of non-linear differential equations. © 1968 Springer-Verlag.