Stationary solution of the Tang – Statz – Demars system of equations for YAG : Nd-laser

O. L. Golovkov, G. A. Kuptsova, V. A. Stepanov

Ryazan State University named for S.A. Yesenin

Abstract: The paper focuses on deciding between two notations of the Tang – Statz – DeMars system of equations for a YAG:Nd laser, explaining the generation of two wavelengths: of 1064,2 nm and of 1061,5 nm at a temperature of 300 K. In the former case relaxation transitions between homogeneous inversions and inversion gratings between the ^{4}F_{3/2} multiplet sublevels were used. In the latter case we have used the condition, which supposed that the inversions of the ^{4}F_{3/2} multiplet sublevels always followed the Boltzmann distribution. We found two solutions of the equations in question taking into account three lines of amplification and two upper sublevels of levels. Calculations performed showed it was incorrect to insert the relaxation transitions between inversion gratings populations of the ^{4}F_{3/2} multiplet sublevels.If the universal character of the Boltzmann distribution in populations of the ^{4}F_{3/2} multiplet sublevels is taken into account it supplies reliably an adequate description of the generation spectra of longitudinal mode assemblage for a YAG:Nd laser.