Frequency- and time-dependent gain characteristics of dye lasers

The approach used by McCumber for treating phonon-terminated lasers is applied to investigate the gain properties of dye lasers and is extended to include effects arising from population buildup in the triplet-level system and associated triplet-triplet absorptive losses. The gain is expressed in terms of time-dependent excited-state populations and spectral emission and/or absorption functions. For a given optical-pump pulse, a computer program is used to solve rate equations for the populations up to threshold and to calculate the gain as a function of time and frequency. The gain varies with frequency over the broad fluorescence bands characteristic of dye molecules and with time until the threshold for laser action is reached. Experiments using rhodamine 6G verify the predicted dependence of the laser frequency and time of threshold on cavity
Q
and demonstrate laser frequency tuning by adjusting the opening time of an intracavity
Q
switch. No variation of laser frequency is expected for fluorescing molecules exhibiting large Stokes shifts; this is observed for 7-hydroxycoumarin. Computer calculations of the gain for anthracene and rhodamine B illustrate the dependence of gain properties on the rate of intersystem crossing and triplet-triplet absorption. An estimate of the rate of intersystem crossing for rhodamine B in methanol is obtained from a comparison of predicted and observed laser threshold conditions. Requirements for achieving flashlamp-pumped laser action are shown to depend upon both flashlamp and dye properties and are analyzed using the above approach.