Organic Dye Laser Threshold

This paper describes the results of an investigation of the interrelated physical parameters that determine laser threshold for three organic dyes: rhodamine B, rhodamine 6G, and fluorescein. Not only are these dyes (rhodamine 6G in particular) among the most widely used and important laser dyes, but insights into the threshold condition derived from our studies of these particular dyes should be generally applicable to future dye laser research. Our detailed characterization of threshold for these dyes and our novel insights result from the use of triplet state spectral data in a thorough and quantitative way for the first time, coupled with the physically realistic approximation that the triplet population is proportional to the singlet excited state population. For the case of self-tuning of the laser emission wavelength, solutions to the threshold equations are presented that establish relations between all the parameters affecting lasing: critical inversion, emission wavelength, extrinsic losses, dye concentration, length of active medium, and triplet to excited singlet population ratio. For reasonably high extrinsic cavity losses, the critical inversion is a simple power law function of extrinsic loss, and the emission wavelength is self-tuned in such a manner that the ratio of extrinsic losses to intrinsic singlet absorption losses is substantially constant. There exists a region of low, but still physically realizable, cavity losses, where laser action is determined exclusively by intrinsic characteristics of the dyes (triplet absorption, singlet emission, and absorption). Asymptotic limits on the maximum wavelength of emission and on the minimum critical inversion appear in this region, beyond which there is no point in reducing extrinsic cavity losses. The fraction of triplet state molecules also determines long wavelength cutoffs for an externally tuned laser. Methods are outlined for measuring the ratio of triplet state to excited singlet state populations for dyes with known triplet absorption spectra and for determining semiquantitatively the triplet effects in dyes where this information is not known. A final interesting conclusion is that molecular modifications of rhodamine 6G cannot be expected to improve its threshold characteristics as a laser dye by much more than a factor of 4.