THEORY OF PULSED DYE-LASERS INCLUDING DYE-MOLECULE ROTATIONAL RELAXATION

In this paper a phenomenological semiclassical theory of pulsed-laser-pumped dye-laser light amplifiers is presented. The theory accounts for the broadband radiation absorption and emission characteristics of dye molecules in liquid solvents. Dye-molecule fluorescence, vibrational, rotational, and electric polarization relaxation processes are represented by phenomenological relaxation rates. In general, it is found that due to dye-molecule rotational relaxation the laser-pumped dye medium is optically anisotropic. The pump- and dye-laser beams propagate through the dye medium as essentially transverse electromagnetic waves whose amplitude and polarization state changes. The theory is applicable to pulse durations tau less-than-or-similar-to 10-100 ns including the ultrashort pulse regime. The regime tau greater-than-or-similar-to 1 ps in which the pump- and dye-laser pulse lengths are long compared to the dye-molecule vibrational and electric polarization relaxation times is considered in detail. Amplification of partially polarized quasimonochromatic light is described by a self-consistent set of equations for the components of the pump- and dye-laser light coherency matrices and the orientation populations of the lowest vibronic levels of the dye molecule's S0 and S1 electronic states. The interaction of the pump- and dye-laser beams with the dye molecules is characterized by complex electric susceptibility tensors. Kramers-Kronig or Hilbert transform relations are found that permit dye-molecule absorption and emission cross sections to be used to calculate the pump- and dye-laser susceptibility tensors. All the physical parameters in the theory may be determined by conventional experimental techniques. When the dye-molecule rotational relaxation rate gamma-R is much larger than the fluorescence rate gamma-F, tau-1, and the pump-laser absorption and dye-laser stimulated emission rates, then the dye-molecule electric susceptibility tensors are diagonal. The laser-pumped dye-laser medium is optically isotropic. When these conditions do not hold the medium is optically anisotropic and coherency matrices may be used to describe the propagation of the pump- and dye-laser beams. This procedure is illustrated for the case of transversely pumped dye lasers. In the small-signal regime analytic solutions for the dye-laser-light coherence matrix components are developed for arbitrary initial polarization state, pulse duration, and gamma-F/gamma-R. In the large-signal regime numerical solutions are obtained for the amplification of short, (tau-gamma-F, tau-gamma-R)<< 1, and quasi-steady-state (tau-gamma-F,tau-gamma-R)>> 1, pulses for arbitrary values of gamma-F/gamma-R when the pump- and dye-laser polarizations are parallel. In general, it is found that for a wide range of physical conditions of interest dye-molecule rotational relaxation is important, and significant changes in the amplification characteristics of the medium, i.e., the rate of amplification, amplification efficiency, and polarization state of the light, will occur.