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 \ensuremath{\tau}\ensuremath{\lesssim}10--100 ns including the ultrashort pulse regime. The regime \ensuremath{\tau}\ensuremath{\gtrsim}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 ${\mathit{S}}_{0}$ and ${\mathit{S}}_{1}$ 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 ${\ensuremath{\gamma}}_{\mathit{R}}$ is much larger than the fluorescence rate ${\ensuremath{\gamma}}_{\mathit{F}}$, ${\mathrm{\ensuremath{\tau}}}^{\mathrm{\ensuremath{-}}1}$, 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 coherency matrix components are developed for arbitrary initial polarization state, pulse duration, and ${\ensuremath{\gamma}}_{\mathit{F}}$/${\ensuremath{\gamma}}_{\mathit{R}}$. In the large-signal regime numerical solutions are obtained for the amplification of short, (\ensuremath{\tau}${\ensuremath{\gamma}}_{\mathit{F}}$,\ensuremath{\tau}${\ensuremath{\gamma}}_{\mathit{R}}$)\ensuremath{\ll}1, and quasi-steady-state (\ensuremath{\tau}${\ensuremath{\gamma}}_{\mathit{F}}$,\ensuremath{\tau}${\ensuremath{\gamma}}_{\mathit{R}}$)\ensuremath{\gg}1, pulses for arbitrary values of ${\ensuremath{\gamma}}_{\mathit{F}}$/${\ensuremath{\gamma}}_{\mathit{R}}$ 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.