Page 191 - Tunable Lasers Handbook

5 Dye Lasers 169

7.1 ---
I "2,O
I +

Sl

NOJl
SO
N0,o
FIGURE 2 Energy-level diagram illustrating excitation and emission transitions of laser dye mole-
cules. Absorption cross sections are written as o,~,,,~,(,,,,,,,, the emission cross section as oe(,,,,,,,,].
and

The literature on rate equations for dye lasers is quite extensive. Representa-
tive and detailed treatments on the subject have been given by [l0-19]. Here, a
set of rate equations, applicable to transverse laser excitation and intrinsic broad-
band emission, is considered. In reference to the energy diagram of Fig. 2, the
population equation can be written as

where summation over S refers to the electronic states and summation over v con-
siders all the vibrational levels within each electronic state. A similar description
applies to the summation over the triplet states NTY.
Pump laser intensity I#), at a wavelength compatible with the S,+S, transi-
tion, populates a higher vibrational level (1 ,n) at the first excited electronic state.
The cross section corresponding to this transition is o,,(~,~). This is followed by
rapid intraband radiationless deexcitation to the N, ,0 vibrational level from where
transitions to a vibrational manifold at the ground electronic state give origin to
broadband emission ZI(x,t,3L). The emission cross section is o~(~,~). Intensity $(t>
excitation of S, may occur with a cross section o,~(,,~) emission reabsorption
and