Page 193 - Tunable Lasers Handbook

5 Dye Lasers 171

Z,(.u,t,h) = z;(xJ,k) + zy(r,t,h). (7)

where the various coefficients are described in Fig. 2. In Eq. (7) Zj(s,t,h) represents
propagation in the positive x direction and IT (s,r,h) refers to propagation in
the opposite direction. The units are molecules cm-3 for populations, photons
cm-2 s-1 for intensities, square centimeters for cross sections, and seconds for time.
The broadband nature of the emission is a consequence of the involvement
of the vibrational manifold of the ground electronic state represented by the
summation terms of Eqs. (2). (5), and (6). Because the gain medium exhibits
homogeneous broadening, the introduction of intracavity dispersive elements
(see Chapter 2) enables all the excited molecules to contribute efficiently to
narrow-linewidth emission.
Replacing the vibronic manifolds by single levels and neglecting absorptive
depopulations of N,,o and Nl.o. Eqs. (1) to (5) reduce to

and

This simplified set of equations is similar to the rate equation system considered
by Teschke et ai. [ 111. Using available excitation parameters from the literature.
Eqs. (8) to (12) can be solved numerically for the case of pulsed excitation.
The numerical approach is particularly relevant for pulsed excitation in the
nanosecond range because the dynamic occurs in the transient regime. Also.
excitation in the nanosecond domain allows for some simplification because the
triplet states can be neglected. Examples of numerical solutions considering