Page 93 - Tunable Lasers Handbook

74 Charles Freed

5. ADDITIONAL CHARACTERISTICS OF REGULAR BAND CO,
LASER TRANSITIONS

We can define the molecular quantum efficiency of an emitted laser photon
in the regular band as

E[00~1)-E[1000,0P 0.1 I or !I
rl IlId = (3)
E(OOO1]

It becomes clear from Eq. (3) and the energy-level diagram of Fig. 4 that theo-
retical quantum efficiencies of about 45 and 40% are possible for the 9.4- and
10.4-pm laser transitions, respectively, in the regular band of CO,. The
"wallplug" efficiencies of CO, lasers is lower. of course, as a result of inevitable
losses during excitation. Hoa.&er, actual efficiencies as high as 30% have been
achieved due to the remarkably efficient collisional excitation and deexcitation
processes, as summarized in the previous section of this chapter.
Another. spectroscopically highly useful characteristic of cw CO, lasers is
the fact that the entire output power corresponding to the total inversion
between two vibrational levels may be extracted in a single P(J) or R(J) transi-
tion. An explanation of this characteristic may be found from examination of
the vibrational-rotational lifetimes of the excited molecules in the various
energy levels.
The vibrational level radiative lifetime T~~~ of an excited molecule in the
(0001) upper laser level is -3 sec. Its actual lifetime is determined by collisions
with other molecules and, therefore, is pressure dependent. At typical operating
pressures characteristic to relatively small cw CO, lasers the vibrational-level
lifetime. including radiative and collisional relaxation. is about T,,~~ - 10-3 sec.
The energy spacing between the relevant vibrational levels is much greater than
the kinetic energy of the molecules. which is about 0.025 eV at room tempera-
ture. Thus the vibrational thermalization rate is very small, about 103 sec-1. The
spacings of the rotational levels, on the other hand are smaller than the kinetic
energy of the molecules and the rotational lifetime is only about 10-7 sec. Thus a
molecule can experience a very large number of thermalizing rotational colli-
sions during its lifetime in a given vibrational level. This results in a Boltzmann
distribution of the inolecules among the various rotational levels of a vibrational
state. Figure 5 illustrates the Boltzmann distribution of population densities, Nr
as a function of the rotational quantum number J for two rotational temperatures,
Trot = 400 K (solid lines) and 1000 K (dashed line), respectively.
The existence of a Boltzmann distribution requires that a change of popula-
tion density in one rotational level be accompanied by appropriate changes in the
population densities of all other rotational levels of the vibrational state in order
to maintain the Boltzmann distribution. Hence, once a laser transition starts
oscillating and begins to deplete the population of the affected rotational level in