Page 165 - Tunable Lasers Handbook

144 Charles Freed

1 1. SMALL-SIGNAL GAIN AND SATURATION INTENSITY OF REGULAR
BAND LASING TRANSITIONS IN SEALED-OFF CO, ISOTOPE LASERS

The stability and most other operational characteristics of rare CO, isotope
lasers are generally similar to the commonly used 12C160, lasers. However, the
small-signal gain coefficient a. and saturation intensity I, of the rare CO, lasing
transitions can be significantly different from corresponding lines of 1Xi60,. It
can be shown that the power output of a laser may be approximated [I211 by

6 =21,Ar, ( __- 1) ,
I, + t,.
where I, is the internal cavity loss per pass, l, is the transmittance of the output
mirror, and L and A are the length and effective cross-section area of the gain
medium, respectively. Equation ( 19) clearly shows that the small-signal gain
coefficient a. and saturation intensity I, are the two salient parameters to be
measured in order to optimize a laser design for a desired output power Po.
The measured values of small-signal gain coefficient a. and saturation
intensity I, will, to a very large degree, depend on a number of experimental
parameters, such as excitation currents, gas pressures, mixtures and mixing
ratios, wall temperatures. and discharge tube diameters. CO, dissociation and
recombination rates and impurity buildup will also critically affect both an and
Z,, and thus output power and CO, laser lifetime. Recirculating gas flow can
lead to very large increases of the small-signal gain coefficient and saturation
intensity by a complex combination of effects involving not only convective
cooling, but also better control of CO, dissociation and recombination rates
and impurity cleanup by means of appropriately chosen catalytic converters.
Clearly. any meaningful measurement of small-signal gain and saturation inten-
sity in a CO, amplifier should be accompanied by a detailed description of the
experimental method and associated parameters. Note that the gas-discharge
scaling laws and other results described by Abrams and Bridges [122] may be
of great value in extrapolation from a given set of data.
Effects due to Fermi resonance play a major role in determining the very
significant variations in gain for the I and I1 bands in the various CO, isotopes.
This was both theoretically and experimentally demonstrated for the first time by
Silver et al. E1231 in 1970. To show the effect of Fermi resonance on the laser
gain, it is only necessary to form the gain ratio of the transitions. Silver et al.
used the gains measured for the WlgO,, QC1602, and 13C1602 I and 11 band
P(20) transitions to obtain their results. The ratios of gain and absorption coeffi-
cients depend directly on the matrix element ratio. which they calculated from
the vibrational state wave functions. Thus, the ratio of gain was given [123] as
g(OOOl-I)/g(OOO1-II) = K(OOO1-I) /K(OOOl-11) where K denoted the J-indepen-
dent portion of the matrix element ratio inferred from gain and loss measure-
ments. The final result obtained for the matrix element ratio was [ 1231: