Page 101 - Tunable Lasers Handbook

a2 Charles Freed

set to about 1.2 kHz [56]. Note that the horizontal scale in the figure is only
2 x lo-' Hz/division and the vertical scale is logarithmic, with 12.5 dB/division.
Using the results from Fig. 7 and the equation for a Lorentzian lineshape, we
calculate the FWHM spectral width of the beat note to be about 9 x Hz.
It took 26.67 min of measurement time to obtain just a single scan with the
frequency resolution of Fig. 7. Because tracking even by a very good servosys-
tem would still be limited by quantum phase noise, the narrow linewidth in Fig.
7 is an indirect but clear confirmation of the high spectral purity of CO, lasers,
as predicted by the Schawlow-Townes formula.
The (so far at least) unsurpassed spectral purity and short-term stabilities
measured in the frequency domain and illustrated in Figs. 6 and 7 were also con-
firmed by analyzing the signal returns from orbiting satellites that were obtained
by a long-range CO, radar at the Firepond facility of MIT Lincoln Laboratory
[56,58-621. Additional confirmation was also obtained at MIT Lincoln Labora-
tory from extensive time-domain frequency stability measurements on pairs of
ultrastable CO, lasers under free-running and phase-locked conditions, and both
in acoustically quiet and in noisy environments [63].

8. LONG-TERM LINE-CENTER STABILIZATION OF CO, LASERS

CO, lasers can possess exceptionally high spectral purity and short-term fre-
quency stability. Long-term stability, however, is generally lacking because all
lasers are more or less tunable over a frequency band that is determined by the
detailed physics of the gain-profile characteristics of each particular laser sys-
tem. In a typical low-pressure (-15-Torr) CO, laser, the width of the gain profile
is about 90 MHz. and is dominated by the -67-MHz Doppler broadening as pre-
viously described in Sec. 6.
The first effective means of overcoming Doppler broadening was predicted
in the "Theory of an Optical Maser," which Lamb developed and published [64]
in 1964 as an "atonement for his own sin of not believing that optical Masers can
be realized" [65] (the word ''laser'' was coined later). Lamb described and pre-
dicted in his purely theoretical paper a standing-wave saturation effect that pro-
duces a narrow resonant change in the level population of a Doppler-broadened
transition interacting with a standing-wave laser field as the laser frequency is
tuned across the center frequency of the transition. This change is superimposed
on a broad background population change, which, for a constant amplitude laser
field, closely follows the Gaussian Doppler line profile as the laser frequency is
tuned within the Doppler linewidth. This standing-wave saturation resonance
results from the nonlinearity of the interaction of the standing-wave field in the
laser cavity with molecules (or atoms) having velocities resonant with the
Doppler-shifted frequency of the field as experienced by the molecules (or
atoms). When the laser is tuned to the center frequency of a particular transition