Page 99 - Tunable Lasers Handbook

80 Charles Freed

coupling loss). In a small CO, laser with L = 50 cm and r,. = 5% Q, is of the order
of 107; thus for a typical power output of 1 to 10 W (which is easily obtainable
with a small TEMOoq mode CO, laser) the quantum-phase-noise-limited linewidth
is less than 10-6Hz. Note that-10-6HHz represents less than 1 part in 1019 of the
output frequency (vo -3 x 1013 Hz) of a CO, laser. This inherent spectral purity of
CO, lasers can be explained as follows: The linewidth AV is inversely propor-
tional to the product of Po and Qf, and the combination of high Po and high
Q, can be simultaneously achieved with relative ease even in a small CO, laser
oscillator. Oscillators in the radio-frequency (rf ) and microwave domain have
either high Po or high Q, but not both together in a single device.
Laser stabilities are most frequently measured in the laboratory from the
results of heterodyne experiments with two lasers. Laser stabilities can be deter-
mined by either frequency-domain (Fourier spectrum) or time-domain (Allan
variance) analysis of the beat-note spectra of the laser pairs. To establish the
spectral purity we can heterodyne two CO, lasers of equal high quality so that
the resulting beat-note spectrum can be apportioned equally to each laser. Two
problems arise, however, in trying to measure the Schawlow-Townes linewidth
of high-quality CO, lasers. The first of these problems is instrumental: The sra-
bility of the available instrumentation itself generally cannot reliably measure
spectral purities of 10-6 Hz or better.
The origin of the second problem is that for well-designed CO, lasers [56]
the so-called technical noise sources dominate over the quantum-phase-noise-
limited Schawlow-Townes linewidth [57]. Examples of technical noise sources
are acoustic and seismic vibrations, and power-supply ripple and noise. These
sources can cause frequency instabilities by perturbing the effective cavity reso-
nance via the sum of fractional changes in the refractive index n and the optical-
cavity length L:
Av=v (% tL)
-+-

As an example, a change of only A (about 1/1000 of the diameter of a
hydrogen atom) in a 50-cm-long CO, laser cavity will cause a frequency shift of
approximately 6 Hz. 4 6-Hz variation in the approximately 3 x lOI3 Hz fre-
quency of a CO, laser corresponds to a fractional instability of 2 x
Figure 6 shows the real-time power spectrum of the beat signal between two
free-running lasers that were designed and built at Lincoln Laboratory [56]. The
spectral width of Fig. 6 implies a frequency stability at least as good as 2 x
The discrete modulation sidebands in the figure were primarily due to ac-power-
line frequency harmonics, cooling fan noise, and slow frequency drift; however,
each spectral line was generally within the 10-Hz resolution bandwidth of the
spectrum analyzer. The measurement of the spectral width was limited to a 10-Hz
resolution by the 0.1-sec observation time that was set by the instrumentation, not
by the laser stability itself.