Page 111 - Tunable Lasers Handbook

92 Charles Freed

Additional precautionary measures should be taken in using the saturated
fluorescence signal. The Einstein coefficient for the upper lasing level (0001) is
about 200 to 300 sec-1 and. therefore, the modulation frequency must be slow
enough so that the molecules in the upper level have enough time to fluoresce
down to the ground state; here radiation trapping [82,83] of the 4.3-~m sponta-
neous emission (because CO, is a ground-state absorber) will show up as a vari-
ation of the relative phase between the reference modulation and the fluores-
cence signal as the pressure is vaned. The phase lag between the reference signal
and the molecular response would increase as the pressure increases because
there are more molecules to trap the 4.3-ym radiation and, therefore, hinder the
response. This phase lag will increase with increasing modulation frequency,
since the molecules will have less time to respond; thus, caution must be taken
when selecting the modulation frequency. A large phase lag will reduce the out-
put voltage (feedback signal) of the phase-sensitive detector; however, it will not
cause a shift in the instrumental zero [76].
In addition to optimizing the frequency at which to modulate the laser, the
amplitude of the modulation (the frequency excursion due to the dithering) was
also considered in the experiments at Lincoln Laboratory [76]. The modulation
amplitude must be large enough such that the fluorescence signal is detectable,
but the amplitude must be kept reasonably small to avoid all unnecessary para-
sitic amplitude modulation and nonlinearities in the piezoelectric response. in
order to avoid distorting the 4.3-pm Lorentzian. The maximum derivative signal
is obtained if the peak-to-peak frequency excursion equals 0.7 FWHM of the
Lorentzian. But such a large excursion should be avoided in order to minimize
the likelihood of introducing asymmetries in the derivative signal. A compro-
mise modulation amplitude based on obtaining sufficient SNR for most J lines
was used. This modulation amplitude corresponded to a frequency deviation of
approximately 300 kHz peak-to-peak on a Lorentzian with an FWHM of about 1
MHz. Experimental results indicated that the modulation frequency should be
kept well below 500 Hz. At such low frequencies, InSb photovoltaic detectors
may have very high llfnoise unless operated at effectively zero dc bias voltage.
This may be best accomplished by a low-noise current mode preamplifier that is
matched to the dynamic impedance of the detector and is adjusted as close as
possible to zero dc bias across the detector (preferably less than 0.001 V).
There are other advantages of the 4.3-pm fluorescence stabilization; because
the fluorescence lifetime is long compared to the reorientating collision time at
the pressures typically employed in the measurements, the angular distribution
of the spontaneous emission is nearly isotropic. This reduces distortions of the
lineshape due to laser beam imperfections. Furthermore, only a relatively short
(3- to 6-cm) fluorescing region is monitored, and the CO, absorption coefficient
is quite small (-10-6 cm-1-Torr-1); this eliminates laser beam focusing effects
due to the spatial variation of the refractive index of the absorbing medium pro-
duced by the Gaussian laser beam profiles [84,85]. Indeed, we have found no