Frequency modulation spectroscopy using dual frequency modulation and detection

FM laser spectroscopy apparatus includes a single modulator for modulating a laser beam with first and second modulation signals (.omega..sub.1, .omega..sub.2). The two modulation signals are generated by mixing a signal from a first oscillator (.omega..sub.1 +.omega..sub.2)/2 and a signal from a second oscillator (.omega..sub.1 -.omega..sub.2)/2 and producing the two modulation signals (.omega..sub.1, .omega..sub.2). The modulator produces three groups of sidebands on the laser beam at the laser frequency plus and minus the two modulation frequencies and at plus and minus the difference between the two modulation signal frequencies. The apparatus provides practical high frequency FM spectroscopy as required for the observation of pressure broadened spectral features.

BACKGROUND OF THE INVENTION 
This invention relates generally to laser spectroscopy, and more 
particularly the invention relates to frequency modulation laser 
spectroscopy. 
Advances in laser technology have created powerful new tools for 
spectroscopy. Frequency modulation (FM) laser spectroscopy is a sensitive 
optical spectroscopy technique for measuring absorption and dispersion in 
an optical medium. As discussed by Cooper and Gallagher in "Double 
Frequency Modulation Spectroscopy: High Modulation Frequency Low Bandwidth 
Detectors", Applied Optics, Vol. 24, No. 9, 1 May 1985, Pages 1327-1334, 
one of the most promising areas for the application of FM spectroscopy is 
in the detection of atmospheric trace gases and hazardous materials. 
Absorptions as small as 10.sup.-4 have been easily detected with FM 
spectroscopy using either single mode or multimode CW lasers, and an 
optimized visible wavelength FM system should be capable of detecting an 
absorption as small as 10.sup.-6 with a one second integration time. 
In FM laser spectroscopy a laser beam of frequency .omega..sub.o is phase 
modulated at frequency .OMEGA. which is usually greater than the line 
width .DELTA..omega..sub.o of the laser. Typical values are .OMEGA.=500 
MHz and .DELTA..omega..sub.o =1 MHz. In the limit of low modulation index, 
the laser beam acquires sidebands at .omega..sub.o .+-..OMEGA. and when 
the modulated laser beam impinges on a square law detector, such as a 
photodiode, each sideband beats with the carrier to produce a component of 
the photo current at .OMEGA.. When there is no absorption the two beat 
signals are 180.degree. out of phase and therefore cancel. If prior to 
photodetection the modulated beam traverses a medium whose complex index 
of refraction differs for the two sidebands, the sideband cancellation is 
incomplete and a photocurrent at .OMEGA. is produced. 
In generating the FM sideband, Cooper and Gallagher modulate a laser beam 
using two modulators, one modulator frequency being 2.OMEGA.+.sigma. and 
the other modulation frequency being .OMEGA.. The circuitry is somewhat 
complex in the number of components and in optical and electronic 
alignment. 
SUMMARY OF THE INVENTION 
An object of this invention is improved demodulation for FM spectroscopy. 
Another object of the invention is practical high frequency FM laser 
spectroscopy for the observation of pressure broadened spectral features. 
A feature of the invention is the use of a single modulation driven at two 
frequencies in generating side bands for spectroscopic analysis of an 
optical medium. 
Briefly, a laser beam is modulated using one modulator operating at two 
high frequencies, .omega..sub.1 and .omega..sub.2, which differ in 
frequency by .DELTA. (i.e. .DELTA.=.omega..sub.1 -.omega..sub.2). This 
modulation puts sidebands on the modulated laser beam, .omega..sub.0, at 
.omega..sub.0 .+-..omega..sub.1, .omega..sub.0 .+-..omega..sub.2, and 
.omega..sub.0 .+-..DELTA.. Beat notes at .DELTA. come from the carrier 
.omega..sub.0 beating with each of the two nearby sidebands at 
.omega..sub.0 .+-..DELTA. and from the sidebands at .omega..sub.0 
.+-..omega..sub.1 beating with the sidebands at .omega..sub.0 
.+-..omega..sub.2. 
By scanning the laser frequency, .omega..sub.0, and therefore the sidebands 
across an absorption frequency range, the frequencies of absorption can be 
detected. The sign of the beat note contribution from the sidebands at 
.omega..sub.0 .+-..omega..sub.1 and .omega..sub.o .+-..omega..sub.2 are 
positive and the contribution from the carrier at .omega..sub.0 and the 
sidebands at .omega..sub.0 .+-..DELTA. is negative. The total beat note 
contribution is equal to zero when there is no absorption or dispersion. 
When either of the sidebands at .omega..sub.0 .+-..omega..sub.1 or 
.omega..sub.0 .+-..omega..sub.2 is absorbed the total beat note 
contribution is negative. When the carrier .omega..sub.o or the sidebands 
at .omega..sub.0 .+-..DELTA. are absorbed, then the total beatnote 
contribution is positive. 
The invention and objects and features thereof will be more readily 
apparent from the following detailed description and appended claims when 
taken with the drawing.

DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENT 
Referring now to the drawings, FIG. 1 is a functional block diagram of FM 
laser spectroscopy apparatus in accordance with one embodiment of the 
invention. A beam from laser 10 is applied to a modulator 12. The 
modulation signals .omega..sub.1 and .omega..sub.2 for the modulator 12 
are derived from oscillators 14 and 16 and mixer 18. The two frequencies 
differ by .DELTA. (.DELTA.=.omega..sub.1 -.omega..sub.2). Oscillator 14 
generates a frequency of .DELTA./2 or (.omega..sub.1 -.omega..sub.2)/2. 
Oscillator 16 generates a frequency of (.omega..sub.1 +.omega..sub.2)/2. 
Mixer 18 produces an output at the sum and difference of the two 
oscillator frequencies, or .omega..sub.1 and .omega..sub.2. The two 
frequencies are applied through amplifier 20 as the modulation signals to 
modulator 12. 
The modulated carrier signal from laser 10 is then applied through an 
absorption cell 22 for spectral analysis of a gas therein. The signal 
received after passing through the absorption cell 22 is detected at 24. 
The detected signal is then applied to a mixer 26 where it is mixed with a 
signal at the frequency .DELTA. obtained by applying the .DELTA./2 signal 
from oscillator 14 through frequency doubler 28. The output of mixer 26 is 
then recorded at 30. 
FIGS. 2A-2C illustrate the frequency spectrum of the unmodulated laser 
beam, .omega..sub.0, in FIG. 2A, the frequency spectrum of the laser beam 
modulated by a single signal, .omega..sub.1, as shown in FIG. 2B, and the 
frequency spectrum using the two modulation signals of the circuitry of 
FIG. 1 as shown in FIG. 2C. The signs of the different sidebands are 
indicated by the directions of the arrows. The groups of sidebands 
illustrated in FIG. 2C which lead to beat notes at frequency .DELTA. are 
grouped together in groups +1, 0, and -1 as illustrated. The group 
designations indicate the average displacement in terms of (.omega..sub.1 
+.omega..sub.2)/2. The signs of the beat note contributions at frequency 
.DELTA. are determined by the signs of the products of the groups 1, 0, 
and -1. As shown in FIG. 2C beat note contributions from +1 and -1 are 
positive in sign, and the contributions from 0 are negative in sign. In 
the limit of low modulation indices .beta..sub.1 and .beta..sub.2 at 
frequencies .omega..sub.1 and .omega..sub.2 in the case of practical 
interest, one may ignore higher sidebands, and the beat notes at .DELTA. 
from group 0 come from the carrier beating with each of two nearby 
sidebands. The beat note signals from +1, 0, and -1 are given by 
EQU .GAMMA.+1=.GAMMA.-1=J.sub.1 (.beta..sub.1)J.sub.o (.beta..sub.2)J.sub.o 
(.beta..sub.1)J.sub.1 (.beta..sub.2) 
EQU .GAMMA..sub.o =-J.sub.o (.beta..sub.1)J.sub.o (.beta..sub.2)J.sub.1 
(.beta..sub.1)J.sub.1 (.beta..sub.2)-J.sub.o (.beta..sub.1)J.sub.o 
(.beta..sub.2)J.sub.1 (.beta..sub.2)J.sub.1 (.beta..sub.1) 
where J.sub.o and J.sub.1 are Bessel functions. 
In the limit of low modulation indices J.sub.o (.beta..sub.1)=J.sub.o 
(.beta..sub.2)=1, and clearly the net signal .GAMMA.=.GAMMA..sub.+1 
+.GAMMA..sub.o +.GAMMA..sub.-1 is equal to zero when there is no 
absorption. However when either the +1 group or the -1 group is absorbed a 
negative signal is observed, whereas the absorption of the 0 group results 
in a positive signal. The result of scanning the laser (.omega..sub.o) and 
therefore the sidebands as well, across an absorption is then the curve of 
FIG. 3. This is in fact the case as shown by FIG. 4 of an experimental 
demonstration of this technique using the following parameters and 
components for FIG. 1: 
______________________________________ 
laser Spectra Physics 375 dye laser 
modulator 
8.4 GHz resonant cavity modulator 
absorption 
Na vapor cell 
cell 
detector EG & G FND 100 photodiode 
oscillator 1 
Avantek AVD 7872 (.omega..sub.1 + .omega..sub.2 /2) = 8.38 GHz) 
oscillator 2 
Hewlett Packard 606B 
.omega..sub.1 - .omega..sub.2 = 10 MHz) 
Mixer 1 Watkins Johnson M31A 
amplifier 
Hughes 1277 HO2 Amplifier 8-12 GHz 
doubler Minicircuits FK-5 
Mixer 2 Minicircuits ZFM-3 
recorder HP 7035 B 
______________________________________ 
The invention makes high frequency FM laser spectroscopy very practical. 
High frequency is necessary for the observation of pressure broadened 
spectral features, and allows a wider frequency range for retrieval of 
optically stored information. 
While the invention has been described with reference to a specific 
embodiment, the description is illustrative of the invention and is not to 
be construed as limiting the invention. Various modifications and 
applications may occur to those skilled in the art without departing from 
the true spirit and scope of the invention as defined by the appended 
claims.