CO 2 -laser sideband spectroscopy at ultrahigh resolution

1521 Vol. 10, No. 9/September 1993/J. Opt. Soc. Am. B Pfister et al. CO2-laser sideband spectroscopy at ultrahigh resolution 0. Pfister, F. Guernet...
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Vol. 10, No. 9/September 1993/J. Opt. Soc. Am. B

Pfister et al.

CO2-laser sideband spectroscopy at ultrahigh resolution 0. Pfister, F. Guernet, G. Charton, and Ch. Chardonnet Laboratoire de Physique des Lasers, Unite de Recherche Associ6e No. 282 du Centre National de la Recherche

Scientifique,Institut Galil6e,Universite Paris-Nord,Avenue J.-B. Cl6ment,F-93430Villetaneuse,France F. Herlemont and J. Legrand Laboratoire de Spectroscopie Hertzienne, Unite de Recherche Associ6e No. 249 du Centre National de la Recherche Scientifique, Universit6 de Lille 1, B6timent P5, F-59655 Villeneuve dAscq Cedex, France Received January 19, 1993; revised manuscript

received March 18, 1993

A transit-limited linewidth of 1.46 kHz (half-width at half-maximum) on SiF4 transitions has been obtained in the 9.6-Amregion by saturation spectroscopy with sidebands generated by the mixing of a C0 2-laser line with a microwave source in the range 8-18 GHz. This resolution is an improvement of 2 orders of magnitude with respect to that obtained with this technique by several other groups. This laser sideband technique gives, with isotopic CO2 lasers, complete tunability throughout the range 9-12 Am and, when used in ultrahigh-resolution conditions, opens new fields of study in atomic and molecular spectroscopy. As an illustration we show hyperfine and superhyperfine structures of SiF4 and list absolute frequencies with an accuracy better than 5 kHz.

INTRODUCTION Ultrastable sources with broadband tunability have been and still are a subject of active research for several regions of the electromagnetic spectrum. If we restrict our concern to the optical domain, dye and titanium-sapphire lasers cover the whole 0.4-1.1-/gtm region.

By combination

of a titanium-sapphire laser and an argon laser, full coverage of the 1-5-,m range has been obtained. In the infrared region the most important lasers are CO (3-8 ,um) and CO2 lasers (9-12 ,m), which provide sparse emission windows of 100-MHz width typically every 50 GHz.


though linewidths of a few tens of kilohertz have been reported for diode lasers in the CO-laser operating range,' the liquid-nitrogen-cooled diode lasers available in the 10,um region present a broad linewidth of -1 MHz.2 Thus, when high spectral purity is required, a CO2 laser is a much better starting point, because the linewidth of such a free-running laser can be as narrow as 1 kHz. The use of isotopic species of CO2 and the development of highpressure waveguide lasers cannot give cw emission with more than 5% coverage of the 9-12-,um region. Within this context, the generation of sidebands on the frequency of a CO2 laser by means of an electro-optic crystal driven by a microwave source seemed to give an elegant solution to the tunability problem.3 This technique is now used by many groups thoughout the world with either CO2 (Refs. 4 and 5) or CO (Refs. 6 and 7) lasers and has found various applications, especially in molecular spectroscopy. Until now the resolution obtained by saturation spectroscopy has been limited by the stability of the lasers used. Our aim in the experiment that we present here is to show that the laser sideband technique can provide the same level of resolution that we routinely obtain with our spectrometer. Actually the finite transit time of the molecules across the laser beam is responsible for the linewidth of 1.4 kHz (half-width at half-maximum) obtained in the present ex0740-3224/93/091521-05$06.00

periment, and the spectral purity of the optical and microwave sources is far from being a limitation.

EXPERIMENTAL SETUP The experiment was performed at the Laboratoire de Physique des Lasers in Villetaneuse, where the 10-ttm ultrahigh-resolution spectrometer resides. The setup necessary for the generation of the sidebands was provided by the Laboratoire de Spectroscopie Hertzienne, Universit6 de Lille.5

Figure 1 shows the complete setup.

We used

two CO2 lasers tuned to the frequency of the 9-ILmband P(30) laser line: the first laser is locked to the third derivative of the R(53)F9(+) in the V3 band of SiF4. Thus it acquires a spectral purity of -10 Hz and a long-term stability of a few hertz per minute. The second laser is frequency shifted, and the beat note between the lasers is phase locked to a tunable and highly stable synthesizer, which guarantees good reproduction of the spectral purity of the local oscillator onto the second laser. The size of this phase-locked laser beam is then reduced by a telescope to a waist of less than 1 mm. At this waist is placed the electro-optic crystal, which generates the sidebands. This CdTe crystal is a 3 mm X 3 mm X 40 mm prism that

is inside a microwave guide. Additional alumina slabs were included between this waveguide and the crystal 8 to match the phase velocities of the microwave (13 GHz) and the optical wave in the crystal. This electro-optic modulator is used as a traveling-wave device, and its actual operating range is 8-18 GHz. The microwave source is in an HP 83731A synthesizer, which is followed by a traveling-wave amplifier that produces 20 W of power. Wehave determined some spectral characteristics of this synthesizer. Figure 2 shows a beat note at 5 MHz recorded by a spectrum analyzer between the frequency of 13.005 GHz of this synthesizer and the tenth harmonic of C)1993 Optical Society of America


Pfister et al.

J. Opt. Soc. Am. B/Vol. 10, No. 9/September 1993

Fig. 1. Overview of the experimental setup. For this experiment two telescopes, the electro-optic modulator (EOM)and a grid polarizer (GP) have been implemented in the path of the spectroscopy laser. This represents an easy change from the previous setup. (Note that the microwave synthesizer and the traveling-wave amplifier that drive the crystal are not shown here.) R.F., radio frequency; (-lock, phase lock.

listed in this paper. However, its effect during the time of recording is negligible for the relative calibration of the spectra, which is essential for the fitting for the hyperfine

structures. .0

1 J.


No more than 10-4 of the laser power is transferred to each sideband, whose polarization is perpendicular to that of the carrier. A second telescope expands the laser beam to its original size. A polarizer placed at the focal point of this telescope allows one to eliminate -99.9% of the carrier. The unavoidable residual carrier is still approximately three times more powerful than each sideband. Then the laser beam is sent to the 18-m-long absorption cell, where it is expanded to a waist of 3.5 cm and gener-

ates a triple standing wave for a total path length of Fig. 2. Beat note between the frequency 13.005GHz of the microwave synthesizer HP 83731A, which drives the electro-optic crystal, and the tenth harmonic, 1.3 GHz, produced by a Marconi synthesizer 2030. The resolution of the spectrum analyzer is 10 Hz.

1.3 GHz produced by a Marconi synthesizer. A peak whose width is limited by the resolution of the spectrum analyzer (10 Hz) is visible 30 dB above some residual fre-

quency noise. This gives the upper limit for the spectral purity of the microwave synthesizer at 13 GHz. In a similar way, we checked the synthesizer's accuracy by comparing this beat note of 5 MHz with a precise frequency reference at 5 MHz. A shift of 18 kHz was found, which comes essentially from the microwave synthesizer. Unfortunately we did not phase lock this synthesizer to our reference quartz during the experiment, and a new shift of 12 kHz after 15 days of the experiment was measured. This illustrates the long-term drift of this synthesizer, which requires -1 month of warm-up. This drift, although partly compensated for, is responsible for a small fraction of the uncertainty of the absolute frequencies

108 m. A quarter-wave plate and a second polarizer permit the counterpropagating beam to be sent to a HgCdTe detector. It was remarkable to observe on this detector that the sidebands and the residual carrier, which are easily distinguished by application of 100% amplitude modulation to the microwave, do not overlap exactly. This confirms a previous observation with a setup that included a Fabry-Perot resonator. When we optimize the sideband signal onto the detector, the residual carrier represents less than 20% of the total signal. One possible interpretation is that most of the residual carrier comes from the multiple reflections off the numerous Brewster plates inside the first polarizer. The reflections introduce a small depolarization, and the resulting beam at the carrier frequency propagates with a slightly different direction from the sideband beam because of imperfections in the parallelism of the Brewster-plate faces. An angle of 5 X l0-5 rad between the two beams after the polarizer may be responsible for such an effect, which is significant in our experiment because of the long path length between the polarizer and the detector. This is fortunate,

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Pfister et al .

because the major part of the noise associated with the residual carrier does not affect the signal anymore. Of course, the two sidebands cannot be separated with this setup.


Finally, with a laser output power of 1 W, 50

in each sideband was available for the experiment; a saturation

power of 1 iW is typically necessary

for effi-

cient detection of strong molecular transitions with our spectrometer.

RESULTS To illustrate


ence laser." Wehave found that VSiF4 R(53)F?(+) - Vco 29P(30) = -1411.25(10) kHz. The C0 2 -laser line frequency is already




VCo 2 9P(3o) =

31 101 492 187.7(37) kHz.

The microwave synthesizer is maintained at a fixed frequency, which allows us to reach the studied SiF4 line while the rf synthesizer that drives the phase-lock loop between the two CO2 lasers is scanned. This provides a precise frequency scan of the sideband used for spectroscopy. By checking the whole set of our experimental data, we can estimate that the microwave frequency that drives

the electro-optic modulator drifted with a rate of some possibilities of this technique, we have

recorded several magnetic hyperfine structures of rovibrational transitions in the v 3 band of 2 5SiF4. All these lines are accessible by laser sideband spectroscopy with a '2C' 60 2 laser emitting on the P(30) line at 9.6 ,um. To our knowledge, these lines have been previously observed only by Doppler-limited diode-laser spectroscopy,9 and a typical accuracy of 10 MHz was then obtained. The most precise rovibrational constants were previously calculated with laser sideband and infrared rf double-resonance spectroscopy in the V3 band of SiF4 corresponding to J values of less than 40.Qo However, the theoretical calculations performed at the Laboratoire de Spectronomie Moleculaire et Instrumentation Laser (Dijon, France) by G. Pierre gave rise to predicted absolute frequencies within 100 kHz to 1 MHz of our experimental observations. Twenty rovibrational transitions located between -17.2 and -9.5 GHz from the C0 2-laser line have been recorded, and their absolute frequencies have been determined. During the experiment the reference laser was always locked to the R(53)FI'(+) line of SiF4, which is close to the C0 2-laser line center. We have measured the frequency difference between this reference line and the C0 2-laser line recorded at high resolution by using a technique that allows compensation for any frequency drift of the refer-

-500 Hz/day at 13 GHz during the 2 weeks of the experiment. Because of other frequency fluctuations on the time scale of a few hours, which were observed in systematic tests but not controlled during the experiment, we estimate the uncertainty of the frequency difference between each recorded SiF4 line and the R(53)F'(+) line to be 2 kHz. Table 1 gives a list of the 20 recorded rovibrational lines with the distance from the reference SiF4 line and their absolute frequency. The uncertainty of 4.5 kHz comes mainly from the 3.7 kHz of uncertainty in the absolute frequency of the C0 2-laser line. Each of these frequencies is actually the position of the center of gravity of the hyperfine structure of the corresponding rovibrational line. Some lines form clusters [i.e., R(47)A(-), F 2(+), E'] for which only the center of gravity of the whole structure can be given. Finally, it is noticeable in the case of R(46)E 5 , R(49)F' 0(-), R(49)FP(+) that the center of the hyperfine structure is shifted because of hyperfine mixing with neighboring rovibrational levels. This effect can be responsible for a shift of a few kilohertz between the observed center and the rovibrational line center after deconvolution of the hyperfine structure. Besides the capability of providing precise absolute frequencies of molecular lines, the laser sideband spectroscopy technique is most interesting for its resolving power.

Table 1. Absolute Frequencies of Fundamental Lines in the Shift from the Line (kHz)b

Identification of the




Band of 2"SiF4 Absolute Frequency (kHz)

R(48)A2 (-) R(48)A2 (+)

-17 155 397.5(20) -17 155 242.9(20)

31084335 379.0(45) 31084335533.6(45)

R(46)A2(+) R(46)Fl(-)

-16 703896.7(20) -16 703 827.0(20)

31084 786879.8(45) 31084 786949.5(45)

-16 703 792.2(20)c

31084 786 984.3(45)

-14 730 603.9(20)

31086 760 172.6(45)

-14 367 175.2(20)

31087123 601.3(45)

-14 342 347.7(20) -14328331.6(20) -13 462 813.1(20) -13462 765.7(20) -13369471.3(20)

31087 148428.8(45) 31087 162444.9(45) 31088027963.4(45) 31088028010.8(45) 31088 121305.2(45)

-13 368 445.4(20)' -13 367 405.0(20)'

31088 122 331.1(45) 31088 123 371.5(45)

-13 366363.9(20) -12 942 945.7(20) -12 337505.1(20) -11522 184.0(20) -11322 656.9(20) -9586477.7(20)

31088 124412.6(45) 31088547830.8(45) 31089 153271.4(45) 31089 968 592.5(45) 31090 168 119.6(45) 31091904298.8(45)



R(45)F°(+), Fl(-) R(46)A2 (-), F9(+), E


R(48)Fl(-) R(49)F 2(+),E7 , Fll(-) R(47)Fl(-) R(47)Fl(+) R(49)A2(+) R(49)Fl°(-) R(49)Fl'(+)

R(49)A2(-) R(46)Fio(+), Fl°(-) R(47)A2(-), F2(+), El R(50)F1(-), E°, F°(+) R(46)A3(+), F1'(-), E7 R(47)A2g(+),Fll(-), E°

aThese notations use the representations of the point group Td. When the isomorphicpermutation inversion group is used, the followingchanges have to be performed: A 2 (-) - A1 ; F1 (-) -> F2. line of SiF4 is 31101490 776.5(37) kHz. bThe absolute frequency of the R(53)Fl9(+) 'These lines are shifted by tensorial hyperfine interactions.


Pfister et al. Pitre l

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(Perturbed hyperfinestructure)

36 kHz HWHM= 1.46 kHz


(Hyperfinestructure in a superfinecluster)

24 kHz HWHM= 1.55 kHz


(intermediate case betweenhyperfine and superhyperfinestructures)

slightly perturbed by the coupling with the R(49)A2A-) line, which is only 2 MHz away. The half-width at halfmaximum is 1.46 kHz, a resolution that is essentially that obtained with this spectrometer in its standard operating mode. The resolution is mainly due to the finite transit time of the molecules through the laser beam, and the spectral purity of the sideband is not a limitation in this experiment. Figure 3(b) shows the hyperfine structure of the cluster R(46)FP'(+), Fi'0(-). The cluster forms two degenerate triplets, which are not coupled because they are of opposite parity. Figure 3(c) shows the hyperfine structure of the cluster R(48)A20(-), F'(+), Fo'(-), A'(+). The hyperfine structure of each rovibrational component is strongly perturbed by the tensorial hyperfine couplings, and several crossover resonances appear on this spectrum. Figure 3(d) shows the superhyperfine structure of the cluster R(47)A20(+),Fl(-), E0 , which can be interpreted as resulting from a spontaneous symmetry breaking of the group Td into a group D2d. We have successfully tried several modulation techniques for signal detection. Figures 3(a) and 3(b) correspond to a high-frequency modulation (100-200 kHz) applied to the microwave source, whereas in Fig. 3(c) and 3(d) a low-frequency modulation (-4.5 kHz) is applied, which results in a derivative line shape. These four examples illustrate the great variety of structures that can be recorded thanks to this laser sideband technique. For instance, no known cluster of the type of R(48)A2'(-), Fo(+), Fo?(-), AO(+) is in quasi-coincidence with a laser line of any isotopic species Of CO2. By contrast, thanks to the broadband tunability offered by the laser sideband technique, each kind of cluster in the 1)3 band of 25SiF4 has been accessible in the present experiment, although it

concerns only the limited spectral region around the 9

300kHzHWHM = 3.33 kHz


P(30) '2 C16 0 2 laser line. Although superhyperfine structures have been already observed in the 1)3 band of SF these are the first to our knowledge published for a Td molecule since their prediction by Harter and Patterson. 14 Their analysis is in progress but is beyond the scope of this paper. CONCLUSIONS

("Tetragonal" superhyperfinestructure)

We have demonstrated that laser sideband spectroscopy allows one to conduct ultrahigh-resolution


40 kHz


HWHM= 2.76 kHz


Fig. 3. Four examples of magnetic hyperfine structures in the 3 band of SiF4, recorded by laser sideband spectroscopy. When we use only the 12 C160 2 emission line 9P(30), the broadband tunability of the sideband allows us to explore a wide variety of physical situations.

This is illustrated in Fig. 3 by several hyperfine struc-

tures. Figure 3(a) shows the hyperfine structure of

R(49)Fi' 0(-). This triplet comes from the total spin of the fluorines I = 1, imposed by the Pauli principle. It is


Narrow structures induced by magnetic hyperfine interactions have been resolved, and absolute frequencies of several molecular lines have been obtained with an accuracy essentially imposed by the precision of the C0 2-laser line. Obviously, the broadband tunability of this technique opens new perspectives for ultrahigh-resolution spectroscopy. The major interest would not be the capability of recording a whole vibrational band, which is currently accomplished by Fourier-transform spectroscopy. More interesting will be the possibility of selecting the best set of transitions within the whole 9-12-Am region for studying a particular


The choice is no longer

limited by the quasi-coincidences with the C0 2-laser lines, a constraint that is dramatic for light molecules such as ammonia or phosphine. Alternative methods exist for reaching full tunability in this spectral region. The most promising one is certainly provided by differencefrequency generation.1 5 16 Two laser emissions, usually in

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Pfister et al.

the visible, are mixed inside the crystal (LiNbO3, LiIO3, AgGaS2, or AgGaSe2 , depending on the desired spectral region), which generates the difference frequency. The whole spectrum between 1 and 18 Aumcan thus be covered by tuning one laser. However, we do not believe that, in

the short term, this technique can be competitive with the laser sideband method for ultrahigh-resolution spectroscopy. The main reason is the required spectral purity, which is of a few tens of hertz. Whereas this purity is easily achieved in the sideband method, thanks to a welldesigned CO2 laser and a highly stable microwave source, it is more problematic in difference-frequency generation, since this spectral purity has to be achieved for two visible sources. Ar' lasers and dye or titanium-sapphire lasers are commonly used in such experiments, and extremely fast stabilization systems would be necessary.'7 So far the reliability of such a setup does not compare with that of the laser sideband method used here.


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M. Havenith,


tional Conferenceon High ResolutionInfrared and Microwave Spectroscopy (Cechoslavak Spectroscopic Society, Prague, 1992), paper J8. 8. G. Magerl, W Schupita, and E. Bonek, IEEE J. Quantum Electron. QE-18, 1214 (1982). 9. C. W Patterson, R. S. McDowell, N. G. Nereson, and B. J. Krohn, J. Mol. Spectrosc. 91, 416 (1982). 10. L. J6rissen, H. Prinz, W A. Kreiner, Ch. Wenger, G. Pierre,

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ment of the sideband modulation technique at the


Laboratoire de Spectroscopie Hertzienne-Lille has been made possible thanks to the support of Direction de la Recherche et des Etudes Techniques-France.


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Legrand, and W Urban, in Proceedings of the XIIth Interna-

We thank G. Pierre for having provided very promptly a list of calculated frequencies of SiF4 lines, which proved to be very reliable. We are also grateful to HP-France for having loaned to us the highly stable microwave synthesizer that drove the electro-optic modulator. The develop-




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