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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 21 — Oct. 17, 2005
  • pp: 8357–8364
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Doppler-free spectroscopy of xenon in the mid-infrared using difference-frequency radiation

G. Rusciano, A. C. De Luca, F. Pignatiello, and A. Sasso  »View Author Affiliations


Optics Express, Vol. 13, Issue 21, pp. 8357-8364 (2005)
http://dx.doi.org/10.1364/OPEX.13.008357


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Abstract

We report on the first Doppler-free spectroscopy investigation of an atomic species, xenon, performed in the mid-infrared using difference-frequency radiation. The absorption saturated spectrum of the xenon 6p[3/2]2→5d[5/2]3 transition (2p6→3d’1 in Paschen notation) at 3.1076 μm was investigated using about 60 microwatts of cw narrowband radiation (Δv=50 kHz) generated by difference-frequency mixing in a periodically-poled Lithium Niobate crystal. A single frequency Ti: Sapphire laser (power 800 mW) and a monolithic diode-pumped Nd:YAG laser (300 mW) were used as pump and signal waves respectively. We used natural enriched xenon, which contains nine stable isotopes, two of which, 129Xe and 131Xe, exhibit a hyperfine structure owing to their nuclear spin. The small isotope displacements expected for this atom and the complex hyperfine structure of the odd isotopes make it difficult to fully resolve the recorded saturated-absorption spectra. In spite of this, we have been able to analyze the isolated 129Xe F’’=5/2→F’=7/2 hyperfine component by means of first-derivative FM spectroscopy.

© 2005 Optical Society of America

1. Introduction

2. Experimental set-up

Fig. 1. Scheme of the experimental setup. Mid-IR radiation is produced by difference-frequency generation in a periodically poled lithium niobate crystal by using a Ti:Sapphire (pump) laser and a Nd:YAG (signal) laser. The produced mid-IR beam is retroreflected through the discharge cell to observe sub-Doppler saturation spectra. L: lens; OI: optical isolator; HWP: half-wave plate; P: polarizer; M: mirror; DM: dichroic mirror; GF: germanium filter; BS: beam splitter; Doubled Nd-YVO: frequency-doubled Neodymium: Yttrium Orthovanadate laser.

The experiment was realized with the apparatus schematically shown in Fig. 1. Mid-IR radiation was generated through difference-frequency mixing in a periodically poled lithium niobate (PPLN) optical crystal. A Ti: Sapphire laser (Coherent, Mod. MBR110) emitting about 1.6 W of narrowband (50kHz) tunable (0.7-1.0 μm) radiation (single scan up to 40 GHz) was used as pump beam. A diode-pumped Nd- YAG laser (Innolight, Model Mephisto 500) consisting of a monolithic ring cavity which emits a maximum power of 500 mW (Δv=10 kHz) was used as signal beam. The two laser beams were combined by a dichroic mirror and focused into a 19-mm-long PPLN (Crystal Technology). Within the Ti:Sapphire tunability it was possible to produce 60 μW of mid-IR radiation (idler) from 2.8 to 3.2 μm, with pump and signal powers of 800 mW and 300 mW respectively. The mid-IR radiation wavelength was determined by measuring the Ti: Sapphire wavelength with a traveling Michelson interferometer (accuracy of one part in 107) while the Nd-YAG wavelength was obtained from calibration curves provided by the manufacturer. Finally, DFG frequency scans were accomplished by tuning the Ti-Sa laser frequency and calibrated by using a 300 MHz free-spectral range (FSR) confocal Fabry-Perot interferometer. Excited xenon atoms were produced by means of a radio-frequency discharge (power 50 Watt, frequency 60 MHz) whose details have been described elsewhere [20

20 . G. D’Amico , G. Pesce , and A. Sasso , “ Isotope-shift and hyperfine-constant measurements of near-infrared xenon transitions in glow discharges and on a metastable Xe(P-3(2)) beam ,” Phys. Rev. A 60 , 4409 – 4416 ( 1999 ). [CrossRef]

]. With that discharge, typical excited atom densities in the lower level 2p6 were of the order of 107 atoms/cm3. Sub-Doppler saturation spectra were observed by retroreflecting the laser beam back through the discharge cell [21

21 . G. M. Tino , L. Hollberg , A. Sasso , M. Inguscio , and M. Barsanti , “ Hyperfine-structure of the metastable S-2(5) state of O-17 using an AlGaAs diode-laser at 777 nm ,” Phys. Rev. Lett. 64 , 2999 – 3002 ( 1990 ). [CrossRef] [PubMed]

]; in this simple geometry, the incoming beam acts as pump and the reflected beam as probe. The mid-IR beam was focused by a 20 cm focal-length lens to a waist of about 800 μm in the region of maximum intensity of the plasma discharge near one end of a 20-cm long Pyrex discharge tube (internal diameter= 7 mm). The focal plane of the focusing lens was almost coincident with the plane of the reflecting mirror. Finally the reflected beam, separated from the incoming beam by a 10% beam-splitter, was collected onto the active area of a liquid-nitrogen InSb detector (Hamamatsu, Model PN5968). Since the available DFG power was too low to observe a saturation dip in direct absorption, we used first-derivative Frequency Modulation (FM) saturation spectroscopy. In this case, phase sensitive detection was performed by modulating the Nd:YAG laser frequency by few MHz by means of a piezoelectric transducer applied to its cavity length. This modulation occurred at a frequency of 10 kHz which was the same frequency as the one used as reference signal for a lock-in amplifier.

3. Results and discussion

Typical Doppler-limited and Doppler-free absorption spectra of the 6p[3/2]2→5d[5/2]3 transition are shown in Fig. 2.

Fig. 2. Doppler-free (a) and Doppler-limited (b) spectra of the 2p6→3d’1 transition at 3.1076 μm. The saturation dips are not observed in the Doppler profile, while they are enhanced (indicated by arrows) with derivative spectroscopy using FM spectroscopy.

Fig. 3. (a) A simplified energy-level scheme of Xe showing the mid-IR transition investigated in this work. In part (b) and (c) are shown the hyperfine structure levels of the 129Xe and 131Xe respectively. The circled numbers are the normalized intensities of the hyperfine components.

On the basis of similarity of this spectrum with that obtained for near-IR Xe lines (ref. [20

20 . G. D’Amico , G. Pesce , and A. Sasso , “ Isotope-shift and hyperfine-constant measurements of near-infrared xenon transitions in glow discharges and on a metastable Xe(P-3(2)) beam ,” Phys. Rev. A 60 , 4409 – 4416 ( 1999 ). [CrossRef]

]), we suggest that this peak corresponds to the most intense F’’=5/2→F’=7/2 hyperfine component of 129Xe. Figure 4 shows the experimental spectrum of this peak (modulation amplitude =3 MHz): the wide and the sharper resonances correspond to the first-derivative of the Doppler and homogeneous line-profile respectively. The experimental line-shape was fitted with the derivative of the sum of a Gaussian and a Lorentzian curve as shown in Fig. 4. The agreement is rather good, although some little deviations could reflect the presence of some weak line blended in the profile. The best-fit parameters give a Doppler width of 128±3 MHz FWHM (which corresponds to a discharge temperature of 450 K) and a homogeneous width of 30±1 MHz FWHM. Therefore, the agreement between the experimental and fitted parameters confirms our hypothesis that the analyzed peak is effectively a single hyperfine component. Its width of 30 MHz can be considered to be the natural width of the investigated transition since, pressure broadening and power broadening can be neglected in our experimental conditions of low pressure and low radiation power. Moreover, even time-of-flight broadening, which in our case is of the order of 1.8 MHz, can be assumed ineffective on the observed homogeneous width. Knowing the lifetime of the lower level (τ(2p6)=40 ns) [22

22 . A. A. Radzig and B. M. Smirnov in “Reference Data on Atoms, Molecules, and Ions,” Springer Series in Chemical Physics - Berlin ( 1980 ).

], we can give an estimation of the radiative lifetime of the upper level 3d’1 of 6.0±0.2 ns.

Fig. 4. Saturated-absorption dip of the hyperfine component recorded as first-derivative FM spectrum. The continuous line represents the result of a fit procedure where the experimental points are compared to the derivative of the sum of a Gaussian and Lorentzian profile.

In order to estimate the saturation intensity Isat of the investigated transition, we have measured the contrast H referred to the ratio between the sub-Doppler signal and the Doppler profile by varying the laser intensity I. This analysis was performed taken into account the different modulation index for the two line-profiles, Gaussian and Lorentzian, when a given modulation amplitude was fixed. The linear behavior of H versus the laser intensity (see Fig. 5) means that the intensities used in our experiment are quite smaller than Isat. Therefore the contrast, which is given by H=(1+I/Isat)1/2(1+2I/Isat)1/2 [23

23 . V. S. Letokhov and V. P. Chebotayev in Nonlinear Laser Spectroscopy , Springer Verlag Series in Optical Sciences Berlin ( 1977 ).

], becomes H12I/Isat, and from a linear fit of the data shown in Fig. 5 results in Isat = 9.2(5) mW/cm2, which is typical for atomic transitions. Moreover, from the expression of Isat=ε0h2cΓ22μ2, where Γ2π is the sub-Doppler HWHM, the dipole moment μ of the investigated transition can be inferred: μ=3.7(1)∙10-29 C∙m.

Fig. 5. Behavior of the experimental contrast H versus the mid-IR radiation intensity.

4. Conclusions

In conclusion, we have demonstrated the possibility to perform high resolution spectroscopy of atomic species using difference frequency radiation at low power. This opens interesting possibilities for absolute frequency measurements to provide new secondary frequency standards in the mid-IR. Indeed, the frequencies of the two lasers used for frequency mixing can be precisely measured: the Hall’s group [24

24 . J. Hall , L. Ma , M. Taubmann , B. Tiemann , F. Hong , O. Pfister , and J. Ye , “ Stabilization and frequency measurement of the I-2-stabilized Nd : YAG laser ,” IEEE Trans. Instrum. Meas. 48 , 583 – 586 ( 1999 ). [CrossRef]

] has provided very precise absolute frequency measurements of a frequency-doubled Nd:YAG laser locked to iodine lines, while, nowadays, frequency comb technique [25

25 . R. Holzwarth , T. Udem , T. Hansch , W. Knight , W. J. Wadsworth , and P. St. J. Russel , ” Optical frequency synthesizer for precision spectroscopy ,” Phys. Rev. Lett. 85 , 2264 – 2267 ( 2000 ). [CrossRef] [PubMed]

] allows direct measurements of frequency within the Ti:Sapphire laser emission spectrum. Of course, using enriched xenon samples, simplified spectra are available (single odd isotope line or isolated HFS component) which make easier such kind of measurements. Moreover, the use of enriched samples can make feasible even the HFS and IS studies of the highly xenon excited levels investigated in this work.

References and links

1 .

M. M. J. Van Herpen , S. Li , S. E. Bisson , S. Te Lintel Hekkert , and F. J. M. Harren , “ Tuning and stability of a continuous-wave mid-infrared high-power single resonant optical parametric oscillator ,” Appl. Phys. B 75 , 329 – 333 ( 2002 ) [CrossRef]

2 .

D. Richter , A. Fried , B. P. Wert , J. G. Walega , and F. K. Tittel , “ Development of a tunable mid-IR difference frequency laser source for highly sensitive airborne trace gas detection ,” Appl. Phys. B 75 , 281 – 288 ( 2002 ). [CrossRef]

3 .

K. Namjou , S. Cai , E. A. Whittaker , J. Faist , C. Gmachl , F. Capasso , D. L. Sivco , and A. Y. Cho , “ Sensitive absorption spectroscopy with a room-temperature distributed-feedback quantum-cascade laser ,” Opt. Lett. 23 , 219 – 221 ( 1998 ) [CrossRef]

4 .

D. G. Lancaster , D. Richter , R. F. Curl , and F. K. Tittel , “ Real-time measurements of trace gases using a compact difference-frequency-based sensor operating at 3.5 μm ,” Appl. Phys. B 67 , 339 – 345 ( 1998 ) [CrossRef]

5 .

S. Stry , P. Hering , and M. Murtz , “ Portable difference-frequency laser-based cavity leak-out spectrometer for trace-gas analysis ,” Appl. Phys. B 75 , 297 – 303 ( 2002 ) [CrossRef]

6 .

A. Hecker , M. Havenith , C. Braxmaier , U. Stroner , and A. Peters , “ High resolution Doppler-free spectroscopy of molecular iodine using a continuous wave optical parametric oscillator ,” Opt. Commun. 218 , 131 – 134 ( 2003 ) [CrossRef]

7 .

D. Mazzotti , P. De Natale , G. Gagliardi , C. Fort , J. A. Mitchell , and L. Hollberg , “ Saturated-absorption spectroscopy with low-power difference-frequency radiation ” Opt. Lett. 25 , 350 – 352 ( 2000 ) [CrossRef]

8 .

J. T. Remillard , D. Uy , W. H. Weber , F. Capasso , C. Gmachl , A. L. Hutchinson , D. L. Sivco , J. N. Baillargeon , and A. Y. Cho , “ Sub-Doppler resolution limited Lamb-dip spectroscopy of NO with a quantum cascade distributed feedback laser ” Opt. Express 7 , 243 – 248 ( 2000 ) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-7-243 [CrossRef] [PubMed]

9 .

P. Maddaloni , G. Gagliardi , P. Malara , and P. De Natale , “ A 3.5-mW continuous-wave difference-frequency source around 3 mu m for sub-Doppler molecular spectroscopy ” Appl. Phys. B 20 , 141 – 145 ( 2005 ). [CrossRef]

10 .

S. Borri , P. Cancio , P. De Natale , G. Giusfredi , D. Mazzotti , and F. Tamassia “ Power-boosted difference-frequency source for high-resolution infrared spectroscopy ” Appl. Phys. B 76 , 473 ( 2003 ) [CrossRef]

11 .

J. Bauche and R. J. Champeau , “ Recent progress in the theory of atomic isotope shifts ” Adv. At. Mol. Phys. 37 , 39 – 86 ( 1976 ). [CrossRef]

12 .

D.A. Jackson , F.R. S. , and M.-C. Coulombe , “ Isotope shifts in the arc spectrum of xenon ,” Proc. R. Soc. Lond. A 338 , 277 – 281 ( 1974 ) [CrossRef]

13 .

D.A. Jackson , F.R. S. , M.-C. Coulombe , and J. Bauche , “ Isotope shifts in the arc spectrum of xenon II ” Proc. R. Soc. Lond. A 343 , 453 – 459 ( 1975 ). [CrossRef]

14 .

W. Fischer , H. Huhnermann , G. Kromer , and H. J. Schafer , “ Isotope shift in the Atomic Spectrum of Xenon and Nuclear Deformation Effects ,” Z. Phys. 270 , 113 – 120 ( 1974 ). [CrossRef]

15 .

W. Borchers , E. Arnold , W. Neu , R. Neugart , K. Wendt , and G. Ulm , “ Xenon Isotopes far from Stability studied by Collisional Ionization Laser Spectroscopy ,” Phys. Lett. B 216 , 7 – 10 ( 1989 ). [CrossRef]

16 .

H. Geisen , T. Krumpelmann , D. Neuschafer , and Ch. Ottingen , “ Hyperfine splitting measurements on the 6265 Å and 6507 Å lines of seven Xe isotopes by lif on a beam of metastable Xe( 3 P 0,2 ) atoms ,” Phys. Lett. A 130 , 299 – 304 ( 1988 ). [CrossRef]

17 .

M. D. Plimmer , P.E.G. Baird , C.J. Foot , D.N. Stacey , J.B. Swan , and G.K. Woodgate , “ Isotope shift in xenon by Doppler-free two-photons laser spectroscopy ” J. Phys. B: At. Mol. Opt. Phys. 22 , L241 – L244 ( 1989 ). [CrossRef]

18 .

U. Sterr , A. Bard , C. J. Sansonetti , S. L. Rolston , and J. D. Gilapsy , “ Determination of the xenon 6s[3/2](2)-6s’[1/2](0) clock frequency by interferometric wavelength measurements ,” Opt. Lett. 20 , 1421 – 1423 ( 1995 ). [CrossRef] [PubMed]

19 .

M. Walhout , H. J. L. Megens , A. Witte , and S. L. Rolston , “ Magnetooptical trapping of metastable xenon -isotope-shift measurements ,” Phys. Rev. A 48 , R879 – R882 ( 1993 ). [CrossRef] [PubMed]

20 .

G. D’Amico , G. Pesce , and A. Sasso , “ Isotope-shift and hyperfine-constant measurements of near-infrared xenon transitions in glow discharges and on a metastable Xe(P-3(2)) beam ,” Phys. Rev. A 60 , 4409 – 4416 ( 1999 ). [CrossRef]

21 .

G. M. Tino , L. Hollberg , A. Sasso , M. Inguscio , and M. Barsanti , “ Hyperfine-structure of the metastable S-2(5) state of O-17 using an AlGaAs diode-laser at 777 nm ,” Phys. Rev. Lett. 64 , 2999 – 3002 ( 1990 ). [CrossRef] [PubMed]

22 .

A. A. Radzig and B. M. Smirnov in “Reference Data on Atoms, Molecules, and Ions,” Springer Series in Chemical Physics - Berlin ( 1980 ).

23 .

V. S. Letokhov and V. P. Chebotayev in Nonlinear Laser Spectroscopy , Springer Verlag Series in Optical Sciences Berlin ( 1977 ).

24 .

J. Hall , L. Ma , M. Taubmann , B. Tiemann , F. Hong , O. Pfister , and J. Ye , “ Stabilization and frequency measurement of the I-2-stabilized Nd : YAG laser ,” IEEE Trans. Instrum. Meas. 48 , 583 – 586 ( 1999 ). [CrossRef]

25 .

R. Holzwarth , T. Udem , T. Hansch , W. Knight , W. J. Wadsworth , and P. St. J. Russel , ” Optical frequency synthesizer for precision spectroscopy ,” Phys. Rev. Lett. 85 , 2264 – 2267 ( 2000 ). [CrossRef] [PubMed]

OCIS Codes
(300.6210) Spectroscopy : Spectroscopy, atomic
(300.6460) Spectroscopy : Spectroscopy, saturation

ToC Category:
Research Papers

History
Original Manuscript: August 29, 2005
Revised Manuscript: September 27, 2005
Published: October 17, 2005

Citation
G. Rusciano, A. De Luca, F. Pignatiello, and A. Sasso, "Doppler-free spectroscopy of xenon in the mid-infrared using difference-frequency radiation," Opt. Express 13, 8357-8364 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-21-8357


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References

  1. M. M. J. Van Herpen, S. Li, S. E. Bisson, S. Te Lintel Hekkert, and F. J. M. Harren, �??Tuning and stability of a continuous-wave mid-infrared high-power single resonant optical parametric oscillator,�?? Appl. Phys. B 75, 329-333 (2002) [CrossRef]
  2. D. Richter, A. Fried, B. P. Wert, J. G. Walega, and F. K. Tittel, �??Development of a tunable mid-IR difference frequency laser source for highly sensitive airborne trace gas detection,�?? Appl. Phys. B 75, 281-288 (2002). [CrossRef]
  3. K. Namjou, S. Cai, E. A. Whittaker, J. Faist, C. Gmachl, F. Capasso, D. L. Sivco, and A. Y. Cho, �??Sensitive absorption spectroscopy with a room-temperature distributed-feedback quantum-cascade laser,�?? Opt. Lett. 23, 219-221 (1998) [CrossRef]
  4. D. G. Lancaster, D. Richter, R. F. Curl, and F. K. Tittel, �??Real-time measurements of trace gases using a compact difference-frequency-based sensor operating at 3.5 µm,�?? Appl. Phys. B 67, 339-345 (1998) [CrossRef]
  5. S. Stry, P. Hering, and M. Murtz, �??Portable difference-frequency laser-based cavity leak-out spectrometer for trace-gas analysis,�?? Appl. Phys. B 75, 297-303 (2002) [CrossRef]
  6. A. Hecker, M. Havenith, C. Braxmaier, U. Stroner, and A. Peters, �??High resolution Doppler-free spectroscopy of molecular iodine using a continuous wave optical parametric oscillator,�?? Opt. Commun. 218, 131-134 (2003) [CrossRef]
  7. D. Mazzotti, P. De Natale, G. Gagliardi, C. Fort, J. A. Mitchell, and L. Hollberg, �??Saturated-absorption spectroscopy with low-power difference-frequency radiation�?? Opt. Lett. 25, 350-352 (2000) [CrossRef]
  8. J. T. Remillard, D. Uy, W. H. Weber, F. Capasso, C. Gmachl, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, and A. Y. Cho, �??Sub-Doppler resolution limited Lamb-dip spectroscopy of NO with a quantum cascade distributed feedback laser�?? Opt. Express 7, 243-248 (2000) <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-7-243">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-7-243</a> [CrossRef] [PubMed]
  9. P. Maddaloni, G. Gagliardi, P. Malara, and P. De Natale, �??A 3.5-mW continuous-wave difference-frequency source around 3 mu m for sub-Doppler molecular spectroscopy�?? Appl. Phys. B 20, 141-145 (2005). [CrossRef]
  10. S. Borri, P. Cancio, P. De Natale, G. Giusfredi, D. Mazzotti, and F. Tamassia �??Power-boosted difference-frequency source for high-resolution infrared spectroscopy�?? Appl. Phys. B 76, 473 (2003) [CrossRef]
  11. J. Bauche and R. J. Champeau, �??Recent progress in the theory of atomic isotope shifts�?? Adv. At. Mol. Phys. 37, 39-86 (1976). [CrossRef]
  12. D.A. Jackson, F.R.S. and M.-C. Coulombe, �??Isotope shifts in the arc spectrum of xenon,�?? Proc. R. Soc. Lond. A 338, 277-281 (1974) [CrossRef]
  13. D.A. Jackson, F.R.S. and M.-C. Coulombe, and J. Bauche, �??Isotope shifts in the arc spectrum of xenon II�?? Proc. R. Soc. Lond. A 343, 453-459 (1975). [CrossRef]
  14. W. Fischer, H. Huhnermann, G. Kromer, and H. J. Schafer, �??Isotope shift in the Atomic Spectrum of Xenon and Nuclear Deformation Effects,�?? Z. Phys. 270, 113-120 (1974). [CrossRef]
  15. W. Borchers, E. Arnold, W. Neu, R. Neugart, K. Wendt, and G. Ulm, �??Xenon Isotopes far from Stability studied by Collisional Ionization Laser Spectroscopy,�?? Phys. Lett. B 216, 7-10 (1989). [CrossRef]
  16. H. Geisen, T. Krumpelmann, D. Neuschafer and Ch. Ottingen, �??Hyperfine splitting measurements on the 6265 �? and 6507 �? lines of seven Xe isotopes by lif on a beam of metastable Xe(3P0,2) atoms,�?? Phys. Lett. A 130, 299-304 (1988). [CrossRef]
  17. M. D. Plimmer, P.E.G. Baird, C.J. Foot, D.N. Stacey, J.B. Swan and G.K. Woodgate, �??Isotope shift in xenon by Doppler-free two-photons laser spectroscopy�?? J. Phys. B: At. Mol. Opt. Phys. 22, L241-L244 (1989). [CrossRef]
  18. U. Sterr, A. Bard, C. J. Sansonetti, S. L. Rolston, and J. D. Gilapsy, �??Determination of the xenon 6s[3/2](2)-6s'[1/2](0) clock frequency by interferometric wavelength measurements,�?? Opt. Lett. 20, 1421-1423 (1995). [CrossRef] [PubMed]
  19. M. Walhout, H. J. L. Megens, A. Witte, and S. L. Rolston, �??Magnetooptical trapping of metastable xenon-isotope-shift measurements,�?? Phys. Rev. A 48, R879-R882 (1993). [CrossRef] [PubMed]
  20. G. D�??Amico, G. Pesce, A. Sasso, �??Isotope-shift and hyperfine-constant measurements of near-infrared xenon transitions in glow discharges and on a metastable Xe(P-3(2)) beam,�?? Phys. Rev. A 60, 4409-4416 (1999). [CrossRef]
  21. G. M. Tino, L. Hollberg, A. Sasso, M. Inguscio, and M. Barsanti, �??Hyperfine-structure of the metastable S-2(5) state of O-17 using an AlGaAs diode-laser at 777 nm ,�?? Phys. Rev. Lett. 64, 2999-3002 (1990). [CrossRef] [PubMed]
  22. A. A. Radzig and B. M. Smirnov in �??Reference Data on Atoms, Molecules, and Ions,�?? Springer Series in Chemical Physics - Berlin (1980).
  23. V. S. Letokhov and V. P. Chebotayev in Nonlinear Laser Spectroscopy, Springer Verlag Series in Optical Sciences Berlin (1977).
  24. J. Hall, L. Ma, M. Taubmann, B. Tiemann, F. Hong, O. Pfister, J. Ye, �??Stabilization and frequency measurement of the I-2-stabilized Nd : YAG laser,�?? IEEE Trans. Instrum. Meas. 48, 583-586 (1999). [CrossRef]
  25. R. Holzwarth, T. Udem , T. Hansch, W. Knight, W. J. Wadsworth, P. St. J. Russel, �??Optical frequency synthesizer for precision spectroscopy,�?? Phys. Rev. Lett. 85, 2264-2267 (2000). [CrossRef] [PubMed]

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