Measurements of the frequency shift in the CO2

laser stabilized by using a gain curve Tomizo Kurosawa and Hirokazu Matsumoto

National Research Laboratory of Metrology, 1-4, Ume-zono 1-chome, Tsukuba, Ibaraki 305, Japan Received 19 October 1987. 0003-6935/88/101911-03$02.00/0. © 1988 Optical Society of America. In the interferometric measurement of distances up to

several tens of meters, a long wavelength such as a CO2 laser is very advantageous as the light source for an interferome­ter,1 because the long wavelength makes it less sensitive to mechanical vibration and air turbulence compared with a visible wavelength. The CO2 laser can oscillate on many transitions in the 9-11-μm wavelength range and has been a particularly attractive source for multiwavelength interfer-ometry,2-4 because the frequencies of most of these transi­tions are known5 with an accuracy of 10-11 and have good transmission through a clear atmosphere. A CO2 laser locked to the power maximum in the gain curve has usually been used as the light source. In the case of such a simply conveniently stabilized CO2 laser, the operating frequency is shifted by several megahertz from the molecular transition frequency depending on gas pressure and discharge current.6

The frequency shift leads to a systematic error of measure­ment7 and is a serious problem in the absolute measurement of distance with an accuracy of better than 10-7; other prob-

Fig. 1. Experimental apparatus used for frequency calibration of the CO2 laser locked to the power maximum in the gain curve by referring to the CO2 laser stabilized on the Lamb dip of the 4.3-μm

fluorescence.

lems are accurate information of the refractive index of the moist air and the diffraction correction.

In this Letter frequency shifts of a CO2 laser locked to the peak of the gain curve have been measured by referring to a CO2 laser stabilized on the Lamb dip of the 4.3-μm fluores­cence emitted by CO2 gas. These results were independent­ly confirmed by simultaneous distance measurements rang­ing from 0.1 to 5 m with an accuracy of 5 × 10-8 using a 633-nm He-Ne and a CO2 laser interferometer.

Figure 1 is a schematic diagram of the apparatus used for the frequency calibration of the CO2 laser locked to the power maximum in the gain curve. The CO2 laser 1 used as the light source of the distance measuring interferometer is the ML3800 type made by Canadian MPB Technology Co. The laser cavity is 50 cm long and composed of a Ge plane output mirror (T = 10%) and a spherical mirror with a 2-m radius of curvature. This commercial sealed-off-type CO2 laser is operated at 9.5 kV and 5.7 mA, and the maximum output power is ~3 W at the 10P(20) line. Unfortunately, operating conditions such as excitation voltage and current cannot be changed; also the pressure and ratio of gas mixture are unknown. The signatures of the CO2 laser are obtained by translating the mirror mounted on a piezoelectric trans­ducer (PZT). The CO2 laser 1 is stabilized at the peak of the gain curve by dithering the cavity length with a frequency of 524 Hz and its 5-MHz modulation width, using a phase-sensitive detector. The frequency offset due to the dc off­sets generated in the stabilizer was estimated to be less than ±200 kHz. The reference CO2 laser 2 with a cavity length of 1.3 m is composed of a Ge spherical mirror (R = 85%) mount­ed on the PZT and a grating (90 lines/mm) for the selection of an oscillating line. Laser 2 has an intracavity CO2 absorp­tion cell filled with 9.3-Pa (70-mTorr) gas pressure during the experiment. The modulation signal from laser 1 is fed to laser 2 through a phase shifter. The phase shifter is adjusted so that the frequency spread of the beat signal becomes minimum. Laser 2 is stabilized by the Freed-Javan meth­od,8 locking to the zero crossing point of the first derivative signal of 4.3-μm saturated fluorescence emitted from the absorption cell. The oscillating frequency is denoted vƒ· The output power is typically 1W, and its frequency stability is better than 3 × 10-10. To determine the sign of the

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Table I. Frequency Shifts and Spectrum Width of the Beat Notes for Six Different P/R Lines in the 10.4 μm Band

Fig. 2. (a) Relationship of oscillating frequency in three CO2 lasers: vp is the frequency of laser 1 locked to the power maximum in the gain curve, vƒ is the frequency of laser 2 stabilized on the Lamb dip of the 4.3-μm fluorescence, and v0 is the frequency of laser 3 offset-locked —20 MHz away from vƒ. (b) Beat notes generated by mixing three beams in the HgCdTe detector: vp — vƒ = 5.5 MHz; vƒ — v0 = 20

MHz; and vp - v0 = 25.5 MHz.

frequency shift of laser 1, another CO2 laser 3 is necessary and is offset-locked to laser 2, - 2 0 MHz/20 MHz away from vƒ. The structure and performance are similar to that of laser 2. Three beams were combined collinearly with paral­lel polarization and focused with a 50-cm focal length spheri­cal mirror onto the HgCdTe detector (Labimex R005) oper­ating at room temperature. To avoid detector breakdown, each incident power onto the detector was reduced to 30-40 mW. The output signal from the detector was fed to a low-noise amplifier and then displayed on the spectrum analyzer. We coincide a marker signal from the oscillator with the center of the beat signal displayed on the spectrum analyzer and read the beat frequency with a frequency counter.

When laser 3 was offset-locked to laser 2, —20 MHz away from vƒ as shown in Fig. 2(a), beat notes are as shown in Fig. 2(b). The beat frequency (vp—vƒ), where vp is the frequency of laser 1, is 5.5 MHz for the 10P(20) line. The width of the beat signal is ~1.6 MHz. The frequency v0 is of laser 3. The beat frequencies are vƒ—v0 = 20 MHz and vp — v0 = 25.5 MHz, respectively. The frequency spread of these beat signals is approximately equal to the modulation width of laser 1 with 5 MHz because laser 3 is unmodulated. For the offset-locked No. 3 laser 20 MHz away from vƒ, the beat frequencies were obtained as vp — vƒ= 5.5 MHz, v0 — vƒ = 20 MHz, and v0 -

vp = 14.5 MHz. Accordingly the 10P(20) line of laser 1 is shifted by +5.5 MHz from vƒ. In this way we measured for six different lines in the 10.4-μm band, P(18), P(20), P(22), R(20), R(22), and R(24). The reproducibility of measure­ments for each line was restricted to ~0.5 MHz due to the frequency fluctuation, power variation, and dc offsets of the stabilizer for laser 1. Measured values are listed in Table I, classified into two groups. From Table I averaged frequency shifts are +(5.3 ± 0.5) MHz for three lines of the P-branch and +(2.9 ± 0.7) MHz for three lines of the R-branch, respec­tively. The frequency shift for the 10i?(20) line is smaller than that of the 1 0 R ( 2 2 ) and 10R(24) lines. The servo-lock stability of the 10R(20) line was poor because of strong competition of the 10R(18) in the neighborhood of the peak of the 1 0 R ( 2 0 ) line. In general, it is believed that the sources of the frequency shift are due to the effect of collisions between excited and ground state molecules and changes in the refractive index of the lasing medium arising from dis­charge current variations. The difference between the mea­sured shifts in the P- and R-branches cannot be explained; it seems to relate somewhat to the effects of the small signal gain coefficients.

The frequency shifts cause a systematic error of 2 X10 - 7 in the absolute distance measurements; in fact, we confirmed this in the simultaneous distance measurements in the 0.1-5-m range using the Hewlett-Packard (HP) 633-nm He-Ne laser interferometer and the CO2 laser interferometer.9 The HP laser was calibrated by referring to an iodine stabilized 633-nm He-Ne laser10; the measurements were carried out using the P(20) and R(22) lines of the 10.4-μm band in the normal atmospheric air. The values of the distance mea­sured by the CO2 laser interferometer using the corrected oscillating wavelength are in good agreement with those measured by the HP laser interferometer within an accuracy of 5 × 10 - 8 . In this case, the diffraction effect for the CO2 laser interferometer was corrected by 1.2 × 10 - 7 (see Ref. 11), and the refractivity was corrected by 5 × 10 - 8 (see Ref. 9).

In summary, frequency shifts are +(5.3 ± 0.5) MHz for three lines of the P-branch and +(2.9 ± 0.7) MHz for three lines of the R-branch in the 10.4-μm band. Absolute dis­tance measurements with an accuracy of the order of 10 - 8 in normal atmospheric air have been demonstrated using the CO2 laser interferometer with wavelength calibrated by pre­cise correction of the refractive index and the diffraction effect.

References 1. K. M. Baird, "The Role of Interferometry in Long Distance

Measurement," Metrologia 4, 135 (1968).

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2. C. W. Gillard, N. E. Buholz, and D. W. Ridder, "Absolute Dis­tance Interferometry," Opt. Eng. 20, 129 (1981).

3. H. Matsumoto, "Synthetic Interferometric Distance-Measuring System Using a CO2 Laser," Appl. Opt. 25, 493 (1986).

4. C. J. Walsh, "Measurements of Absolute Distances to 25 m by Multiwavelength CO2 Laser Interferometry," Appl. Opt. 26, 1680 (1987).

5. L. C. Bradley, K. L. Soohoo, and C. Freed, "Absolute Frequen­cies of Lasing Transitions in Nine Isotopic Spacies," IEEE J. Quantum Electron. QE-22, 234 (1986).

6. H. W. Mocker, "Pressure and Current Dependent Shifts in the Frequency of Oscillation of a CO2 Laser," Appl. Phys. Lett. 12, 20 (1968).

7. C. J. Walsh, "Frequency Shifts in a Line Center Stabilized CO2 Laser," IEEE J. Quantum Electron. QE-22, 1928 (1986).

8. C. Freed and A. Javan, "Standing-Wave Saturation Resonances in the CO2 10.6μ Transitions Observed in a Low-Pressure Room-Temperature Absorber Gas," Appl. Phys. Lett. 17, 53 (1970).

9. H. Matsumoto, T. Kurosawa, and S. Iwasaki, "Verification of the Accuracy of a CO2 Laser Interferometer for Distance Mea­surement," Metrologia, 25 (1988), to be published.

10. S. Iwasaki and T. Sakurai, "A Wavelength Calibration of Com­mercial Wavelength Stabilized He-Ne Laser," Oyo Buturi 49, 870 (1980) (in Japanese).

11. J.-P. Morchalin et al., "Accurate Laser Wavelength Measure­ment with a Precision Two-Beam Scanning Michelson Interfer­ometer," Appl. Opt. 20, 736 (1981).

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