Sun et al. Vol. 16, No. 9 /September 1999 /J. Opt. Soc. Am. B 1447

Infrared–microwave double-resonancespectroscopy of CH3OH by

use of sidebands of CO2 laser lines

Zhen-Dong Sun, Fusakazu Matsushima, Shozo Tsunekawa, and Kojiro Takagi

Department of Physics, Toyama University, Toyama 930-8555, Japan

Received February 2, 1999

An infrared–microwave double-resonance technique using microwave sidebands of CO2 laser lines as an in-frared source has been applied for observation of rotational lines of the methanol molecule. Frequencies ofmore than 50 rotational lines in the excited C—O stretching vibrational state (vco 5 1) have been measuredwith good precision and have been compared with those reported in infrared studies. Many of them agreewithin several megahertz, although some lines show differences of .10 MHz. The pressure dependence ofthe double-resonance signals for two low-J microwave transitions belonging to the ground and the vco 5 1states, respectively, have been observed for sample pressures as high as 0.4 Torr. For the former transitionthe signal has been observed to change its sign at higher pressures. Rate equation analysis explains the ob-served pressure dependence quantitatively and allows us to understand the physical processes involved in thedouble resonance. © 1999 Optical Society of America [S0740-3224(99)01109-1]

OCIS codes: 300.6390, 300.6370, 300.6360, 300.6320, 300.6190.

1. INTRODUCTIONMicrowave sidebands of CO2 laser lines are promising in-frared sources in the 9–11-mm wavelength region becauseof their tunability, high power, high spectral purity, andhigh accuracy of synthesized frequencies. The high out-put power (several milliwatts or more) of the sidebandsenables us to observe the infrared–microwave double-resonance signals of molecules. Previously the sidebandswere used in radio-frequency–infrared double-resonancespectroscopy1 or in microwave–radio-frequency multipleresonance with a molecular-beam electric-resonancespectrometer.2,3 However, the sidebands have not beenused in a more conventional infrared–microwave double-resonance spectroscopy for observing many rotationallines of molecules in vibrationally excited states.

In Section 3 of the present paper it is reported thatmany rotational transitions of methanol in the first ex-cited C—O stretching vibrational state (vco 5 1) havebeen observed with a large signal-to-noise ratio and withthe frequency precision of a microwave spectrometer bythe double-resonance technique with microwave side-bands. Although rotational lines of the CH3OH moleculein the vco 5 1 state were previously observed directly bymicrowave spectroscopy,4–6 the intensities of the lineswere generally weak and their identifications were noteasy. The double-resonance method allows us to observerotational lines with good signal-to-noise ratios and to es-tablish definite identifications for observed transitions.The torsion–rotation energy levels of CH3OH given byMoruzzi et al.7 in the ground and the vco 5 1 vibrationalstates are widely used as basic data for this fundamentalmolecule, which has a large-amplitude torsional motion,and as practical data for the far-infrared lasers pumpedby CO2 lasers. The precision of the data in the vco 5 1state is based mainly on Doppler-limited Fourier trans-

0740-3224/99/091447-08$15.00 ©

form spectroscopy. The data obtained here are useful fortesting the accuracy of the term values listed in Ref. 7 andare helpful in refining those values.

In Section 4 of this paper the pressure dependence ofdouble-resonance signals of CH3OH has been studied tohelp us understand the physical processes involved in thedouble resonance. The observed dependence has beenanalyzed by a rate-equation approach developed by Shi-moda and Takami.8–11 Previous studies8,9 of the pres-sure dependence of the double-resonance signals of mol-ecules relied on an accidental coincidence of laser linestunable over small frequency ranges with infrared transi-tions. In the present study, because of the wide tunabil-ity of the microwave sidebands, we have selected twolow-J double-resonance schemes in which only the J5 1, 2 levels are involved, and we have observed thepressure dependence of these double-resonance signals.We have analyzed the pressure dependence quantita-tively by the rate-equation approach because the numberof M components involved in the double resonance issmall.

2. EXPERIMENTThe experimental setup for double-resonance spectros-copy is shown in Fig. 1. The microwave sidebands of theCO2 laser lines generated in a waveguide-type microwavemodulator developed by Cheo and co-workers12,13 wereused as an infrared source. The infrared beam of 10–15W from a CO2 laser (Edinburgh PL3) stabilized at thegain maximum was focused by lens L1 on a Ge prism ofthe modulator as the input beam. A microwave power of;20 W in the 8–18 GHz frequency range produced by asynthesized sweeper (Wiltron 68147A) and a TWT ampli-fier (Hughes 8020H15F) was fed to the modulator. The

1999 Optical Society of America

1448 J. Opt. Soc. Am. B/Vol. 16, No. 9 /September 1999 Sun et al.

output beam from the modulator with a beam transmis-sion of ;20% was collimated by lens L2. It consisted of acarrier and two sidebands of a CO2 laser line with a typi-cal sideband-to-carrier ratio of 0.8%. The double-resonance cell was a 1.2-m section of a WR-28 waveguide(cross section of 7.11 mm 3 3.56 mm) with two bent arms,which were used to introduce and monitor the microwaveradiation. The microwave power from an OKI klystron,which was frequency modulated to a few megahertz indepth by adding a 100-kHz square wave to the klystronreflector voltage, was introduced to the double-resonancecell through an attenuator. The laser beam and the mi-crowave were polarized in the same direction. For selec-tion of a desired sideband, the laser beam passingthrough the cell was filtered by a Fabry–Perot interfer-ometer (Burleigh RC150) with a free spectral range of50 GHz and a finesse of 70 and was detected by a HgCdTedetector. The 100-kHz component of the detector outputwas processed by a phase-sensitive detector to yield adouble-resonance signal. The pressure of methanol wasmeasured with a Pirani gauge calibrated by an oilmanometer.

3. OBSERVATION OF ROTATIONALTRANSITIONS OF CH3OH IN THE vco 5 1VIBRATIONAL STATEMicrowave sidebands of CO2 laser lines were tuned to theinfrared transitions of CH3OH, the frequencies of whichhave been given by Moruzzi et al.7 Microwave transi-tions in the vco 5 1 state were searched for frequenciesnear those predicted from the term values given in Ref. 7.In most cases the lines sought were observed near thepredicted frequencies. A recorder tracing of the double-resonance signal of CH3OH at the sample pressure of 10mTorr for the vt 5 0, E, 11 ← 20 transition in the vco5 1 state is shown in Fig. 2, and the relevant energy lev-els involved in this double resonance are shown in Fig. 3.The observed peak-to-peak signal width of 2 MHz camefrom the modulation depth of the microwave frequency.The pressure broadening and the microwave power

Fig. 1. Experimental setup for CO2 laser sideband microwavedouble-resonance spectroscopy. B.S., beam splitter; L1–L3,ZnSe lenses; M1–M3, mirrors; TWTA, traveling-wave tube am-plifier; F.P., Fabry–Perot interferometer; PSD, phase-sensitivedetector.

broadening were estimated to be 0.4 MHz and severaltenths of a megahertz, respectively. For some lines mi-crowave powers were attenuated to remove line distor-tions caused by the saturation of microwave absorption.Figure 4 shows the dependence of the intensity of thedouble-resonance signal shown in Fig. 2 on the infraredfrequency around the line center. The full width in thisfigure corresponds to a Doppler width of 68 MHz for theinfrared transition. It is noted that this transition was

Fig. 2. Recorder tracing of the microwave transition vco 5 1,vt 5 0, E, 11 ← 20 of CH3OH at 64,199.93 MHz with the infraredtransition 20 , vco 5 1 ← 10 , vco 5 0.

Sun et al. Vol. 16, No. 9 /September 1999 /J. Opt. Soc. Am. B 1449

easily observed at an infrared frequency tuned 70 MHzfrom the line center.

The 52 lines observed in the 40–100-GHz frequencyrange are listed in Tables 1 (A symmetry species) and 2 (Esymmetry species). They include 31 lines for the tor-sional ground state (vt 5 0), 13 lines for vt 5 1, and 8lines for vt 5 2. The lines with asterisks were observedwith a waveguide CO2 laser, tunable by 6120 MHz fromthe line centers, used as an infrared power source. Allthe lines were observed with large signal-to-noise ratios,and their frequencies were measured with a precision of10 kHz, except for asterisked lines measured with a pre-cision of 50 kHz.

Deviations of predicted frequencies from observed fre-quencies given in Tables 1 and 2 are shown in a histo-gram in Fig. 5. These deviations reflect the accuracies ofinfrared transitions in the fundamental band of the C—O

Fig. 3. Energy levels relevant to the signal shown in Fig. 2.

Fig. 4. Dependence of the double-resonance signal (scheme 1)on infrared frequency shift from its line center.

stretching vibration given in Ref. 7. Most of the devia-tions are less than several megahertz, but some of themare tens of megahertz.

4. PRESSURE DEPENDENCE OF THEDOUBLE-RESONANCE SIGNALS OF CH3OHTwo low-J double-resonance schemes were selected forstudy of pressure dependence because the theoreticalanalysis is simple for low-J transitions. In the firstscheme (scheme 1) for E, vt 5 0 (see Fig. 3), infrared andmicrowave transitions are vco 5 1, 20 ← vco 5 0, 10 and11 ← 20 for vco 5 1, respectively. In the second scheme(scheme 2) also for E, vt 5 0 (see Fig. 6), the lowest levelis shared by the infrared transition vco 5 1, 121 ← vco5 0, 221 and the microwave transition 10 ↔ 221 in theground state.

A. Measurement of Absorption Coefficients andDetermination of Transition MomentsThe absorption coefficients of the two infrared transitionsinvolved in the two double-resonance schemes were mea-sured to determine their transition moments. Observedvalues of 2ln(I/I0) for each infrared transition at variouspressures are shown in Figs. 7 and 8, respectively, whereI and I0 are detected infrared powers with and without asample in the double-resonance cell. The absorption co-efficients ag(n0) (inverse centimeters times inverse torrs)at the line center n0 listed in Table 3 were determinedfrom the least-squares fit to the equation 2ln(I/I0)5 ag pl, where p is the sample pressure in torr and l isthe cell length in centimeters (l 5 120 cm).

The absolute line intensity Sif for a transition betweenthe initial state i and the final state f is given by14

Sif 58p3

3hcn ifL

T0

Te

ZrZium~1, 0 !u2@1 2 exp~2hn if /kT !#

3 exp@2hc~E 2 W0!/kT#A~J8, K8, J9, K9!. (1)

In Eq. (1) the product of the partition functions is as-sumed to be ZrZi 5 34,700 for T 5 297 K with e 5 4(Ref. 15); m(1, 0) is the transition moment of the vibra-tional transition for vco 5 1 ← 0, which is defined by^0u(]m/]q)qu1&, where m is the dipole moment operatorand q is the nondimensional normal coordinate of this vi-bration; and A(J8, K8, J9, K9) is the Honl–Londonfactor.15 The absorption coefficient ag(n0) at line centeris related to Sif (inverse square centimeters times inverseatmospheres) by the relation

ag~n0! 5 Siff ~n0 , T !/760, (2)

where f (n0 , T) is a normalized Doppler-broadened line-shape function at n0 and T.16,17

From the observed values of ag(n0), Sif and um(1, 0)u foreach infrared transition have been determined from Eqs.(1) and (2), which are shown in Table 3. From calculated

1450 J. Opt. Soc. Am. B/Vol. 16, No. 9 /September 1999 Sun et al.

Table 1. Observed A Symmetry Transitions of CH3OH

CO2Laser Line

Microwave Frequencyof Laser Sidebanda

(MHz)

InfraredTransition

(vco 5 1 ← 0) vt

RotationalTransition(vco 5 1)

nobs(MHz)

Obs. 2 Calc.b

(MHz)

9P(10) 215 980 1441 ← 1341 0 1531 ← 1441 74 875.79 7.87215 980 1442 ← 1342 0 1532 ← 1442 75 239.09 20.48

16 961 1512 ← 1412 0 1512 ← 1511 102 649.89 21.759P(12) 213 910 1312 ← 1212 0 1312 ← 1311 781 23.60 2.18

28741 1322 ← 1222 1 1322 ← 1212 88 971.30 20.5128789 1321 ← 1221 1 1321 ← 1211 95 168.53 25.08

9P(14) 216 014 1211 ← 1111 0 1212 ← 1211 67 066.53 0.269P(16) 15 987 1141 ← 1041 0 1141 ← 1231 68 646.78 223.39

15 987 1142 ← 1042 0 1142 ← 1232 68 548.76 5.44213 274 1111 ← 1011 1 1221 ← 1111 47 426.43 216.03

9P(20) 216 593 812 ← 712 0 722 ← 812 70 840.60 20.969P(28) 216 400 201 ← 101 2 201 ← 101 95 145.72 23.019P(34) 121* 211 ← 212 1 211 ← 111 95 285.69 0.17

214 938 1222 ← 1221 1 1222 ← 1112 42 152.81 10.0017 213 001 ← 101 2 101 ← 001 47 573.32 17.54

a A waveguide CO2 laser was used for lines with asterisks.b Calc. refers to the predicted frequency.

values of Sif given by Dang-Nhu et al.14 we obtain a valuefor um(1, 0)u of 0.195 6 0.004 D, which agrees well with theaverage value for um(1, 0)u of 0.192 D in Table 3. In thefollowing analysis we use this average value.

B. Observed Pressure Dependence of the Double-Resonance SignalsThe observed pressure dependence of the double-resonance signals for schemes 1 and 2 at various sidebandpowers and constant microwave powers are shown inFigs. 9 and 10 by small and large filled circles, respec-tively. For scheme 1 the signal intensities increase lin-early with pressure at low pressures, reach a maximumat 10–20 mTorr, and then decrease slowly as pressure in-creases. The signals were observed with good signal-to-noise ratios for pressures as high as ;250 mTorr for aninfrared power of several milliwatts. For scheme 2 thesignal intensities also reach a maximum at 10–20 mTorr;they then decrease with increasing pressures until theybecome zero at crossover pressures pc , and the signalschange their signs at higher pressures. The inversion ofthe double-resonance signal with increasing sample pres-sure was first observed by Shimoda and Takami,8,9 whoused a 3.5-mm He–Xe laser for the H2CO molecule.

C. Calculation of the Pressure Dependence of theDouble-Resonance SignalsThe theory of infrared–microwave double resonance forthe case in which the two radiations are strong was pre-sented by Takami and Shimoda.8–11

For energy level scheme 2 (Fig. 6), where microwaveand infrared transitions are between levels 2 ↔ 1 and 3— 1, respectively, the change in the infrared absorptionat peak frequency v31 that is due to microwave pumpingat the resonant frequency v21 is given as9

DP

5Ap\vuxu2

ku

N10@1 2 exp~2apl !#

apl

3 5 1 2d

2

h

h 1 1

S 1 13h 1 4

4h 1 4j D 1/2

1 F1 13h 1 4

4h 1 4j exp~2apl !G1/2

21

~1 1 j!1/2 1 @1 1 j exp~2apl !#1/26 . (3)

In Eq. (3), d 5 (N10 2 N2

0)/N10 (Ni

0 is the unperturbedpopulation of level i) and N3

0 is neglected because N30

! N10; uxu/2p 5 m13E/h and uxmu/2p 5 m12Em /h are the

infrared and microwave Rabi frequencies, respectively; j5 ttcuxu2 and h 5 tc

2uxmu2 are the infrared and micro-wave saturation parameters, respectively, where tc is thelifetime of level i (tc 5 t1 5 t2 5 t3 is assumed) and1/2pt is the homogeneous width; and tc and t are given interms of the gas pressure p and the transit time throughthe laser beam ts as

tc21 5 C1p, (4)

t 21 5 tc21 1 ts

21, (5)where18 C1/2p 5 20 MH z / Torr and 1/2pts 5 23 kHz,corresponding to a laser beam diameter of 3.0 mm. Ithas been shown that Eq. (3) is also applicable to scheme 1for uxu 5 m12E/\, uxmu 5 m23Em /\, and d 5 0.19

As is mentioned in Section 2, the infrared and the mi-crowave radiations are polarized in the same direction,which is defined as the space-fixed Z axis. If we neglectthe collision-induced transitions between levels with dif-

Sun et al. Vol. 16, No. 9 /September 1999 /J. Opt. Soc. Am. B 1451

ferent M, the infrared and the microwave transitions oc-cur always within the same M components. In eitherscheme 1 or 2 the transitions occur between the same Mcomponents (M 5 0, 1, 21) of the J 5 1 and J 5 2 lev-els. Therefore we treat these three sets of components asindependent in the double-resonance process and take thesum of the signal intensities for all the M components asthe observed signal intensity.

The transition moment for the infrared transition is

m 5 m~1, 0 !@~J 1 1 !2 2 K2#1/2@~J 1 1 !2 2 M2#1/2

~J 1 1 !@~2J 1 1 !~2J 1 3 !#1/2 ,

(6)

where J 5 1, K 5 0 and J 5 1, K 5 21 for schemes 1and 2, respectively. The transition moment for the mi-crowave transition is

mm 5 mbIsK8sK

@~J 2 K !~J 2 K 2 1 !#1/2~J2 2 M2!1/2

2J~4J2 2 1 !1/2 ,

(7)

where J 5 2, K 5 0 and J 5 2, K 5 21 for schemes 1and 2, respectively; mb 5 1.412 D (Ref. 20) is the b com-ponent of the dipole moment of CH3OH; and IsK8

sK , theoverlap integral of the torsional wave functions, has beengiven as 0.97002 for the ground state7 (scheme 2) and cal-culated to be 0.93469 for vco 5 1 (scheme 1) by assumingappropriate molecular constants for vco 5 1.

The dashed curves in Figs. 9 and 10 show the least-squares fit of Eq. (3) to the observed pressure dependencefor schemes 1 and 2, respectively, with x and xm taken asthe fitting parameters. The x and xm values depend onM, and those for M 5 61 are shown in Table 4. The la-

Table 2. Observed E Symmetry Transitions of CH3OH

CO2Laser Line

Microwave Frequencyof Laser Sidebanda

(MHz)

InfraredTransition

(vco 5 1 ← 0) vt

RotationalTransition(vco 5 1)

nobs(MHz)

Obs. 2 Calc.b

(MHz)

9P(6) 212 766 175 ← 165 0 166 ← 175 93 334.28 25.8014 735 184 ← 174 0 184 ← 193 69 671.70 0.53

210 016 1822 ← 1722 1 1822 ← 1721 101 151.35 20.72210 016 1822 ← 1722 1 1923 ← 1822 75 184.45 3.40

9P(8) 29417 161 ← 151 0 162 ← 161 49 908.35 1.608503 1623 ← 1523 1 1522 ← 1623 65 439.36 25.63

214 387 142 ← 132 2 133 ← 142 52 228.78 4.938983 153 ← 143 2 162 ← 153 43 291.24 3.31

9P(10) 217 749 1427 ← 1327 1 1526 ← 1427 74 636.39 21.449P(12) 27704 132 ← 122 0 132 ← 131 48 996.95 20.53

215 155 1324 ← 1224 0 1225 ← 1324 92 943.03 3.7711 226 141 ← 131 0 142 ← 141 49 335.91 20.93

216 081 1422 ← 1322 1 1321 ← 1422 68 086.48 20.8828341 123 ← 113 2 123 ← 132 99 980.74 29.04

9P(14) 211 117 1226 ← 1126 1 1127 ← 1226 69 884.78 1.369P(16) 29173 111 ← 101 0 112 ← 111 48 392.32 11.81

11 881 113 ← 103 0 122 ← 113 46 350.71 227.189P(26) 211 831 20 ← 10 2 20 ← 10 95 109.71 1.459P(30) 216 528 20 ← 10 0 11 ← 20 64 199.93 2.679P(34) 121* 21 ← 21 0 21 ← 11 95 708.44 22.10

121* 21 ← 21 0 22 ← 21 47 879.89 26.26217 322 122 ← 122 0 122 ← 121 48 674.30 227.28217 360 81 ← 81 0 82 ← 81 47 882.63 21.72216 449 21 ← 31 2 21 ← 11 95 087.98 9.40212 547 121 ← 221 2 221 ← 121 95 138.91 219.71

9P(36) 27577 1325 ← 1325 0 1325 ← 1424 46 077.90 1.0027786 182 ← 182 0 182 ← 181 49 994.07 0.68

212 408 164 ← 164 0 155 ← 164 81 034.04 22.86213 678 1623 ← 1623 0 1722 ← 1623 78 050.80 13.92216 582 196 ← 196 0 205 ← 196 50 844.77 21.83218 242 192 ← 192 0 192 ← 191 49 713.69 0.31

10 406 1323 ← 1323 0 1323 ← 1224 78 007.35 6.4510 406 1323 ← 1323 0 1323 ← 1422 72 275.16 23.30

9P(38) 16 000 2026 ← 2026 1 1925 ← 2026 70 562.80 28.649P(40) 8556 193 ← 193 1 193 ← 204 68 955.42 25.549P(42) 133* 41 ← 51 0 42 ← 41 47 820.38 22.81

133* 41 ← 51 0 50 ← 41 79 089.58 22.87

a A waveguide CO2 laser was used for lines with asterisks.b Calc. refers to the predicted frequency.

1452 J. Opt. Soc. Am. B/Vol. 16, No. 9 /September 1999 Sun et al.

ser powers shown in this table are obtained by assuminga laser beam diameter of 3.0 mm. They are close to thelaser power input to the cell as measured by a powerme-ter. Microwave powers are obtained from the xm valuesby assuming a TE10 mode for the microwave radiation inthe double-resonance cell. The microwave powers thusdetermined are reasonable for our experimental condi-tions.

In the least-squares fit for the double-resonance signalsfor scheme 1, the value of x is sensitive to the optimumpressure popt , giving the maximum signal intensity. Thederivative of Eq. (3) with respect to p has a complicatedform, and it is not easy to determine the value of popt ana-lytically. However, it is shown numerically that thedouble-resonance signal becomes maximum at the infra-red saturation parameter j ' 1.0 for apl ! 1. Therefore

Fig. 5. Histogram of the deviations between observed and pre-dicted frequencies appearing in Tables 1 and 2.

Fig. 6. Energy level scheme of CH3OH including the microwavetransition 10 ↔ 221 in the ground state for E species and vt5 0.

popt is the pressure corresponding to j ' 1.0. At thispressure the infrared Rabi frequency approximates thecollisional relaxation rate. The observed pressure depen-dence is characteristically understood to imply that for p, popt the infrared transition is saturated and the signalincreases with pressure (number of molecules) and thatfor p . popt the signal decreases with the decrease insaturation.

In the least-squares fit for scheme 2, the value of x isalso sensitive to the optimum pressure, giving the maxi-

Fig. 7. Observed dependence of 2ln(I/I0) for the vco 5 1, 20— vco 5 0, 10 transition for E, vt 5 0 of CH3OH on sample pres-sure. Deviations from the straight line arise from experimentaluncertainties.

Fig. 8. Observed dependence of 2ln(I/I0) for the vco 5 1, 121— vco 5 0, 221 transition for E, vt 5 0 of CH3OH on samplepressure. Deviations from the straight line arise from experi-mental uncertainties.

Table 3. Observed Values of ag , Sif , and m(1, 0)for vco 5 1 — 0 in vt 5 0 of CH3OH

Transition(vco 5 1 ← 0,vt 5 0)

ag

(cm21 Torr21)Sif

(cm22 atm21)um(1, 0)u(debye)

E, 20 ← 10 0.042 6 0.004 0.078 6 0.007 0.184 6 0.018E, 121 ← 221 0.038 6 0.004 0.070 6 0.007 0.201 6 0.02Average 0.192 6 0.019

Sun et al. Vol. 16, No. 9 /September 1999 /J. Opt. Soc. Am. B 1453

mum signal intensity at lower pressure, popt , where j' 1.0. The signal intensity vanishes at the crossoverpressure pc , where j ' 4d (Ref. 9; in our case d ' 0.01).This relation can be easily shown analytically from Eq. (3)for apl ! 1. The inversion of the double-resonance sig-nal at pressures higher than pc has already beenexplained8,9: the saturation effect of the infrared transi-tion decreases and the population difference at the ther-mal equilibrium between levels 1 and 2 contributes di-rectly to the double-resonance effect. We refer to thepressure regions as saturation or population regions ac-

Fig. 9. Observed pressure dependence (filled circles) and calcu-lated pressure dependence (dashed curves) of the double-resonance signal corresponding to the microwave transition 11— 20 in the vco 5 1 state of CH3OH (scheme 1) for the input in-frared powers of (a) 8.2 and (b) 5.9 mW.

Fig. 10. Observed pressure dependence (filled circles) and cal-culated pressure dependence (dashed curves) of the double-resonance signal corresponding to the microwave transition10 ↔ 221 in the ground state of CH3OH (scheme 2) for the inputinfrared powers of (a) 11.3 and (b) 7.8 mW.

Table 4. Rabi Frequencies for zMz 5 1 Determinedfrom the Pressure Dependence of the

Double-Resonance Signal

uxu/2p(MHz)

Power of CO2Laser Sideband

P (mW)uxmu/2p(MHz)

Microwave PowerPm (mW)

Scheme 10.276 3.9 1.52 7.30.228 2.7

Scheme 20.376 9.5 2.21 5.30.316 6.7

cording to whether p , pc or p . pc , respectively. Thevalue of xm is not sensitive to the values of popt or pc butis sensitive to the pressure that gives the minimum (thelargest negative) signal, pmin . The value of pmin in-creases with both x and xm; its analytical expression isnot simple, which is discussed below.

5. DISCUSSION AND CONCLUSIONThe microwave sidebands of the CO2 laser lines were usedas an infrared source in the 10-mm region for theinfrared–microwave double resonance. It has beenshown in Section 3 that many microwave transitions ofCH3OH in the excited vibrational state of C—O stretchinghave been observed with high precision. Most of the ob-served frequencies agree within several megahertz withthe frequencies calculated from the term values for thevco 5 1 state given in Ref. 7, but some of them deviate bymore than 10 MHz. We attempted to refine the term val-ues by adding the observed rotational frequencies to theterm values in Ref. 7 by least-squares fitting. Althoughthe refinement gives differences of pairs of term valuesprecisely, the precision of the term values themselveshave not been much improved. For their determinationhigh-precision measurement of infrared transitions in-volved in the double-resonance scheme is needed. Therotational frequencies determined here are useful inthemselves, together with the microwave data,3,4 for theanalysis of the torsion–rotation spectrum of CH3OH inthe vco 5 1 state.

In Section 4 physical processes in the double resonancehave been studied quantitatively by observation of thepressure dependence of the double-resonance signals.The observed pressure dependence has been successfullyreproduced by Eq. (3) with x and xm used as fitting pa-rameters. More directly, the values of x and xm can beestimated by observation of the pressures popt , pc , andpmin . For the double resonance of either scheme 1 or 2, xcan be obtained from j ' 1 at the pressure popt . Forscheme 2, x can also be determined from j 5 4d at thepressure pc . Because j ! 1 for pressures higher than pc(population region), Eq. (3) with apl ! 1 is reduced to asimpler form by neglecting O(j2) terms:

DP 5Ap\vN1

0uxu2

4kuh

h 1 1 S j

42 d D . (8)

This equation gives pmin as

pmin 51

2C1A2d$3x2 1 4dxm

2

1 @~3x2 1 4dxm2 !2 2 14dx2xm

2 #1/2%1/2. (9)

As we already know the value of x from pc , we can esti-mate the value of xm from pmin . Equation (9) shows thatpmin depends on the microwave power as well as the laserpower.

For all the observed transitions, the optimum pressurewas 10–20 mTorr for sideband powers of several milli-watts. Rotational transitions in the vco 5 1 state havebeen observed with good signal-to-noise ratios at thesepressures. The microwave sidebands of the CO2 laser

1454 J. Opt. Soc. Am. B/Vol. 16, No. 9 /September 1999 Sun et al.

lines, which have wide tunability and high output power,have been proved to be a convenient infrared source fordouble-resonance spectroscopy.

ACKNOWLEDGMENTSZ. D. Sun acknowledges the financial support of the Japa-nese Government. We thank Suguru Ogura for his en-thusiastic help in this experiment. This work was sup-ported in part by a Grant-in-Aid for Scientific Research(B) from the Ministry of Education, Science, Sports andCulture of Japan (09490014).

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