Vol. 5, No. 4/April 1988/J. Opt. Soc. Am. B 745

Intracavity absorption detection of magnetic-dipoletransitions in 1802 and the determination of the b 12g+(v = 2)

state rotational constants

W. T. Hill III

Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742

A. L. Schawlow

Department of Physics, Stanford University, Stanford, California 94305

Received October 29, 1987; accepted November 13, 1987

Intracavity absorption spectroscopy was employed to obtain the b 1g+(v = 2) X 31g-(V = 0), magnetic-dipolespectrum of the isotopic 1802 molecule. Values for the rotational constants B2and D2 (1.2067 0.0005 cm-1 and 4.7+ 0.5 X 10-6 cm-1 , respectively) were deduced subsequently from 50 of the AN = -1 transitions.

INTRODUCTION

In this paper we report experimental measurements of the Band D constants for the = 2 level of the b g+ electronicstate of 1802. The constants were determined from an anal-ysis of a pressure-broadened absorption spectrum of theb ;g+(v = 2) X 3 g-(v = 0) transitions near 635 nm.These extremely weak magnetic-dipole transitions (peak ab-sorption coefficient, 10-6 cm-1) were observed by usinglaser intracavity absorption spectroscopy'- 4 and composethe isotopic counterpart to the (2-0) band of the atmospher-ic absorption bands of 1602 studied by Babcock and Herz-berg.5 Although Babcock and Herzberg did measure the (0-0) and (1-0) bands of the 180160 and 170160 isotopic species,they did not report observations of the isotopic dimers, 1802,and 1702. The X 32g- state of the 1802 molecule has beenthe subject of several investigations in which Raman6 "7 andmicrowave8'9 techniques were employed. These studieshave provided a variety of molecular constants for theX 32g- state. To the best of our knowledge, no experimen-tal determination of the b g+ state constants of 1802 hasbeen reported.

b 11g+ - X 3 Xg- TRANSITION

The details of the atmospheric absorption bands of 02 andthe 32g- and lg+ electronic states are treated extensively inthe literature and will not be repeated here. Only the morepertinent features will be summarized in this section. (SeeRefs. 5, 8, and 10 for more details.)

To a good approximation, 1802 obeys Hund's case (b), inwhich N (-K, since A = 0), describing the rotation of themolecule, couples to the total electronic spin S to producethe total angular momentum J such that J = N + S. Thusthree J levels are possible for each N in the X 3 2g- state (S =1), and in the b 2g+ state J = N (S = 0). Because 1802 iscomposed of two identical spin zero particles, alternate Nlevels are missing from the spectrum.

The 32g- and g+ states are connected by both magnetic-dipole and electric-quadropole operators; the bulk of thetransition strength, however, has magnetic-dipole charac-ter.5 Four types of transition are observed in the spectrum.Two of these transition have AN = -1 and are designatedPP(N) and PQ(N) transitions (P branch). The other twotransitions have AN = +1 and are designated RR(N) andRQ(N) transitions (R branch) (see Fig. 1). The notationused is AIVAJ(N").

EXPERIMENTAL PROCEDURE

The intracavity absorption measurements were made withthe apparatus shown in Fig. 2. The 1802 (92% at. wt., pur-chased from Monsanto Research Corporation) was con-tained in a 1-m intracavity cell with Brewster-angle windowsand placed inside an Ar+-pumped, untuned, cw jet-streamdye-laser cavity with an overall length of -1.5 m. The threeresonator mirrors were high reflectors (-99.98%) and hadtheir back surfaces wedged at 10° to prevent spurious reflec-tions from channeling the spectrum into narrow-frequencybands (i.e., to prevent the mirrors from behaving as eta-lons).3 "11 The cell Brewster windows were 1 cm thick, whichwas large enough to prevent them from behaving as low-finesse 6talons as well." The measurements were made at02 pressures ranging from 100 to 500 Torr, depending on theabsorption strengths. To reduce the asymmetry in the ab-sorption line profiles of the strongest lines, Kr buffer gas (upto 500 Torr) was added to broaden the lines.3"' As dis-cussed in Ref. 11, this process permitted a more accuratemeasurement of the absorption center. Partial pressures inthis range will cause frequency shifts of less than 0.01 cm-1.12

The bandwidth of the laser was generally between 2.5 and5.0 nm, and the dye used for the measurements was a mix-ture of Rhodamine 590 and Rhodamine 640. These condi-tions allowed us to generate the necessary radiation between640 and 633 nm. The central wavelength was tuned by

0740-3224/88/040745-04$02.00 © 1988 Optical Society of America

W. T. Hill III and A. L. Schawlow

746 J. Opt. Soc. Am. B/Vol. 5, No. 4/April 1988

P BRANCH

zLa-

R BRANCH

A.P J' = N' = N - 1 N'

az

J' = N' = N + 1

IzOC

3 -- F;: J Nz F2: J = N"N' F.: J" = N + 1 N" F": J = N + 1

g -IL' F.: J = N - 1 F.: J = N - 1

1. Transition diagrams showing the four types of transition that are observed in b lg+ X 3yg spectrum.

DUAL-PENCHART RECORDER

Fig. 2. Schematic of the apparatus showing the broadband, untuned cw dye laser with the intracavity Brewster cell and the detection system,consisting of a scanning monochromator, a confocal interferometer, and a dual-pen chart recorder.

moving the Ar+ pump spot around in the jet stream relativeto the dye-laser spot, as discussed in Ref. 3. The broadbandoutput of the laser was directed into a 1-m Jarrell-Ash scan-ning monochromator with the entrance and exit slits set topass 1-3 GHz of the spectrum. Light leaving the monochro-mator was divided into two beams. One of the beams wasmonitored directly with a photodiode, and the other beamwas sent through an 8-GHz confocal interferometer andmonitored with a photomultiplier (PMT). The signals fromthe detectors were displayed simultaneously by a dual-penchart recorder; the signal from the photomultiplier providedfrequency markers.

Figure 3 shows a typical scan taken in 2-3 min near the (2-0) bandhead. The interference fringes at the bottom of thefigure were calibrated by measuring the separation of thePQ(3 ) and RQ( 1) lines [(a) in Fig. 3]. Both of these transi-

tions involve the same v = 2, N = J = 2 level in the b state.At the same time, the RQ( 1 ) line is coupled to the v = 0, N =1, J = 2 level in the X state, while the PQ( 3 ) line is coupled tothe v = 0, N = 3, J = 2 level in the X state. Hence thespacing between the lines is a measure of the energy separa-tion of the two ground-state levels and is equal to 12.63646 ±0.00004 cm'1 (378.8315 GHz). 8 Thus the spacing betweenfringes, the free spectral range (FSR), is 0.2669 0.0005cm-'. The error is due to the uncertainty in determiningthe position of the absorption lines relative to the fringepeaks; this uncertainty is about 10% of the FSR.

DETERMINATION OF B AND D CONSTANTS

The B and D constants for the b state were determined by aleast-squares fit to combination differences involving the

1T+9

N'

Fig.

W. T. Hill III and A. L. Schawlow

A A

Vol. 5, No. 4/April 1988/J. Opt. Soc. Am. B 747

290 Torr 1802

[a

BANDHEAD(a)

635.0 nm 633.5 nmFig. 3. Typical spectrum showing the band-head region of the b 12g+ A- X 32g- spectrum of 1802.

AN = -1 (P-branch) transitions. Specifically, we defineAap(N) as the spacing between the two nearest PP(N) lines[e.g., the spacing indicated by (b) in Fig. 3 between PP(1) andPP(3) lines] and AQ(N) as the spacing between the twonearest PQ(N) lines. The disadvantage of this approach isthat these combination differences involve different lower-state energy levels, and thus the constants that we derivedepend on the measurement of the spacing between N levelsin the X state. The reason for not using the spacing betweenthe PP(N) and RR(N) lines, which both originate from thesame lower state, is that members of the R branch with N > 9are not resolved (see Fig. 3). A reduction based on the Rbranch would not take advantage of the higher N members.

It is straightforward to show that Aop(N) and AoQ(N) aregiven by

Aorp(N) = A2F2 "(N + 1) - A2F'(N) (1)

and

AaQ(N) = A2F1,(N + 1) - A2F(N).

A2F(N) is the difference in two rotational terms:

A2 F(N) = F(N + 1) - F(N - 1).

In terms of the B and D constants, F(N) is given by

F(N) BN(N + 1) - DN2(N + 1)2.

(2)

(3)

(4)

Substituting expression (4) into Eq. (3) gives

A2 F(N) = (4B - 6D)(N + 1/2) - 8D(N + 1/2)3. (5)

Our approach was to make a least-squares fit to Eq. (5).Values for the ground-state-level spacing were taken fromRaman measurements,6 values for AAp(N) and AuQ(N) weredetermined from our spectrum, and values for A2 F'(N) wereextracted from Eqs. (1) and (2). Table 1 gives the experi-mental values used in the reduction. The values for Aorp(N)are uniformly greater than the values for AoQ(N) in Table 1because the spacing between N levels in the ground statewith different F components (i.e., F1, F2, or F3) is slightly

different.6 9 In particular, A2F1" is greater than A2F2" by anamount equal to the difference between Aup(N) and AuQ(N)values. (Compare columns 2 and 3 of Table 1 with Table 1of Ref. 9.) Unfortunately, the various components of A2F"

Table 1. Combination Differences (in InverseCentimeters)a

N" Aapa /AQa a 2Fb A2F

1 5.55 - 5.55 12.769 7.223 6.10 6.04 6.07 23.004 16.935 6.70 6.67 6.68 33.216 26.547 7.30 7.28 7.29 43.439 36.159 7.86 7.84 7.85 53.642 45.79

11 8.42 8.40 8.41 63.835 55.4213 8.96 8.94 8.95 74.029 65.0815 9.52 9.50 9.51 84.216 74.7117 10.15 10.13 10.14 94.387 84.2519 10.65 10.63 10.64 104.534 93.8921 11.28 11.26 11.27 114.670 103.4023 11.87 11.85 11.86 124.800 112.9425 12.47 12.46 12.46 134.900 122.44

a The uncertainty in these values is '-0.03 cm-'.b Values are taken from Ref. 6 with an uncertainty of -±0.004 cm-'.

Table 2. Reduction (in Inverse Centimeters)

N + 1/2 A2Fexp' A2Fcai'a A2Fep'- A2Fcal'

1.5 7.22 7.24 -0.023.5 16.93 16.89 0.045.5 26.54 26.54 0.007.5 36.15 36.18 -0.039.5 45.79 45.82 -0.03

11.5 55.42 55.45 -0.0313.5 65.08 65.07 0.0115.5 74.71 74.67 0.0417.5 84.25 84.27 -0.0219.5 93.89 93.84 0.0521.5 103.40 103.40 0.0023.5 112.94 112.94 0.0025.5 122.44 122.46 -0.02

a These were calculated using B = 1.2067 cm-1 and D 4.7 X 10-6 cm-1.

W. T. Hill III and A. L. Schawlow

-1

748 J. Opt. Soc. Am. B/Vol. 5, No. 4/April 1988

Table 3. Molecular Constants for b l2;g+ state of 1802(in Inverse Centimeters)

Constant Experimental Reductiona Isotope Ruleb

B2 1.2067 (5) 1.20632D2 4.7 (5) X 10-6 4.285 x 10-6

a Values in parentheses denote the uncertainty in the last digit.b These values are based on the b Z constants of 1602 given in Ref. 12: Be

= 1.40037 cm'1; a, = 0.01820 cm-'; De = 5.351 X 10-6 cm-'; = 0.0318 X 10-6cm-1 .

were not resolved in the Raman spectra of Ref. 6, so thevalues given in Table 1 represent the center of gravity of thethree components ( 2F1

1', A2F2", and A2F3"). To accountfor this blending of A2F" components we defined Ao-(N), theaverage of Aap(N) and AaQ(N), from which we calculatedaverage values for A2F'(N) given in the last column of Table1. These average values were the empirical values used inthe least-squares fit.

Table 2 gives the results of the reduction. Table 3 com-pares our experimental values for B2 and D2 with thosevalues derived from the isotope substitution rule' 0 based onthe 1602 constants of Ref. 13. The two sets of constants arein agreement within the accuracy of our measurements.

ACKNOWLEDGMENTS

We are thankful for helpful discussions with M. L. Ginter, U.N. Singh, and W. M. Benesch. This work was supported bythe National Science Foundation (NSF) under grants PHY-84 51284 and PHY-86 04441. W. T. Hill III is a NSF Presi-dential Young Investigator.

REFERENCES

1. T. W. Hdnsch, A. L. Schawlow, and P. E. Toschek, "Ultrasensi-tive response of a cw dye laser to selective excitation," IEEE J.Quantum Electron. QE-8, 802 (1972).

2. R. G. Bray, W. Henke, S. K. Liu, K. U. Reddy, and M. J. Berry,"Measurement of highly forbidden optical transitions by intra-cavity cw dye laser spectroscopy," Chem. Phys. Lett. 47, 213(1977).

3. W. T. Hill III, R. A. Abreu, T. W. Hansch, and A. L. Schawlow,"Sensitive intracavity absorption at reduced pressures," Opt.Commun. 32, 96 (1980).

4. S. J. Harris, "Intracavity laser spectroscopy: an old field withnew prospects for combustion diagnostics," Appl. Opt. 23, 1311(1984).

5. H. D. Babcock and L. Herzberg, "Fine structure of the redsystem of atmospheric oxygen bands," Astrophys. J. 108, 167(1948).

6. W. G. M. Edwards, F. A. M. Good, and D. A. Long, "Purerotational Raman spectra of 1602, 160180, and 1802," J. Chem.Soc. Faraday Trans. II 72, 865 (1976).

7. R. C. Herney and F. P. Molanovic, "Raman spectrum and mo-lecular parameters of 8 02 ," Can. J. Spectrosc. 21, 162 (1976).

8. W. Steinbach and W. Gordy, "Millimeter and submillimeterwave spectrum of 1802," Phys. Rev. A 8, 1753 (1973).

9. Y. Endo and M. Mizushima, "Microwave absorption lines of1802 in its electronic ground state (X 3Z-g)," Jpn. J. Appl. Phys.22, L534 (1983).

10. G. Herzberg, Molecular Spectra and Molecular Structure: I.Spectra of Diatomic Molecules (Van Nostrand Reinhold, NewYork, 1939).

11. W. T. Hill III, T. W. Hansch, and A. L. Schawlow, "Intracavityabsorption profiles: a comment on the observed asymmetry,"Appl. Opt. 24, 3718 (1985).

12. K. J. Ritter, "A high resolution spectroscopic study of absorp-tion line profiles in the A-band of molecular oxygen," Ph.D.dissertation (University of Maryland, College Park, Md., 1986).

13. K. P. Huber and G. Herzberg, Molecular Spectra and Molecu-lar Structure: IV. Constants of Diatomic Molecules (VanNostrand Reinhold, New York, 1979).

W. T. Hill III and A. L. Schawlow