Absolute frequency measurements of N2O laser transitions

Volume 14, number 1

OPTICS COMMUNICATIONS

ABSOLUTE FREQUENCY B.C. WHITFORD,

MEASUREMENTS

May 1975

OF N,O LASER TRANSITIONS

K.J. SIEMSEN, H.D. RICCIUS and G.R. HANES

Division of Physics, National Research Council of Gmaak, Ottawa, Ontario, Canada

Received 11 February 1975

The absolute frequencies of 33 P- and R-branch lines of the N20,OO” 1 -lo”0 laser band have been measured by heterodyning with known CO2 laser frequencies of the OO”1-lo”0 band in a tungsten-nickel diode. These measurements were used to calculate more precise values for the band centre and for the rotational constants.

The N, 0 laser transitions have been used as wavelength standards for Stark laser spectroscopy [l] and in infrared-microwave two-photon absorption experiments [2]. For such high-resolution infrared spectroscopy applications the absolute frequencies of these laser lines need to be known to higher precision. Measurements of the frequencies of 27 P- and R-branch lines of the OO”l-lo”0 band from an NaO laser relative to the known frequencies of the 00 1-10’0 band CO, laser transitions have been reported previously [3]. In those measurements the two lasers were operated pulsed by the use of a rotating Q-switch mirror: consequently, accuracy was limited to a few parts in 106. We have redetermined the absolute frequencies and the rotational constants for N,O by using cw NT0 and CO, lasers, with their lines centred by means of saturated molecular absorption in N,O and CO, [4], respectively. This increases the accuracy by a factor of 50 over the previous measurements of N,O laser frequencies [3]. Furthermore, the uncertainties in the rotational constants obtained by Sokoloff and Javan [3] are reduced 13 to 260 times and estimates of the rotational constants Hool andHloo are obtained. The experimental set-up used was similar to that reported previously [5]. The mixing element was a tungsten-nickel point contact diode. The N,O and CO, lasers had discharge tubes 1.4 m and 0.4 m long, and resonant cavities 1.95 m and 0.95 m long, respectively. The use of two identical gratings blazed at 8 m at one end of each cavity provided single line operation of the N,O laser on P-branch lines fromJ = 3 to 35 and on 70

‘OJ Sfi

u

0.04

Torr

1

=-

r” P 5Y 2 4% z a 30

3 k

2I-

-

INCREASING

FREQUENCY

Fig. 1. Typical recorder tracings of the 4.3 nm and the 4.5 pm fluorescence signals for CO2 and NsO, respectively.

R-branch lines from J = 1 to 40, and on CO, laser lines from P(4) to P(38). Typical power output for each of the two lasers was 200 mW. The N,O laser was operated with a flowing 15% N, - 16% N,O 69% He gas mixture giving a total pressure of 12 torr in the discharge tube, whereas the CO, laser had a commercial sealed-off discharge tube.

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OPTICS COMMUNICATIONS

The technique of observing the standing-wave saturation resonances in the 4.3 pm fluorescence of CO, [4] has been successfully applied to N20. As shown in fig. 1, the intensity of the spontaneous emission at 4.5 pm from the (OO”l-OO”0) band of N20 is comparable to that observed in CO,. The recorder tracings in fig. 1 were obtained by using the same laser and absorption cell under identical experimental conditions. Only the gas mixture in the laser discharge tube and the absorber gas in the cell were changed. The fluorescence signal was observed with a liquid-nitrogen cooled InSb detector. Laser frequency tuning was achieved by means of a piezoelectric tuner causing a small displacement of one of the laser mirrors. The pressure in both absorption cells was kept at 0.04 torr. The radiant energy of approximately 50 mW from each laser, with parallel polarization of the electric field vectors, was focussed with a 3 cm focal length Irtran-2 lens onto the diode junction. The output of the diode was fed into a spectrum analyzer which had been specially calibrated against the NRC 133Cs standard to permit determination of beat frequencies ranging from 0.6 to 35 GHz to within + 5 kHz. Difference frequency signals from the tungsten-nickel diode up to 4 GHz were observed directly on a Tektronix lL20 spectrum analyzer. Those signals above 4 GHz were first downconverted to a frequency below 4 GHz by injecting one of the microwave frequencies 8.255, 10.205, or 11.735 GHz into the tungsten-nickel diode, together with the N,O and CO, laser frequencies. The microwave frequencies were phase-locked to 5 MHz signal from the NRC 133Cs standard. The fundamental microwave frequency, or its second or third harmonic was used, as required, to obtain a diode output below 4 GHz. The frequencies displayed on the spectrum analyzer were measured by comparison with a known marker frequency displayed simultaneously on the CRT, with the dispersion set at 100 kHz/cm. The spectrum of the beat signal was about 150 kHz wide: the centre was visually estimated, as was the displacement of the centre from the reference marker, for each reading. The following procedure was used to obtain each reading: the N,O and CO, laser frequencies were frequency-modulated with a deviation of about 300 kHz and a modulation frequency of 520 Hz by applying a 520 Hz signal to the piezoelectric laser mirror mounts. The laser frequencies were then adjusted to coincide

May 1975

with their respective transition centres by adjusting for a minimum in the 520 Hz amplitude modulation of the fluorescence from the absorption cells. The dither was then turned off, and the position of the beat relative to the marker determined within 2 to 3 seconds. The values of the measured beat frequencies given in table 1 are the result of at least twenty independent readings for each line. The error in marker frequency is negligible. The error in each reading, relative to the marker, is f 20 kHz. The typical standard deviation (I of the individual readings in a set of 20 readings was 62 kHz, the standard deviation of the mean then being 621420 = 14 kHz. Observed NZO absolute frequencies were deduced from the measured beat frequencies and the CO2 transition frequencies derived by the use of the absolute value for R(30) given by Evenson et al. [6] and rotational constants recently determined by Petersen et al. [7]. The rotational constants and the OO’l-10’0 band centre were derived by fitting the observed N,O frequencies to the usual term value expression [8]. Calculated values of N,O frequencies were then obtained from the best tit, and are given in columns 4 and 8 of table 1. The residuals (observed-calculated) are given in columns 5 and 9, and the standard error of the fit is at the bottom. The constants are given in table 2, along with their estimated uncertainties. Fitting was carried out with various numbers of constants, and F tests of the ratio of variances were used to find the highest order terms that were statistically significant. The inclusion of terms up to and includingJ6 (i.e. H coefficients) was significant at the 1% level. The actual values of Hool and HIOOare poorly determined because of the limited range of J that we were able to measure in the P-branch; the errors in the H-values are highly correlated so that only Hool -Hloo = 39.5 * 10.0 X 1O-4 Hz is reasonably well determined. The confidence intervals of our calculated frequencies are given in fig. 2, curve d. They were derived by summing the errors contributed by each of the steps used to obtain the fitted frequencies. The lowest curve (a) in fig. 2 gives the one standard deviation confidence interval of the frequency differences between adjacent CO, lines calculated from the theoretical 71

Volume 14, number 1

OPTICS COMMUNICATIONS

May 1975

Table 1 Measured and calculated absolute frequencies (MHz) of the 00” 1- 10’0 band of Ns 0 P-BRANCH

J

CO2 LINE

OBSERVED N20 - CO2 FREQUENCY

R

CALCULATED N20 FREQUENCY

LINE CALC

-

B

OBSERVED N20 - CO2 FREQUENCY

A

R

N

C

28146116.983

1

28121099.023

28195847.787

2

28095979.523

28220560.376

3 4

28070758.605

28245170.917

28045436.390

28269679.277

5

28020012.994

28294085.322

6

27994488.534

7

~(32)

8

~(32)

9

P(34)

10

P(34)

11

P(36)

12

P(36)

13

PC381

14

p(38)

15

p(38)

-586.570 -26312.918 6589.136 -19338.506 141!2.123 -12016.434 21986.332 -4342.677 -30771.885

-0.039

27917309.890

0.028

27891382.284

-0.008

27865354.160

0.010

27839225.620

-0.007

27812996.763

-0.041

27786667.689

0.024

27760238.493

0.012

17

27707080.105

18

27680351.092

19

27653522.316

20

27626593.860

21

27599565.805

22

27572438.229

23

27545211.208

p(18) P(l’3) P(l6) P(l6) P(l6)

-17183.911 6914.430 -21906.156 1986.287 25775.47U

Li62;;678 P(14) 20959.745 P(14) -6914.319 P(12) -34161.870 P(lD) P(lO) -10890.756 12276.202 P(lO) 35338.964 P(lO) 8404.593 P( '3) P( 6) -17904.519 4844.353 P( 6) P( 4) -20944.776 1593.953 P( 4)

28342589.920 28390683.589 28414575.967

28485633.496

-0.047

28509112.296 28532487.316

0.028 -0.006

28555758.397

0.027

28570925.376

0.006

28601988.089 28624946.370 28670548.954

0.022 -0.011 0.023

28693192.910 28715731.741

26

27462934.184

28760493.298 28782715.656

27

27435310.080

28804832.148

28

27407586.865

28826842.582

29

27379764.597

28848746.762

30

27351843.330

28870544.489

31

27323823.117

32

27295704.005

33

27267486.038

27182239.406

0.055 -0.024

28647800.049

28738165.265

36

0.007 -0.045

27490459.117

27210753.703

0.031

28462051.071

27517884.814

27239169.259

0.034 -0.034

28438365.178

24

34

-0.035

28366688.192

25

35

CALC

28318388.916 0.058

27943136.871

27733709.268

OBS

28171033.280

27968863.122

16

H

CALCULATED N20 FREQUENCY

0

-0.079

28892235.561

R( R( R( R( R(

-9226.609 4) 12250.444 4) 61 -10790.219 10472.087 6) '3) -12049.282

o.ou2

28913819.772 28935296.913

-0.046

28956666.769

0.071

28977929.125 28999083.760

0.021 -0.042

29020130.449

37

27153626.397

38

27124914.702

39

27096104.342

40

27067195.336

41

27038187.698

42

27009081.436

29123736.557

43

26979876.555

29144130.620

44

26950573.056

29164415.045

45

26921170.934

29184589.572

46

26891670.180

29204653.935

47

26862070.779

29224607.866

48

26832372.712

29244451.087

49

26802575.954

29264183.319

50

26772680.477

29283804.274

STANDARD

R(10)

-13003.707

29041068.964

0.025

29061899.071

R(12)

-13653.847

29082620.534

0.008

29103233.112

ERROR

OF FIT = 0.039

edpression after least-squares fitting to those observed in [7]. Intervals that were measured are shown by filled circles; the standard error of the tit is indicated at the sides. The confidence interval for any CO, line is given by summing (quadratically) the confidence

72

co2

OBS

flHZ (26 DEGREES

OF FREEDOfl)

intervals for all the differences between that line and R(30). This results in curve b. (Readers interested in the confidence interval for the absolute CO, frequenties can add quadratically the 25 kHz uncertainty in R(30) to the values in curve b). The values in curve b

Volume 14, number 1

OPTICS COMMUNICATIONS

ing from drift of the lasers between the time of the Lamp dip settings and the reading of the beat frequency on the spectrum analyzer (* 8 kHz). The (quadratic) sums of these errors, which ranged from 19 to 24 kHz, were used to derive weights for the least squares fitting of the molecular constants. The confidence intervals for the calculated N20 frequencies relative to R(30) of CO2 were obtained from the covariance matrix of the molecular constants and are given in curve c. Here the filled circles indicate the N20 frequencies which were actually measured, and the standard error of the fit is given at the sides. Adding the measured R(30) frequency with its 25 kHz standard error results fmally in the one standard deviation confidence interval for the absolute frequencies of the N20 lines (curve d). For a 95% confidence interval these values should be multiplied by 2.06. The standard error of the fit, 39 kHz, is larger than our estimated standard error of the determination of the individual line frequencies. Either we have underestimated some of the errors listed above, or there are other unsuspected sources of variability in the experiment. The confidence intervals for the constants and for the calculated frequencies are not directly affected,

Table 2 Rotational constants of the 00” l-l O”0 band of Nz 0. Values are given in megahertz. Numbers in brackets are the one standard deviation confidence intervals

vo Boo01 Do001 Ho001 B~o~o--Boo~l 4o”o--000~1 H1o~o-Ji00~1 B too0 4 000 HI 000

May 19’75

28146116.983(.51) 12458.1588(12) 5.2536(57) X 1O-3 -2.5(133) X 1O-9 50.83163(59) -8.704(170) X lo-’ 3.95(100) x 10-9 12508.9905(11) 5.1665(46) x 1O-3 1.4(143) x 10-g

are one input to the error budget of the N,O-CO, R(30) frequency differences. Other inputs are: the standard error of setting to the fluorescence Lamb dips described earlier (+ 5 to f 17 kHz, depending on number of determinations), errors arising from the shift of the Lamb dip minima caused by variation in the laser power profile resulting from slight errors in grating setting (estimated as + 15 kHz), errors in spectrum analyzer calibration (? 5 kHz), and errors result-

A

-

B" Lb a0 AAAA~~~~AAAAAAAAAAAb

cl

a" AAAA

0

0

YAA 0

A

AA

CO, vo

0

AA AA

-

A~

.

a

. l o.. I

”

1’

27.50

”

’

lp 20.00

.,..I

l

0. ,

0.

00

I

,

oo

oo(Jou

,

,

I

29.00

29.50 FREQUENCY

o.

A

LT

A

.

,

A A

l ,

. .

..-a ..O ,

,

,

(

,

,

,

29.50

(THz)

Fig. 2. Confidence intervals in kHz as functions of the CO2 and N20 laser frequencies

73

Volume 14, number 1

OPTICS COMMUNICATIONS

since they are derived from the residuals of the fit. We have included no further uncertainty in the value of the band origin, vo for the following reasons. (1) Evenson et al. [6] have included a reasonably generous + 20 kHz in the standard error of the absolute determination of R(30) to cover uncertainty in setting to the true Lamb dip centre in CO,. We do not feel that our settings should be different from his by more than this amount. (2) We would expect the pressure shift in N20 to be similar to that in C02, so that differential errors in Lamb dip location between the two gases should be small. Our constants would, of course, be affected by a failwe of the assumption (made also by Petersen et al. for CO, [7]) that the Lamb dip location error does not vary across the band. One additional factor that might have interfered with the accurate determination of the N20 lines is the expected hyperflne structure in these lines. However, we have estimated this to be negligible. An upper limit of about 6 kHz for the hyperfine splitting in the lines, due to the nitrogen quadrupole moments, can be

74

May 1975

estimated from the ground state coupling factor [9] , the reduction in splitting with J-value [lo] , and the expected weak dependence of the coupling factor on vibrational state [ 111.

References [II F. Shimizu, J. Chem. Phys. 53 (1970) 1149. 121 T. Oka and T. Shimizu, Appl. Phys. Lett. 19 (197 1) 88. 131 D.R. Sokoloff and A. Javan, J. Chem. Phys. 56 (1972) 4028. 141 C. Freed and A. Javan, Appl. Phys. Lett. 17 (1970) 53. 151 B.G. Whitford, K.J. Siemsen and H.D. Riccius, Opt. Commun. 10 (1974) 288.

161 K.M. Evenson, J.S. Wells, F.R. Petersen, B.L. Danielson and G.W. Day, Appl. Phys. Lett. 22 (1973) 192. 171 F.R. Petersen, D.G. McDonald, J.D. Cupp and B.L. Danielson, Phys. Rev. Lett. 31 (1973) 57 3.

181 G. Herzberg, Infrared and Raman Spectra (D. Van Nostrand, Princeton, 1962).

191 M. Sancho and M.D. Harmony, J. Chem. Phys. 45 (1966) 1812.

II01 J. Bardeen and C.H. Townes, Phys. Rev. 73 (1948) 97. III1 N.F. Ramsey, Molecular Beams (Oxford Clarendon Press, 1963).