- Email: [email protected]
Measurement of the strengths of 1 ← 0 and 3 ← 0 transitions of HI using frequency modulation spectroscopy
JOURNAL
OF MOLECULAR
SPECTROSCOPY
(1991)
l&381-388
Measurement of the Strengths of 1 + 0 and 3 + 0 Transitions of HI Using Frequency Modulation Spectroscopy HARIS RIRIS, C. B. CARLISLE, AND D. E. COOPER SRI International, 333 Ravenswood Ave., Menlo Park, Cal$ornia 94025 LIANG-GUO
WANG, ’ AND
T. F. GALLAGHER
Department of Physics. University of Virginia, Charlottesville. Virginia 22901 AND
R. H. TIPPING Department of Physics and Astronomy. University of Alabama, Tuscaloosa, Alabama 35487-0324 The linestrengths for five P-branch lines in the fundamental and seven R-branch lines. including three high-J transitions, in the second overtone band of HI have been measured using frequency modulation spectroscopy. From these data, we have obtained new values for the rotationless dipole-moment matrix elements and Herman-Wallis coefficients for these bands. Combining this new information with previously measured intensity data, we have deduced a refined dipole moment function for HI. 0 1991 Academic Press. Inc. I. INTRODUCTION
In recent years, there has been a significant increase in the number of successful commercial and scientific applications of semiconductor diode lasers. Although diode lasers have been in existence since the early 196Os, their application to spectroscopic problems was limited mainly by their small tuning range, multimode spectral emission, and low power. Diode lasers can be divided into two broad categories: near-IR lasers based on III-V compounds operating in the 750 nm to 1.6 pm range, and Pb-salt diode lasers operating in the 3 to 30 pm range. Pb-salt diode lasers have traditionally been used in the study of molecular spectra because they operate in a spectral region where most molecules exhibit very strong fundamental absorptions. Unfortunately, they require cryogenic cooling and their spectral emission characteristics are rather poor. Near-IR lasers, on the other hand, because of their increasingly diverse commercial applications, have many attractive features, such as room temperature operation, high power, and low threshold currents. Unlike Pb-salt diode lasers, however, they operate in a spectral region where most molecules exhibit only weak overtone transitions. Therefore, a very sensitive detection method has to be used for any spectroscopic application. ’ Present address: NASA Langley Research Center, Hampton, VA 23665. 381
0022-2852191 $3.00 Copyright 0
1991 by Academic Press. Inc.
All rights of reproduction in any form resewed.
382
RIRIS
ET AL.
Frequency modulation spectroscopy (FMS), first demonstrated by Bjorklund ( I ), has the necessary sensitivity for this kind of application. FMS is essentially a form of very sensitive linear absorption spectroscopy. Although it was initially implemented with visible dye lasers and external electrooptic modulators, it is clear that diode lasers are ideally suited for FMS since they can easily be modulated by directly modulating the injection current. Such modulation of the laser at high frequencies (usually in the hundreds of MHz or GHz range) produces microwave sidebands symmetrically spaced about the carrier (laser) frequency (Fig. 1) . When the modulated laser field interacts with a sample, the differential absorption of the sidebands produces a first derivativelike signal against a zero background level. This offers a distinct advantage over direct absorption methods, where the signal is detected as a change in the laser intensity transmitted through a sample and the sensitivity is severely limited by the intensity fluctuations of the laser. Since the FM signal is demodulated at high frequencies, where diode lasers exhibit relatively little excess noise, the sensitivity of the technique is in principle limited only by quantum noise. The relatively high modulation and demodulation frequencies, however, increase the bandwidth requirements for the photodetectors dramatically. Unfortunately, detectors with GHz bandwidths are not widely available, and those that are have very small and damage-sensitive surfaces, thus making the alignment of the laser beam rather cumbersome, especially in the infrared. The purely practical need of reducing the detector bandwidth requirements led to the development of two-tone frequency modulation, which was successfully demonstrated for the first time by Janik et al. (2). Unlike conventional FMS, which is usually referred to as single-tone frequency modulation spectroscopy (STFMS), two-tone FMS (TTFMS) calls for the simultaneous modulation of the laser at two high but closely spaced frequencies separated by Q (for example 1 GHz f MHz). The signal is detected not at the modulation frequency but at the separation frequency Q, and the two-tone lineshape looks like a second TWO - TONE
SINGLE -TONE
FMS SIGNAL
L
I
v
I
FIG. 1. Comparison
I
I
of single-tone
I and two-tone
frequency
modulation
spectroscopy.
INTENSITIES
OF HI TRANSITIONS
383
derivative signal (Fig. 1) . As long as the separation frequency Q lies outside the laser linewidth, the technique is again limited only by quantum noise. For diode lasers which have inherently narrow linewidths, a demodulation frequency of a few MHz is sufficient. FMS has been used with both visible and infrared lasers. Cooper and Gallagher (3) have used it with a cw He-Ne laser and Tran et al. (4) used it with multimode pulsed dye lasers. Osterwalder and Ricket (5) first reported frequency modulation of double heterostructure GaAlAs lasers at microwave frequencies (up to 2.25 GHz) and Lenth (6) and Pokrowsky et al. ( 7) used it to study weak molecular absorptions in the near infrared. Although Lenth (6) was the first to use FMS with GaAlAs lasers, Gehrtz et al. (8) demonstrated the first successful application of FMS with Pb-salt diode lasers. Since then, Cooper and his co-workers (9-12) have explored FMS with both nearand midinfrared diode lasers. In the present study, TTFMS was used with two different diode laser systems to measure intensities of transitions in the fundamental and second overtone bands of hydrogen iodide at 4.7 and 1.55 pm, respectively. The experimental details are discussed in Section II, and the results are discussed in Section III. Using the present results together with intensity data from previous workers, we derive a refined dipole-moment function for HI. II. EXPERIMENTAL
DETAILS
The experimental setups for the mid- and near-infrared systems are shown in Figs. 2(a) and 2(b), respectively. The Pb-salt diode laser exhibited multimode behavior. Thus, the beam was directed through a monochromator to separate the different laser modes. A closed cycle He refrigerator was used to cool down the laser, and the highly divergent beam was collimated by a gold plated off-axis paraboloid. The beam was chopped for lock-in detection and then directed through a l-m single pass cell with CaFz windows. The modulation frequency was approximately 1 GHz f 3 MHz, and a photovoltaic InSb detector with a loo-MHz bandwidth was used to demodulate the signal which was then filtered and amplified before homodyne detection by a double balanced mixer. The lock-in amplifier and the laser injection current were controlled by an AT&T personal computer interfaced to the experiment. The laser wavelength was calibrated using a McPherson monochromator and transitions of the fundamental vibrational band of CO which lie in this region. Five lines of the P branch of the fundamental transition of HI were accessible with our Pb-salt diode laser. The cell was usually filled with ~1-4 Torr of purified HI, and several readings were taken at different pressures; all measurements were made at a temperature of 296 K. The linestrengths of the P( 4)) P( 5 ), P( 6 ) , P( 7 ) , and P( 8 ) transitions were measured by calibrating and deconvoluting the FM signal. The experimental setup for the near-infrared measurements is simpler because no cryogenic equipment is required. The beam from a distributed feedback (DFB) single mode laser was collimated and then directed through a Faraday isolator to reduce feedback into the laser cavity. A single pass 50-cm cell with BK-7 windows, v-coated for 1.55 pm, was filled with l-20 Torr of purified HI. (The amount of HI in the cell was determined by the strength of the particular absorption line under study.) The
384
RIRIS
(a)
(b)
CHOPPER
ET AL.
MoNo_CHRoMAToR
FARADAY
ISOLATOR
J DETECTOR
FIG. 2. (a) Experimental setup for TTFMS TTFMS with a near-infrared laser.
with a Pb-salt
midinfrared
laser. (b) Experimental
setup for
modulation and detection schemes were essentially the same as in the previous case with the exception that the modulation frequency was 320 f 5 MHz, and a 12 bit digitizer interfaced to a PC was used for data acquisition and averaging. The laser wavelength was calibrated using an Instruments SA monochromator. Seven transitions of the R branch of the second overtone were accessible with our laser. The linestrengths of R(2), R(3), R(4), R(5), R( 16), R( 17), and R( 18) transitions were measured. The last three lines were extremely weak, and the fact that they can be seen with only 5-10 Torr of HI in the single pass cell illustrates the usefulness and sensitivity of TTFMS.
385
INTENSITIES OF HI TRANSITIONS
In order to measure the linestrength of a transition, the TTFMS signal must be calibrated using a well known absorption. By optimizing the signal and then keeping all the experimental parameters constant, a linear relationship can be obtained between the magnitude of the direct absorption and the TTFMS signal. This relationship can then be extrapolated to measure very weak transitions that cannot be seen in direct absorption. In our case, we decided to use the HI absorptions as calibration since the direct absorption from some of these transitions could easily be seen with only a few torricellis of HI in the cell. The calibration was then extrapolated for the measurement of the weak high-1 transitions. III. RESULTS
The strength Q(T) of a vibration-rotational transition at temperature T is related to the matrix element of the dipole-moment function, M(x), where x is the dimensionless displacement from equilibrium [x = (R - R,)/ R,] by the well-known expression s, (T)
I/
=
87r3x 1o-36
uif[l - e -hcv,/lkeT]e-hcE,lka~X(,I ((uJIM(x))v’J’)12.
(1)
3hcQ(Tl
TABLE I Linestrengths S (296 K) for the Observed Transitions in the Fundamental and Second Overtone Bands Fundamental Line
s in 10e2'
CQllOleCUl.2
ICOJI M(x)
IlJ-1>1'
P(4)
4.97
8.31
x 10-4
P(5)
3.66
6.73
x 1O-4
P(6)
2.14
4.80
x 10-4
P(7)
1.09
3.26
x 1O-4
P(S)
0.564
2.45
x 1O-4
M(x)
I~J+I>I~
Second Line
S in 10-22
~m/i~lecule
in D2
Overtone ICOJI
R(2)
2.98
1.44 x 10-6
R(3)
3.56
1.55 x 10-6
R(4)
3.60
1.61 x lo+
R(5)
3.01
1.53 x 10-6
R(l6)
0.002
6.41
X 1O-7
R(l7)
0.0011
9.44
x 10-7
R(lS)
0.00060
1.47 x 10-6
in D2
386
RIRIS ET AL.
In this expression, ygis the wavenumber of the transition f= u’J’ + i = vJ, where 2, and J are the vibrational and rotational quantum numbers, respectively; Ei is the initial state energy (cm-‘); Q( T) is the partition function; m = [ J’( J’ + 1) - J( J + 1 )] /2; and the vibration-rotational dipole-moment matrix elements are in debyes (D). The experimental strengths measured in the present work are listed in Table I together with the values of the squares of the corresponding dipole-moment matrix elements. These matrix elements can be written in terms of the rotationless matrix element (Uo l M(x) lu’0) and the Herman-Wallis factor F,“’ (m) defined by I(vJIM(x)~v’J’)I~
= I(vOIM(x)lv’0)~2F~‘(m) = I(IIOI(M(X)I~‘O)(~( 1 + Cfm + D,“‘m2 + . - -) .
(2)
Thevaluesof l(OO(M(x)I lO)l,C 1, and 0: obtained by an unweighted least-squares fit of the data of Table I to Eq. (2) are listed in Table II. We note here that the value for CA obtained through the present measurements differs only slightly from that obtained previously while the value for 0: is approximately an order of magnitude larger; the value obtained for I(00 ( M(x) ( 10) ) is approximately 7% higher than the previous result ( 13). These latter data, together with similar data for other bands, are taken from Ref. (13) in which the original experimental sources are given. Values of I(00l~(-e130)1, c s, and 0; obtained through a weighted least-squares fit in which the weights for the weak high-J transitions were (somewhat arbitrarily) taken as 0.1 are also listed in Table II. The value of Ci is approximately a factor of 2 larger, while D$ differs both in magnitude and sign from the previous result; the rotationless matrix element is approximately 5% higher. Because linestrengths for high-J transitions in the second overtone band (which involve larger Herman-Wallis factors) were measured
TABLE II Rotationless Dipole-Moment Matrix Elements in Debye and Herman-Wallis Coefficients” <001
M(x)
tv'O>
v'
D;'
C;;' Experiment
Theory
Experiment
Theory
1
-4.346
x 10-3
1.67
x 10-l
1.23 x 10-l
7.3 x 10-3
3.1 x 10-3
2
1.796
x 10-3
2.54
x lO-2
3.43
x 10-2
1.5 x 10-3
-4.2 x lO-4
3
-1.178
x 10-3
3.59
x 10-2
1.18
X lO-2
x 1O-3
2.0 x 10-6
4
3.954
x 10-4
1.76
x 10-2
1.43 x 10-2
2.1 x 10-3
1.3 x 10-4
x 1O-4
1.73
x 10-2
1.66 x 10-2
1.5 x 10-3
2.3 x lO-4
5
-1.36
a. All
experimental
second
overtone
references are
those
[W.(4)].
results
bands
to the original calculated
except
are taken
using
work the
those
for the
from Ref. are listed; refined
-2.7
fundamental
(13) in which
the theoretical
dipole-moment
and
the results
function
INTENSITIES OF HI TRANSITIONS
387
in the present work, it is felt that the new values of Ci and 02 are more reliable than previous results. However, because the numerical values of Ci and 0: depend somewhat on the weighting, and because of the small number of transitions measured in the present work, no meaningful error limits can be assigned to the Herman-Wallis coefficients. We note here that the signs of the rotationless matrix elements have been ascertained from the signs and magnitudes of the Herman-Wallis coefficients C;’ for the various bands as in previous work ( 14). Using the values for the rotationless dipole-moment matrix elements together with the experimentally determined permanent dipole-moment coefficient, MO = 0.447 22 D (15) one can obtain a refined dipole-moment function. Representing M(x) by a series expansion M(X)
=
C
Mix’
r=O
(3)
and using the matrix elements (OJI x’ 1v’J’) calculated previously, we obtain M(x) = 0.447 22 - 0.079 413x + 0.5140x’-
2.0397x3 - 0.402x4 - 1.40x5.
(4)
The magnitudes of the first four dipole coefficients are comparable to the previous results ( 13)) while those of the last two are significantly larger; the higher coefficients, however, do not contribute appreciably to the dipole-moment matrix elements. As a self-consistency check on the dipole-moment function given by Eq. (4), we have used it to calculate the Herman-Wallis coefficients C$ and 08’; these results are listed in Table II together with the corresponding experimental values. As can be seen from Table II, there is general overall agreement between these results although some discrepancies remain. Before concluding, there are several points that we would like to make. First, from the present results, particularly in the second overtone band, it is clear that frequency modulation spectroscopy provides a powerful experimental technique for the measurement of the strengths of weak transitions. However, because of the limited frequency coverage, only a small number of transitions in a given band can be measured. This in turn limits the accuracy (in a statistical sense) of the values of the rotationless dipole-moment matrix elements and Herman-Wallis coefficients one can obtain. Nevertheless, the ability to measure weak high-J strengths enables one to extract accurate Herman-Wallis factors. The rotationless matrix elements for both the fundamental and second overtone band are slightly larger than those obtained from previous analyses; as a result, the incorporation of these data allows us to refine the dipolemoment function for HI. ACKNOWLEDGMENTS The authors thank Mr. Glen Sachse, NASA Langley Research Center, and Dr. Lester Andwers, University of Virginia, for the generous loan of equipment. The experimental work was supported by the Electric Power Research Institute and the Center for Innovative Technology. One author (RHT) also thanks Dr. Larry Rothman and the Air Force Geophysics Laboratory for research support. RECEIVED:
December 5, 1990
388
RIRIS ET AL. REFERENCES
1. G. C. BJORKLUND,Opt. Lezt. 5, 15-l 7 ( 1980). 2. G. R. JANIK, C. B. CARLISLE, AND T. F. GALLAGHER, J. Opt. Sot. Am. B Opt. Phys. 3, 1070-1074
(1986). 3. D. E. CARPER AND T. F. GALLAGHER, Opt. Lett. 9,45 l-453 ( 1984). 4. N. H. TRAN, R. KACHRU, P. PILLET, H. B. VAN LINDEN VAN DEN HEUVELL, T. F. GALLAGHER, AND J. P. WATJEN, Appl. Opt. 23, 1353-1360 (1984). 5. J. M. OSTERWALDERAND B. J. RICKETT, IEEE J. Quantum Electron QE-16, 250-252 ( 1980). 6. W. LENTH, Opt. Lett. 8,575-577 (1983). 7. P. POKROWSKY, W. ZAPKA, F. CHU, AND G. C. BJORKLUND,Opt. Commun. 44, 175-179 (1983). 8. M. GEHRTZ, W. LENTH, A. T. YOUNG, AND H. S. JOHNSTON,Opt. Lett. 11, 132-I 34 ( 1980). 9. D. E. CARPER AND J. P. WATJEN, Opt. Lett. 11,606-608 ( 1986). 10. D. E. CARPER AND R. E. WARREN, J. Opt. Sot. Am. B Opt. Phys. 4,470-480 ( 1987). II. D. E. CARPER AND C. B. CARLISLE, Opt. Lett. 13,719-721 (1988). 12. C. B. CARLISLE, D. E. COOPER,AND H. PREIER,Appl. Opt. 28,2567-2576 ( 1989). 13. J. F. OGILVIE, W. R. RODWELL, AND R. H. TIPPING, J. Chem. Phys. 73, 5221-5229 (1980). 14. R. H. TIPPING AND R. M. HERMAN, .I Mol. Spectrosc. 36, 404-413 ( 1970); R. H. TIPPING AND A. FORBES,J. Mol. Spectrosc. 39, 65-72 ( 197 I ). IS. F. A. VAN DIJK AND A. DYMANUS, Chem. Phys. Lett. 5,387-389 ( 1970).
OF MOLECULAR
SPECTROSCOPY
(1991)
l&381-388
Measurement of the Strengths of 1 + 0 and 3 + 0 Transitions of HI Using Frequency Modulation Spectroscopy HARIS RIRIS, C. B. CARLISLE, AND D. E. COOPER SRI International, 333 Ravenswood Ave., Menlo Park, Cal$ornia 94025 LIANG-GUO
WANG, ’ AND
T. F. GALLAGHER
Department of Physics. University of Virginia, Charlottesville. Virginia 22901 AND
R. H. TIPPING Department of Physics and Astronomy. University of Alabama, Tuscaloosa, Alabama 35487-0324 The linestrengths for five P-branch lines in the fundamental and seven R-branch lines. including three high-J transitions, in the second overtone band of HI have been measured using frequency modulation spectroscopy. From these data, we have obtained new values for the rotationless dipole-moment matrix elements and Herman-Wallis coefficients for these bands. Combining this new information with previously measured intensity data, we have deduced a refined dipole moment function for HI. 0 1991 Academic Press. Inc. I. INTRODUCTION
In recent years, there has been a significant increase in the number of successful commercial and scientific applications of semiconductor diode lasers. Although diode lasers have been in existence since the early 196Os, their application to spectroscopic problems was limited mainly by their small tuning range, multimode spectral emission, and low power. Diode lasers can be divided into two broad categories: near-IR lasers based on III-V compounds operating in the 750 nm to 1.6 pm range, and Pb-salt diode lasers operating in the 3 to 30 pm range. Pb-salt diode lasers have traditionally been used in the study of molecular spectra because they operate in a spectral region where most molecules exhibit very strong fundamental absorptions. Unfortunately, they require cryogenic cooling and their spectral emission characteristics are rather poor. Near-IR lasers, on the other hand, because of their increasingly diverse commercial applications, have many attractive features, such as room temperature operation, high power, and low threshold currents. Unlike Pb-salt diode lasers, however, they operate in a spectral region where most molecules exhibit only weak overtone transitions. Therefore, a very sensitive detection method has to be used for any spectroscopic application. ’ Present address: NASA Langley Research Center, Hampton, VA 23665. 381
0022-2852191 $3.00 Copyright 0
1991 by Academic Press. Inc.
All rights of reproduction in any form resewed.
382
RIRIS
ET AL.
Frequency modulation spectroscopy (FMS), first demonstrated by Bjorklund ( I ), has the necessary sensitivity for this kind of application. FMS is essentially a form of very sensitive linear absorption spectroscopy. Although it was initially implemented with visible dye lasers and external electrooptic modulators, it is clear that diode lasers are ideally suited for FMS since they can easily be modulated by directly modulating the injection current. Such modulation of the laser at high frequencies (usually in the hundreds of MHz or GHz range) produces microwave sidebands symmetrically spaced about the carrier (laser) frequency (Fig. 1) . When the modulated laser field interacts with a sample, the differential absorption of the sidebands produces a first derivativelike signal against a zero background level. This offers a distinct advantage over direct absorption methods, where the signal is detected as a change in the laser intensity transmitted through a sample and the sensitivity is severely limited by the intensity fluctuations of the laser. Since the FM signal is demodulated at high frequencies, where diode lasers exhibit relatively little excess noise, the sensitivity of the technique is in principle limited only by quantum noise. The relatively high modulation and demodulation frequencies, however, increase the bandwidth requirements for the photodetectors dramatically. Unfortunately, detectors with GHz bandwidths are not widely available, and those that are have very small and damage-sensitive surfaces, thus making the alignment of the laser beam rather cumbersome, especially in the infrared. The purely practical need of reducing the detector bandwidth requirements led to the development of two-tone frequency modulation, which was successfully demonstrated for the first time by Janik et al. (2). Unlike conventional FMS, which is usually referred to as single-tone frequency modulation spectroscopy (STFMS), two-tone FMS (TTFMS) calls for the simultaneous modulation of the laser at two high but closely spaced frequencies separated by Q (for example 1 GHz f MHz). The signal is detected not at the modulation frequency but at the separation frequency Q, and the two-tone lineshape looks like a second TWO - TONE
SINGLE -TONE
FMS SIGNAL
L
I
v
I
FIG. 1. Comparison
I
I
of single-tone
I and two-tone
frequency
modulation
spectroscopy.
INTENSITIES
OF HI TRANSITIONS
383
derivative signal (Fig. 1) . As long as the separation frequency Q lies outside the laser linewidth, the technique is again limited only by quantum noise. For diode lasers which have inherently narrow linewidths, a demodulation frequency of a few MHz is sufficient. FMS has been used with both visible and infrared lasers. Cooper and Gallagher (3) have used it with a cw He-Ne laser and Tran et al. (4) used it with multimode pulsed dye lasers. Osterwalder and Ricket (5) first reported frequency modulation of double heterostructure GaAlAs lasers at microwave frequencies (up to 2.25 GHz) and Lenth (6) and Pokrowsky et al. ( 7) used it to study weak molecular absorptions in the near infrared. Although Lenth (6) was the first to use FMS with GaAlAs lasers, Gehrtz et al. (8) demonstrated the first successful application of FMS with Pb-salt diode lasers. Since then, Cooper and his co-workers (9-12) have explored FMS with both nearand midinfrared diode lasers. In the present study, TTFMS was used with two different diode laser systems to measure intensities of transitions in the fundamental and second overtone bands of hydrogen iodide at 4.7 and 1.55 pm, respectively. The experimental details are discussed in Section II, and the results are discussed in Section III. Using the present results together with intensity data from previous workers, we derive a refined dipole-moment function for HI. II. EXPERIMENTAL
DETAILS
The experimental setups for the mid- and near-infrared systems are shown in Figs. 2(a) and 2(b), respectively. The Pb-salt diode laser exhibited multimode behavior. Thus, the beam was directed through a monochromator to separate the different laser modes. A closed cycle He refrigerator was used to cool down the laser, and the highly divergent beam was collimated by a gold plated off-axis paraboloid. The beam was chopped for lock-in detection and then directed through a l-m single pass cell with CaFz windows. The modulation frequency was approximately 1 GHz f 3 MHz, and a photovoltaic InSb detector with a loo-MHz bandwidth was used to demodulate the signal which was then filtered and amplified before homodyne detection by a double balanced mixer. The lock-in amplifier and the laser injection current were controlled by an AT&T personal computer interfaced to the experiment. The laser wavelength was calibrated using a McPherson monochromator and transitions of the fundamental vibrational band of CO which lie in this region. Five lines of the P branch of the fundamental transition of HI were accessible with our Pb-salt diode laser. The cell was usually filled with ~1-4 Torr of purified HI, and several readings were taken at different pressures; all measurements were made at a temperature of 296 K. The linestrengths of the P( 4)) P( 5 ), P( 6 ) , P( 7 ) , and P( 8 ) transitions were measured by calibrating and deconvoluting the FM signal. The experimental setup for the near-infrared measurements is simpler because no cryogenic equipment is required. The beam from a distributed feedback (DFB) single mode laser was collimated and then directed through a Faraday isolator to reduce feedback into the laser cavity. A single pass 50-cm cell with BK-7 windows, v-coated for 1.55 pm, was filled with l-20 Torr of purified HI. (The amount of HI in the cell was determined by the strength of the particular absorption line under study.) The
384
RIRIS
(a)
(b)
CHOPPER
ET AL.
MoNo_CHRoMAToR
FARADAY
ISOLATOR
J DETECTOR
FIG. 2. (a) Experimental setup for TTFMS TTFMS with a near-infrared laser.
with a Pb-salt
midinfrared
laser. (b) Experimental
setup for
modulation and detection schemes were essentially the same as in the previous case with the exception that the modulation frequency was 320 f 5 MHz, and a 12 bit digitizer interfaced to a PC was used for data acquisition and averaging. The laser wavelength was calibrated using an Instruments SA monochromator. Seven transitions of the R branch of the second overtone were accessible with our laser. The linestrengths of R(2), R(3), R(4), R(5), R( 16), R( 17), and R( 18) transitions were measured. The last three lines were extremely weak, and the fact that they can be seen with only 5-10 Torr of HI in the single pass cell illustrates the usefulness and sensitivity of TTFMS.
385
INTENSITIES OF HI TRANSITIONS
In order to measure the linestrength of a transition, the TTFMS signal must be calibrated using a well known absorption. By optimizing the signal and then keeping all the experimental parameters constant, a linear relationship can be obtained between the magnitude of the direct absorption and the TTFMS signal. This relationship can then be extrapolated to measure very weak transitions that cannot be seen in direct absorption. In our case, we decided to use the HI absorptions as calibration since the direct absorption from some of these transitions could easily be seen with only a few torricellis of HI in the cell. The calibration was then extrapolated for the measurement of the weak high-1 transitions. III. RESULTS
The strength Q(T) of a vibration-rotational transition at temperature T is related to the matrix element of the dipole-moment function, M(x), where x is the dimensionless displacement from equilibrium [x = (R - R,)/ R,] by the well-known expression s, (T)
I/
=
87r3x 1o-36
uif[l - e -hcv,/lkeT]e-hcE,lka~X(,I ((uJIM(x))v’J’)12.
(1)
3hcQ(Tl
TABLE I Linestrengths S (296 K) for the Observed Transitions in the Fundamental and Second Overtone Bands Fundamental Line
s in 10e2'
CQllOleCUl.2
ICOJI M(x)
IlJ-1>1'
P(4)
4.97
8.31
x 10-4
P(5)
3.66
6.73
x 1O-4
P(6)
2.14
4.80
x 10-4
P(7)
1.09
3.26
x 1O-4
P(S)
0.564
2.45
x 1O-4
M(x)
I~J+I>I~
Second Line
S in 10-22
~m/i~lecule
in D2
Overtone ICOJI
R(2)
2.98
1.44 x 10-6
R(3)
3.56
1.55 x 10-6
R(4)
3.60
1.61 x lo+
R(5)
3.01
1.53 x 10-6
R(l6)
0.002
6.41
X 1O-7
R(l7)
0.0011
9.44
x 10-7
R(lS)
0.00060
1.47 x 10-6
in D2
386
RIRIS ET AL.
In this expression, ygis the wavenumber of the transition f= u’J’ + i = vJ, where 2, and J are the vibrational and rotational quantum numbers, respectively; Ei is the initial state energy (cm-‘); Q( T) is the partition function; m = [ J’( J’ + 1) - J( J + 1 )] /2; and the vibration-rotational dipole-moment matrix elements are in debyes (D). The experimental strengths measured in the present work are listed in Table I together with the values of the squares of the corresponding dipole-moment matrix elements. These matrix elements can be written in terms of the rotationless matrix element (Uo l M(x) lu’0) and the Herman-Wallis factor F,“’ (m) defined by I(vJIM(x)~v’J’)I~
= I(vOIM(x)lv’0)~2F~‘(m) = I(IIOI(M(X)I~‘O)(~( 1 + Cfm + D,“‘m2 + . - -) .
(2)
Thevaluesof l(OO(M(x)I lO)l,C 1, and 0: obtained by an unweighted least-squares fit of the data of Table I to Eq. (2) are listed in Table II. We note here that the value for CA obtained through the present measurements differs only slightly from that obtained previously while the value for 0: is approximately an order of magnitude larger; the value obtained for I(00 ( M(x) ( 10) ) is approximately 7% higher than the previous result ( 13). These latter data, together with similar data for other bands, are taken from Ref. (13) in which the original experimental sources are given. Values of I(00l~(-e130)1, c s, and 0; obtained through a weighted least-squares fit in which the weights for the weak high-J transitions were (somewhat arbitrarily) taken as 0.1 are also listed in Table II. The value of Ci is approximately a factor of 2 larger, while D$ differs both in magnitude and sign from the previous result; the rotationless matrix element is approximately 5% higher. Because linestrengths for high-J transitions in the second overtone band (which involve larger Herman-Wallis factors) were measured
TABLE II Rotationless Dipole-Moment Matrix Elements in Debye and Herman-Wallis Coefficients” <001
M(x)
tv'O>
v'
D;'
C;;' Experiment
Theory
Experiment
Theory
1
-4.346
x 10-3
1.67
x 10-l
1.23 x 10-l
7.3 x 10-3
3.1 x 10-3
2
1.796
x 10-3
2.54
x lO-2
3.43
x 10-2
1.5 x 10-3
-4.2 x lO-4
3
-1.178
x 10-3
3.59
x 10-2
1.18
X lO-2
x 1O-3
2.0 x 10-6
4
3.954
x 10-4
1.76
x 10-2
1.43 x 10-2
2.1 x 10-3
1.3 x 10-4
x 1O-4
1.73
x 10-2
1.66 x 10-2
1.5 x 10-3
2.3 x lO-4
5
-1.36
a. All
experimental
second
overtone
references are
those
[W.(4)].
results
bands
to the original calculated
except
are taken
using
work the
those
for the
from Ref. are listed; refined
-2.7
fundamental
(13) in which
the theoretical
dipole-moment
and
the results
function
INTENSITIES OF HI TRANSITIONS
387
in the present work, it is felt that the new values of Ci and 02 are more reliable than previous results. However, because the numerical values of Ci and 0: depend somewhat on the weighting, and because of the small number of transitions measured in the present work, no meaningful error limits can be assigned to the Herman-Wallis coefficients. We note here that the signs of the rotationless matrix elements have been ascertained from the signs and magnitudes of the Herman-Wallis coefficients C;’ for the various bands as in previous work ( 14). Using the values for the rotationless dipole-moment matrix elements together with the experimentally determined permanent dipole-moment coefficient, MO = 0.447 22 D (15) one can obtain a refined dipole-moment function. Representing M(x) by a series expansion M(X)
=
C
Mix’
r=O
(3)
and using the matrix elements (OJI x’ 1v’J’) calculated previously, we obtain M(x) = 0.447 22 - 0.079 413x + 0.5140x’-
2.0397x3 - 0.402x4 - 1.40x5.
(4)
The magnitudes of the first four dipole coefficients are comparable to the previous results ( 13)) while those of the last two are significantly larger; the higher coefficients, however, do not contribute appreciably to the dipole-moment matrix elements. As a self-consistency check on the dipole-moment function given by Eq. (4), we have used it to calculate the Herman-Wallis coefficients C$ and 08’; these results are listed in Table II together with the corresponding experimental values. As can be seen from Table II, there is general overall agreement between these results although some discrepancies remain. Before concluding, there are several points that we would like to make. First, from the present results, particularly in the second overtone band, it is clear that frequency modulation spectroscopy provides a powerful experimental technique for the measurement of the strengths of weak transitions. However, because of the limited frequency coverage, only a small number of transitions in a given band can be measured. This in turn limits the accuracy (in a statistical sense) of the values of the rotationless dipole-moment matrix elements and Herman-Wallis coefficients one can obtain. Nevertheless, the ability to measure weak high-J strengths enables one to extract accurate Herman-Wallis factors. The rotationless matrix elements for both the fundamental and second overtone band are slightly larger than those obtained from previous analyses; as a result, the incorporation of these data allows us to refine the dipolemoment function for HI. ACKNOWLEDGMENTS The authors thank Mr. Glen Sachse, NASA Langley Research Center, and Dr. Lester Andwers, University of Virginia, for the generous loan of equipment. The experimental work was supported by the Electric Power Research Institute and the Center for Innovative Technology. One author (RHT) also thanks Dr. Larry Rothman and the Air Force Geophysics Laboratory for research support. RECEIVED:
December 5, 1990
388
RIRIS ET AL. REFERENCES
1. G. C. BJORKLUND,Opt. Lezt. 5, 15-l 7 ( 1980). 2. G. R. JANIK, C. B. CARLISLE, AND T. F. GALLAGHER, J. Opt. Sot. Am. B Opt. Phys. 3, 1070-1074
(1986). 3. D. E. CARPER AND T. F. GALLAGHER, Opt. Lett. 9,45 l-453 ( 1984). 4. N. H. TRAN, R. KACHRU, P. PILLET, H. B. VAN LINDEN VAN DEN HEUVELL, T. F. GALLAGHER, AND J. P. WATJEN, Appl. Opt. 23, 1353-1360 (1984). 5. J. M. OSTERWALDERAND B. J. RICKETT, IEEE J. Quantum Electron QE-16, 250-252 ( 1980). 6. W. LENTH, Opt. Lett. 8,575-577 (1983). 7. P. POKROWSKY, W. ZAPKA, F. CHU, AND G. C. BJORKLUND,Opt. Commun. 44, 175-179 (1983). 8. M. GEHRTZ, W. LENTH, A. T. YOUNG, AND H. S. JOHNSTON,Opt. Lett. 11, 132-I 34 ( 1980). 9. D. E. CARPER AND J. P. WATJEN, Opt. Lett. 11,606-608 ( 1986). 10. D. E. CARPER AND R. E. WARREN, J. Opt. Sot. Am. B Opt. Phys. 4,470-480 ( 1987). II. D. E. CARPER AND C. B. CARLISLE, Opt. Lett. 13,719-721 (1988). 12. C. B. CARLISLE, D. E. COOPER,AND H. PREIER,Appl. Opt. 28,2567-2576 ( 1989). 13. J. F. OGILVIE, W. R. RODWELL, AND R. H. TIPPING, J. Chem. Phys. 73, 5221-5229 (1980). 14. R. H. TIPPING AND R. M. HERMAN, .I Mol. Spectrosc. 36, 404-413 ( 1970); R. H. TIPPING AND A. FORBES,J. Mol. Spectrosc. 39, 65-72 ( 197 I ). IS. F. A. VAN DIJK AND A. DYMANUS, Chem. Phys. Lett. 5,387-389 ( 1970).