Millimeter-wave studies of the ^13CH_3F laser: the effects of buffer gases and the spectroscopy of the laser states

336 J. Opt. Soc. Am. B/Vol. 2, No. 2/February 1985

Millimeter-wave studies of the 13CH3F laser: the effects ofbuffer gases and the spectroscopy of the laser states

William H. Matteson and Frank C. DeLucia

Department of Physics, Duke University, Durham, North Carolina 27706

Received May 30, 1984; accepted October 2, 1984

Millimeter-wave spectroscopic techniques have been used to study the effects of buffer gases (helium and hexane)on the 13CH3F optically pumped far-infrared laser. The continuous tunability over a wide spectral region and ab-solute frequency reference of this technique, coupled with the accurately known rotational transition moments,have made possible a number of new measurements and calculations. In this work the diagnostic probe was coprop-agated with the C0 2-laser pump beam through the 3CH 3F. The model that we have previously described, whichdistinguishes among different kinds of rotational transitions, also accounted for these new experimental results.Also reported in this paper are the results of a spectroscopic study of 13CH 3F in its ground and V3 = 1 excited vibra-tional states.

1. INTRODUCTION

We have previously reported the use of millimeter-wavespectroscopic techniques to study collision-induced energytransfer processes in the 3CH 3F optically pumped far-in-frared (FIR) laser.' In that paper is a review of vibrationaland rotational collisional energy-transfer processes and adiscussion of earlier studies of both optically pumped FIRlasers and spectroscopic techniques. In this paper we extendthese studies to include the effects of buffer gases. Our ex-perimental technique has allowed us to acquire kinds of in-formation about optically pumped FIR lasers that have notbeen available previously. This is because the spectroscopictechniques that we have developed 2 4 have broad continuouscoverage (<100->1000 GHz) in the spectral region of theFIR-laser operation. This makes possible absolute obser-vations not only of the lasing transition itself but also of manytransitions that are collisionally coupled. Furthermore, be-cause rotational transitions are observed, the technique isespecially sensitive to the rotational nonequilibrium that isresponsible for the lasing. The data acquired in this work arediscussed in the context of a model that we have previouslyreported.' This model makes possible an accurate descriptionof the 3CH 3F system in the context of a small number ofphysically meaningful parameters.

2. EXPERIMENT

The measurements reported in this paper were made with thesystem shown in Fig. 1, which can be divided into four mainparts:

(1) A sample cell in which the C0 2-laser pump and themillimeter-wave diagnostic probe copropagate,

(2) A tunable millimeter-wave spectrometer,(3) A line-tunable CO2 laser, and(4) A computer-based control and signal-processing

system.

The C0 2-laser pump beam passes through a mechanicalchopper that is synchronized with the frequency sweep of thediagnostic spectrometer. This allows spectra to be recorded

both with and without laser pumping almost simultaneously(the sweep rate is typically 15 Hz) and virtually eliminatesproblems associated with system drifts. The unpumpedspectra also serve as absolute references by the knownBoltzmann populations of the levels. Since we are primarilyinterested in collisional processes rather than effects producedby high pump powers, low (<1-W/cm 2) CO 2 pump energydensities are used.

The pump beam and the millimeter-wave diagnostic probecopropagate through the copper sample cell. For most of ourmeasurements, the cell was 1 cm in radius and 105 cm long;the radius was increased to 2.5 cm in the remainder. At theoutput end of the cell, the C0 2-laser power was sampled sothat the pump power absorbed by the molecules could becalculated. The rest was absorbed in the Teflon window thattransmitted the millimeter-wave power to the 1.5-K InSbdetector.

3. MODEL

The system described above provides a wealth of detailedinformation that is usually not available for the modeling ofoptically pumped FIR lasers. These lasers are among themost difficult to model properly because their inversions arebetween rotational states. A typical molecule has between102 and 104 thermally populated rotational levels, and thenumber of strong collisional transition probabilities thatconnect these states is even larger. Furthermore, rotationalrelaxation processes are rapid.

Critical to the construction of a realistic model is an un-derstanding of which of the multitude of levels are in equi-librium. Although a good theoretical understanding of col-lisional processes is useful, there is no substitute for directexperimental information of the type that can be obtainedfrom the system described above. The model that we devel-oped is shown in Fig. 2. This is the same model that we haveused previously.' 13CH 3F is a symmetric top whose rotationalenergies are given by

E = BJ(J + 1) - DjJ2 (J + 1)2 - DJKJ(J + 1)K 2 - DKK4 ,

(1)

0740-3224/85/020336-07$02.00 © 1985 Optical Society of America

W. H. Matteson and F. C. DeLucia

Vol. 2, No. 2/February 1985/J. Opt. Soc. Am. B 337

Correction Signal

I I Computer

Fig. 1. Block diagram of apparatus.

Excited Pool (V3=1)

PVd

Ground Pool (V3=O0)Fig. 2. Outline of the energy transfer model for 3CH 3F.

where J is the total angular momentum and K its projectionon the body-fixed-symmetry axis, B the rotational constant,and Dj, DJK, and DK distortion parameters. The excitedvibrational state that contains the lasing levels is V3 = 1. Byobserving a large number of transitions for which K # 3 inboth the ground and the excited vibrational states, we havefound that a rotational equilibrium at the translational tem-

perature exists. This conclusion comes from observations ofthe type shown in Figs. 3 and 4. These figures show that theonly effect of the CO2 laser pump on K 3 transitions in V3= 1 is to enhance all transitions by the same amount, in thiscase about 1.6 (this is not obvious from this figure because theyare normalized differently). Actual quantitative measure-ments are made at higher resolution. This is a somewhatsurprising experimental result because collisional transitionsfor which AK 5z 3 are strongly forbidden by spin statistics.In an earlier work, we showed how a vibrational exchangeprocess of the form

CH 3F(J, K, V3 = 0) + CH3 F(J', K', V3 = 1)CH3 F(J", K, V3 = 1) + CH3 F(J" ',K', V3 = 0) + AE (2)

is both a high-probability process and one that transcends thepure rotational selection rule.1

The demonstration of rotational equilibrium among thedifferent K states is a more stringent test of rotational equi-librium than would be a similar demonstration among Jstates. This is because the K states, although leading totransitions that are conveniently close together in frequency,are widely spaced in energy. Furthermore, the electric-dipoletransitions that equilibrate J states are extremely long rangeand highly probable. Thus we conclude that in each vibra-tional state all K F 3 states are essentially in thermal equi-librium with one another.

These observations lead to the concept of a ground-statepool and an excited-state pool. These two pools contain allthe levels for which K Fd 3. Within the pools the populationsare given by a Boltzmann distribution with an ambient tem-perature. The only experimental deviation that we observefrom this simple concept is a small, but distinct, enhancementof K = 0 states relative to K = 1 and K = 2 at higher pressure.This is presumably due to the pure rotational AK = 3 tran-sitions that are allowed.



too

90

80 _

70

60

3 50

40

30

20

±0

Frequency

Fig. 3. Spectrum of the V3 = 1, J = 4-5 transition in thermal equi-librium at a pressure of 25 mTorr.

100

90

80

70

60

50

40

30

20

to

0

Frequency

Fig. 4. Spectrum of the v3 = 1, J = 4-5 transition at a pressure of25 mTorr with the CO2 pump laser on.

2 0

(D 40 /

E-Jo0

o 60

700 to 20 30 40 50

Pressure (mTorr)

Fig. 5. Ratio of the pumped/unpumped absorption coefficients forthe V3 = 1, J = 4-5, K = 3 transition.

The exchange of population between the two pools isquantified by PVu (the probability of a collision causing atransition by a molecule from the lower pool to the upper pool)and its inverse PVd. Microscopic reversibility requiresthat

PVuPVd = exp(-AEV/kT), (3)

where AE, is the vibrational energy difference and T thetranslational temperature. Population is also exchanged withthe K = 3 stacks through processes that are defined below.

The most dramatic effect of the strong 9(P)32 CO 2 pumpand the one directly responsible for the lasing is the pumpingof population from J = 4, K = 3, u3 = 0 to J = 5, K = 3, V3 =

1. The experimental results are shown in Figs. 3 and 4.Figure 5 shows for the K = 3 lasing transition the ratios of theobserved line strengths, with and without the laser pumping,as a function of pressure. Because J = 5 is connected to ad-jacent J states by strong electric-dipole transitions, these Jstates are also driven far from thermal equilibrium. We havepreviously published the results of a study of this.1 Sincethese J states within K = 3 are not in thermal equilibriumwith one another, we allow the population of each to vary in-dependently. The exchange of population among these isquantified by Pa (the probability of a collision causing atransition from J - J + 1) and its inverse Pd. Microscopicreversibility requires that

Pu = exp(-AEr/kT),Pd 1

(4)

where g, is the degeneracy of the upper state, gl the degen-eracy of the lower state, and AEr the energy separation of thestates.

Since these probabilities are directly related to the dipoletransition matrix element for AJ = :1 transitions and sincethe value of this matrix element should be virtually identicalin both the ground and excited vibrational states (i.e., theelectric-dipole moment does not change much from vibra-tional state to vibrational state), P, and Pd are the same inboth the excited and ground vibrational states. For all AJ

1 transitions considered here we assume that Pd is aconstant. Although this is an approximation, Pd should bea slow function of J and only deviate at J so high as not toaffect our results. Also, we do not include I AJ I > 1 transi-tions in our model. Since these require hard collisions, theyshould be less probable by about an order of magnitude. Ifthe pumped state were at significantly higher J and obser-vations made over a wider J range, it is possible that theseterms could be required for a more accurate model.

We must also account for the collisional transfer of popu-lation between the K Fd 3 pools and the states within K = 3.In this case the net rate is the difference between the rate outof the pool into the K = 3 stack and the reverse process. Therelationship between these probabilities is

Pin EgJK=3 exp(-Er/kT)

Pout EgJK#3 exp(-Er/kT)(5)

where Pout is the probability/collision that a molecule in aparticular J state of K = 3 will make a transition into the ex-cited state pool. Pin is divided according to a Boltzmanndistribution into a Pin' for each J state:

Pn' PgJK=3 exp(-Er/kT)gJ,K=3 exp(-E,/kT)

(6)

The vibrationally resonant V-V transfer discussed in Section3 is capable of providing this type of population transfer.Because it is vibrationally resonant it is expected to have ahigh probability, and it should deposit population in the K 53 pool with a thermal distribution. As in the case of P, andPd, Pin and Pout are the same in both ground and excited vi-brational states.

The parameters discussed above are used in a computerimplementation of a master equation that governs the transferof population among the states and pools defined by themodel. For example, the population change per collision forthe Jth level of V3 = 1, K = 3 is given by

K=2 K. Ki

_ ,- K= . :: . ,:,fkK=

.;, I . . As

5 MHzi-

5 MHz

K=2 K=i K=0

. . ',--

-h . * .' At

- K=3 v:

l

l


I


ANJ = N- ,P. + Nj+lPd + NpoolPi.'

- NJ(P + Pd + Pout) + biJ,5R, (7)

where the transition probabilities per collision (P,, Pd, Pin,Pout) are defined above, and R is the pump rate due to the CO2laser. J,5 is a delta function that provides pumping only intothe J = 5 state. A similar set of equations governs the pop-ulation changes in the ground-state K = 3 stack. The changein population of the excited-state pool per collision is givenby

ANexcited pool = Nground poolPVu - Nexcited poolPVd

+ -(N K=3Pout)-Nexcited poolPin, (8)

where the vibrational transition probabilities per collision(PVu, PVd) are defined above. A similar equation defines thebehavior of the ground-state pool. An iterative nonlinearleast-squares fit is then used to adjust the probabilities so asto best fit the experimental data. A detailed discussion ofthese procedures and the results of a study on pure 13CH 3Fare given in our earlier work.1

At this point, it is important to define a collision moreprecisely. This is because quantitative definitions of differentkinds of collisions can differ by more than an order of mag-nitude. Hard velocity-changing collisions are responsible fordiffusion, and the cross sections for these are typically thegeometrical area of the species (<10 A2). On the other hand,the collisional processes responsible for AJ = ± 1 transitionsare very long range and have much larger cross sections (>100A2). Cross sections for other types of rotational process (e.g.,AK) are intermediate between the two. In our model wedistinguish among these cases.

In our model, the collisionally induced transition proba-bilities (and the pump rate) are defined per collision. Re-flection on the mathematics of the problem leads to the con-clusion that at this point the definition of a collision does notaffect the fitting of the data to the model. Changing thedefinition of a collision by a factor of 10 simply changes all theprobabilities by 10. As a result, for numerical purposes wefixed Pd at 0.167 and adjusted the remaining parameters toreproduce the experimental spectroscopic data.

However, we have two external measures that ultimatelyremove this ratio ambiguity and impose additional checks onthe validity of the model. First, we can measure the CO2 laserpower absorbed. Since this is a per second measurement, itimmediately establishes a relation between our definition ofper collision and per second. Alternatively, we know thepressure-broadening parameter. Since changes in state areresponsible for this broadening, we can relate the two by usingthe total probability for a transition from a particular J state(PT = P + Pd + Pout) and the relation

Av = 1/27r, (9)

where is the lifetime in the state. It is extremely gratifyingthat these two quite different approaches give results that areconsistent to 20%.1

4. PHYSICAL INTERPRETATION OFPARAMETERS

There are four parameters in our model: P/Pd, Pin/Pout,PVU/PVd, and R. We have shown above that because of theratio indeterminancy there are only three independent vari-

ables. However, we have also shown that external measure-ments can be used to eliminate this ratio indeterminancy(effectively defining Pu/Pd) and to provide a value for R.This leaves only two variables to be adjusted to fit the data.In fact, one more of these is calculable, PVUIPVd, under theassumption that vibrational deactivation occurs on the walls.We have demonstrated for pure 13CH 3F that the values forPV,/PVd obtained from our data are essentially identical tothose derived from the geometry of the cell and gas kinetics.'Thus, in our earlier use of this model, only Pin/Pout was usedas an adjustable parameter to fit a large and wide-rangingcollection of data. This is especially gratifying in that the dataextended over more than an order of magnitude in pressureand that the one parameter adjusted in the fit, Pin/Pout, waspressure independent as expected. It is not possible to cal-culate Pin/Pout because little is known about the vibrationalexchange processes of Eq. (2). As far as we know, this is thefirst experimental observation of such a process.

5. BUFFER GASES

Although it is well known that the addition of buffer gases tooptically pumped FIR lasers can change their operationalcharacteristics, only a few quantitative studies have beencarried out. Most have studied power output as a functionof gas pressure. Chang and Lin5 investigated the effects oftwo types of buffer gases, which they called simple (H2, N2,He) and complex (C2H6, C5H12, C6H14). None of these mol-ecules has a permanent electric-dipole moment. The twogroups differ in that the complex species have many low-lyingvibrational modes. Chang and Lin found that the complexspecies increased the power output of the 2CH 3F laser. Ina similar experiment, Lawandy and Koepf6 studied the ad-dition of SF 6 to the same laser system and obtained resultssimilar to those of Chang and Lin for C6H14 (hexane). Bothof these studies ascribed the increase in power to a buffer-gas-induced reduction in vibrational bottlenecking. Changand Lin also report that H2, N2, and He do not increase thepower output of the 12CH 3F laser. However, in a differentpump regime (>100 W) Mansfield 7 has shown that the addi-tion of H2, D2, or He increases the power output of the 119-AmCH 3 0H laser by 30-50%. Although this is an interesting andpotentially useful result, the differences in pump power,molecular type, and FIR frequency make meaningful com-parisons with our work difficult.

Let us consider the effect of buffer gases in the context ofthe model shown in Fig. 2. Those collisions that cause AJ =±1 transitions (described by Pu/Pd) tend to equilibrate thelasing inversion. These processes are highly probable becauselong-range dipole-dipole collisional forces result from thesame matrix element that makes the lasing possible. Theaddition of any buffer gas will further increase the equili-bration rate, but the selection of nonpolar species will mitigatethis substantially. Since this AJ = +1 process is the majorcontributor to pressure broadening, pressure-broadeningstudies provide quantitative information on the equilibrationof the lasing levels. Since the broadening that is due to specieswith permanent electric-dipole moments is typically an orderof magnitude larger than the pressure broadening that is dueto nonpolar species, the latter are the buffer gases of choicewith regard to this process.

Buffer gases also affect the AK processes (PutJPin). Any



increase in this probability helps the inversion by removingmolecules from the K = 3 stack, where the AJ = +A(Pu/Pd)processes tend to equilibrate the inversion. Since these arenot long-range electric-dipole transitions, polar and nonpolarspecies (all other things being equal) are equally effective.Experimentally, this is manifested by our earlier demon-stration that hard collisions are required for this process.

Buffer gases are ordinarily introduced to reduce vibrationalbottlenecking, which in our model is governed primarily byPVU/PVd. In collisional transition processes the net energydefect (the energy transferred from internal to externalcoordinates) must be less than or comparable with kT for theprocess to be rapid. For example, the direct de-excitation ofV3 = 1 of 3CH3F (E 1000 cm-') requires about 104 colli-sions, whereas nearly resonant collisions in the same speciescan go in -1 collision.8 Complex buffer gases have a largedensity of low-lying modes that can sequentially de-excite themixture.

Thus simple considerations lead to the conclusion that thebest buffer gas is a nonpolar, complex species with manylow-lying vibrational states. Furthermore, approximatelyan order of magnitude more of this gas than the lasing speciescan be used before the lasing inversion is seriously reduced.

6. RESULTS-BUFFER GASES

The most direct experimental measure of vibrational bottle-necking is the observation of a transition in the excited-statevibrational pool. In 13CH 3F, we have shown experimentallythat this pool consists of all K 5$ 3 levels. Figure 6 shows theeffect on a pool transition (J = 4-5, K = 2, V3 = 1) of addinghexane to a 1-cm-radius cell that initially contains 15 mTorrof 13CH 3F. Figure 7 shows the same effect in a 2.5-cm-radiuscell that initially contained 36 mTorr of 13CH 3F. In both ofthese cases the addition of He had no observable (<5%) effect.Two important results are immediately apparent withoutdetailed analysis. First, the addition of hexane rapidly relaxesthe excess vibrational population, but helium has little or noeffect. It can also be seen for the pure-gas cases that the ex-cess vibrational population is much greater in the larger-diameter cell, a conclusion that is consistent with wall deac-tivation hypotheses.

These results can be used to do a simple calculation of theprobability that hexane will relax V3 = 1 3CH 3F. A conser-vation argument gives

1.4

E

,1.2 \

0

5 1.1\

0~~~~~~~~~~~~~

1.00 20 40 60 80 100

Total Pressure (mTorr)

Fig. 6. Ratio of the pumped/unpumped absorption coefficient forthe V3 = 1, J = 4-5, K = 2 transition in a 1-cm-radius cell with theaddition of hexane.

C,)

0U

2.2

i.e

1.4

1.0


Fig. 7. Ratio of the pumped/unpumped absorption coefficient forthe V3 = 1, J = 4-5, K = 2 transition in a 2.5-cm-radius cell with theaddition of hexane.

lUII UIi

0.02

0

C,oA

>5

0.01

0.00


Fig. 8. Probability/collision of vibrational decay in the 2.5-cm-radiuscell with the addition of hexane.

R = PVdNex, (10)

where R is the rate at which CO 2 photons are absorbed, PVdthe probability of vibrational decay, and Nex the number ofnonthermal molecules in V3 = 1. We have measured theC0 2-laser power absorbed by pure 13CH 3F and have con-firmed this result in our model calculations of the pump ab-sorption rate R.' Since we are operating in a Doppler-broadened regime and saturation is insignificant, the CO2-laser power absorbed is independent of the buffer-gas pres-sure. Nex is calculated from the data presented in Fig. 7 andthe known Boltzmann population of V3 = 1 levels. The resultof this calculation is shown in Fig. 8. To interpret this graphquantitatively, the relation between per collision and per timemust be specified. To a reasonable approximation all theprobabilities are per collision with 13 CH3F with Pd - 0.167(this definition effectively means that any molecular en-counter that produces a change of quantum state is definedas a collision). This approximation is good because buffergases are 10-20 times less likely to cause a AJ = l transitionthan is 13CH 3F. Thus, with a constant pressure of 13CH 3Fand variable amounts of buffer gas, the data of Fig. 8 shouldhave the form

PVd CPC6 H4, (11)

where C is a constant and PC6H14 the pressure of the hexane.This neglects decay that is due to wall collisions, which isnegligible except at low pressures, and deactivation that is dueto collisions with other 13CH 3F molecules, which is small underall circumstances. These assumptions, which are valid formost reasonable combinations of buffer gas, pressure, and celldiameter, are the crux of the difference between the assertion

I MI I I I

a 20 40 60 80 ioo

I I I I I

20 40 60 80 i00


U. u.


of Chang and Lin5 that a good buffer gas should have a smallmass and the experimental demonstration of Lawandy andKoepf6 of the effectiveness of the relatively heavy SF6. Changand Lin derived mathematically the reasonable result that theaddition of a heavy buffer gas inhibits diffusion of vibra-tionally excited laser molecules to the wall. Although this isclearly true, in the presence of an efficient buffer gas it is alsoinsignificant. In Fig. 8 is plotted this straight line, startingat the constant 3CH 3F pressure of 35 mTorr. At a totalpressure of 70 mTorr, there are approximately equal numbersof kinetic collisions that are due to 13CH3F and C6 H14 . Thefigure shows that at this pressure there are -0.01 transitionsper AJ = +1 collision or -0.2 transitions per kinetic collisionwith hexane. A similar value can be calculated from the datafrom the 1-cm-radius cell, but these calculations are less ac-curate because the effect is smaller. This very fast ratejustifies the assumption above. In fact, so many collisions arerequired for diffusion to the walls under these circumstancesthat the buffer gas could be several orders of magnitude lessefficient and the approximation would still be valid.

Next we consider the direct effect of the buffer gas on thelasing transition. In order to decouple effects that are due tovibrational bottlenecking and to concentrate on the colli-sionally induced AJ = ± 1 transitions, we initially started with15 mTorr of 13CH 3F in the 1-cm-radius cell. As can be seenfrom Fig. 6, the vibrational pool is only moderately enhancedunder these conditions. Figure 9 shows the effect of addinghexane on the J = 5-4, K = 3, V3 = 1 lasing transition. Thisfigure shows that all pressures of hexane reduce the laser gain.Also shown on this plot are the results for the addition of Heas well as our earlier results for pure 13CH 3F. It can be seenthat He and hexane have similar effects, whereas the effectof additional 13CH3F is much larger. This is due to the verylarge cross section, caused by long-range dipole-dipole forces,for AJ = +1 transitions induced by collisions between 13CH3Fmolecules. A detailed interpretation of the effects of adding13CH 3F requires use of the model discussed above because theadditional 13CH 3F causes increased pump absorption, largerunpumped millimeter-wave absorption, etc. It should benoted that because of the somewhat different conditions underwhich each of the three experiments was run, the three datapoints at 15 mTorr do not coincide.

The process quantified by Pout cannot be treated withoutthe use of the complete model and fitting of the entire data

*set. We have outlined these procedures above and discussedthem in detail elsewhere.' Since Pout is really the ratio of

86

a

E

0

.92

a

-4

-8

-12

-16


Fig. 9. Ratio of the pumped/unpumped absorption coefficient forthe V3 = 1, J = 4-5, K = 3 transition in the 1-cm-radius cell with theaddition of hexane (), He (), and 13CH3F (X).

i.e

0

0

0. 0.8

0.4 I I I20 40 60 80 100


Fig. 10. The change in probability of a molecule leaving the K = 3stack as a function of the addition of a buffer gas. The O's showhexane, the &'s He.

Pout/Pd, Fig. 10 shows that this ratio changes from -0.6 forpure 13CH 3F to -1.3 for 13CH 3F diluted in either hexane orHe. We have previously shown that Pout is essentially aconstant with the addition of 13CH 3F. This result is strongevidence that a molecule-molecule process, such as the oneproposed in Eq. (1), is responsible for Pout as well as Pd. Thisis because the addition of more of the same gas simply in-creases the two relaxation rates in the same proportion,thereby keeping the ratio constant. However, if a foreign gaswithout a dipole moment is added, it can be relatively moreefficient at inducing the Pout process than the Pd process.Quantitatively,

Pout(mixture) [N(13 CH 3F) + N(buffer)]= Pout(13 CH 3F) N(13CH 3F) + Pout(buffer) N(buffer)

or

Pout(buffer) Pou t(mixture)Po u t(1

3 CH3 F) Pout(13 CH3 F)

N(13CH 3F) + N(buffer) N(13CH 3F)N(buffer) N(buffer)

where Pout(buffer) is the probability that a collision with abuffer-gas molecule will cause a molecule of 13CH3F in K =3 to relax into the K 3 pool and Pout(13CH 3F) is similarlydefined. Fitting this dependence to the data in Fig. 10, wefind that Pout(buffer)/Pout(1 3CH 3F) = 2.4. Any physical in-terpretation of this number should be made with some cautionbecause Pout is correlated with AJ > 1 processes that are notincluded in the model.

It is interesting to note that although the addition of buffergas to the 12CH 3F laser resulted in an increase in its poweroutput, our experimental results with 3CH 3F do not show asimilar increase. Figure 9 shows that the addition of eitherhexane or He reduces the gain. In fact, this is predicted byour earlier results on pure 13CH 3F in which we concluded thatno vibrational bottleneck existed in our experiments. Thus,although we have shown that hexane efficiently depopulatesthe excited vibrational state, this population did not adverselyeffect the system. However, the addition of hexane doesequilibrate the lasing transition.

7. RESULTS-SPECTROSCOPY

There has been comparatively little work in the shorter-mil-limeter- and submillimeter-wave spectral region and even lesshigh-resolution gas-phase spectroscopy. As a result, the basic

(12)



Table 1. Spectral Constants of 3CH3F (MHz)

Constant This Worka Freund et al.b

Ground stateB 24 862.6427(30) 24 862.36(1)Dj 0.057 683(51) 0.0566(85)DJK 0.42 441(10) 0.407(35)

Excited stateB 24 542.1324(49) 24 542.07(43)Dj 0.055 156(82) 0.056(12)DJK 0.47 788(22) 0.464(24)

a The standard deviation in terms of the place value of the last digit is shownin parentheses.

b Ref. 9.

Table 2. Measured Frequencies of 13CH3F (MHz)

Transition Observed -J - J' K Observed Calculated

Ground state3-4 0 198886.394 0.019

1 198882.982 0.0032 198872.803 0.0093 198855.818 0.000

4-5 0 248597.601 0.0151 248593.330 -0.0112 248580.614 0.0053 248559.322 -0.0674 248529.693 0.012

5-6 0 298301.933 0.0591 298296.749 -0.0332 298281.489 -0.0143 298256.027 -0.0124 298220.380 -0.0095 298174.578 0.025

V3 = 1 Excited state3-4 0 196322.950 0.011

1 196319.084 -0.0322 196307.671 0.0233 196288.526 -0.006

4-5 0 245393.735 -0.0111 245388.899 -0.0682 245374.646 0.0153 245350.788 0.0514 245317.303 0.018

5-6 0 294457.986 0.0521 294452.160 -0.0402 294434.983 -0.0133 294406.397 0.0734 294366.106 -0.074

spectroscopic parameters of important species, including13CH 3F, are only poorly known. Tanaka and Hirota9 havemeasured the J = 0-1 transitions of 3CH 3F in both theground and V3 = 1 excited vibrational states. However, theywere unable to calculate spectral constants because the ad-ditional lines that are necessary fall at higher microwavefrequencies. Freund et al. 10 calculated the spectral constantsshown in Table 1 from a combination of their laser Stark re-sults and microwave results.

Table 2 shows the transition frequencies measured in thiswork. Both the ground-state lines and the excited-state lineswere observed without laser pumping. As pointed out in our

earlier paper,' the measured frequency of the J = 4-5, K = 3,V3 = 1 line at 245 350.807 MHz represents a frequency for thelaser that is unbiased either by pump offset effects or by cavitypulling effects. Table 1 shows the spectroscopic constantsthat are calculated from these observations.

8. SUMMARY

In this paper we have reported the use of millimeter-wavespectroscopy to study the effects of buffer gases in the 13CH 3Flaser. This technique produced important new types of ex-perimental data that were analyzed in the context of a colli-sional energy-transfer model that we had previously proposed.It was shown that the nonpolar He and hexane both madeapproximately equal contributions to the AJ = 1 processesthat tend to equilibrate the lasing transition but that thesecontributions were substantially smaller than those made bythe 3CH 3F itself. On the other hand, hexane was shown tovery efficiently (-every five collisions) relax vibrationallyexcited 13CH 3F, whereas He made no observable contribution.Most importantly, this work and that previously reporteddemonstrate the validity of the proposed model and its abilityto account quantitatively for a large amount of detailed andvaried experimental data. It is significant that only a smallnumber of adjustable parameters were required and that ingeneral these parameters have straightforward physical in-terpretations.

ACKNOWLEDGMENT

This work was supported by the U.S. Army Research Officeunder contract DAAG-29-83-K-0078.

REFERENCES

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Documents

Millimeter-wave studies of the ^13CH_3F laser: the effects of buffer gases and the spectroscopy of the laser states