Spectroscopic analysis of the transverse excitedC3llu B3 llg (00) uv laser band of N2 atroom temperature

Alain Petit, Frangoise Launay, and Jodle Rostas

A new high-resolution spectroscopic study of the 0-0 transition (3371 A) in the N 2 Second Positive Systemexcited by a pulsed transverse electrical discharge has been carried out with a 14-m Czerny-Turner spectro-graph. A detailed rotational analysis of the spectrum has pointed out a few misassignments in the earlierwork of Dieke and Heath. The simple model proposed by Patel has been applied to the nitrogen laser inorder to explain the optical gain formation on the different branches. The experimental results are in rea-sonable agreement with the theoretical model.

1. Introduction

Since the first report of lasing action in the nitrogenSecond Positive System in 1963 by Heard,1 this systemhas been extensively studied by several researchgroups.2-9 Even now, many discrepancies remainamong the published results.

The difference affect the number of lines observed,their corresponding wavenumbers, and their spectro-scopic assignment. Several reasons can be put forwardto explain the cause of these differences:

the kind of discharge used (axial or transverse);the reproductibility of pulses;the resolving power of the spectrographs and the

quality of the wavelength calibration;the use of the classifications of Dieke and Heath

without any other assignment determination.It appeared therefore necessary to make new precise

measurements and calculations from high-resolutionspectra recorded with only one pulse and to comparethese results with those published by Massone et al. 6

and Tocho et al.5 who used both kinds of discharge.

II. Experimental Procedure

The spectrograms were obtained using a laser previ-ously described9; basically it consists of a 240-mmchannel in which the transverse discharge is limited by

Alain Petit is with Commissariat A l'Energie Atomique, Centred'Etudes Nucleaires de Saclay, B. P. 2, 91190 Gif sur Yvette, France;F. Launay is with Observatoire de Paris-Meudon, CR 24 CNRS, 92190Meudon, France; and J. Rostas is with Universit6 de Paris-Sud, La-boratoire de Photophysique Moleculaire du CNRS, 91405 Orsay,France.

Received 10 November 1977.0003-6935/78/1001-3081$0.50/0.© 1978 Optical Society of America.

two T-shaped stainless steel electrodes (Fig. 1). Thechannel section is 15 X 5 mm2, and one of the electrodesis connected to a double plane condensator B made offour rectangular copper sheets (Fig. 1) isolated with adielectric (Mylar) of 400-,gm thickness. The secondelectrode is connected to a high voltage spark gap bymeans of the propagation line A, which has a triangularshape and a very low inductance.

The operating conditions for this kind of laser havebeen already described. 9 While the flow rate of the gasin the channel is not critical, the optimum workingconditions are obtained with a 23-kV charge voltage anda nitrogen pressure of 70 Torr.

A previous study9 of the characteristics of this laserhas shown that the pulse duration is 1 nsec at halfmaximum, and energy measurements made by threedifferent methods have given a mean value of about 0.4mJ/pulse (under optimum conditions). The emissionpeak power is about 400 kW without a mirror.

A low-resolution spectrogram (Fig. 2) obtained witha Hilger prism spectrograph (which gives a plate factorof 10 A/mm) shows three bands belonging to the SecondPositive System (C3ll B 3lIg) the most intense las-ing band, located at 3371 A, corresponding to the 0-0transition. Its output intensity represents 99.9% of thetotal light emitted. In Fig. 2, the principal band hasbeen voluntarily overexposed in order to distinguish thetwo others.

High-resolution spectrograms (Figs. 3 and 4) of theprincipal band (0-0) have been recorded at the Meu-don Observatory using the 14-m Czerny-Turner gratingspectrograph usually associated with the solar tower.For this experiment, the spectrograph was fitted witha 200-mm wide, 600-line/mm ruled Bausch & Lombgrating giving a plate factor of 0.122 A/mm in the sev-enth order. With a 23-Am slit width and Q2 Ilford

1 October 1978 / Vol. 17, No. 19 / APPLIED OPTICS 3081

Fig. 1. Laser diagram.

case of a 31l-3lI transition in which no satellite lines areobserved, it is not possible to determine absolute valuesfor the parameters of the two states. It was thereforenecessary to fix the parameters of one of them arbi-trarily. The spin-orbit constant A and the rotationalconstants (B and D) are given in the literature' 6 1 7 forboth states while approximate values for the spin-spinparameters and a have been calculated ab initio byLefebvre-Brion.18 The calculations were thus per-'formed with a frozen upper state and free lower stateparameters and also with the reverse set. As expectedthey lead to the same values for the parameter differ-ences. The results are given in Table II. A detaileddiscussion of the Hamiltonian and the molecular con-stants will be presented in a separate paper.

IV. Discussion of Results

plates, one pulse was enough to saturate some of therotational lines. The resolving power obtained wasabout 670,000 (resolving limit = 0.005 A).

Spectrograms given in the same order by a thoriumelectrodeless lamp excited by a microwave power unitof 2450 MHz were used for wavelength calibration.

The plates were measured with a semiautomaticcomparator" equipped with a Tomkins-and-Fred12photoelectric setting device and connected to a moir6-fringe counter system, giving the plate position to 1Aim. The reference wavelengths were taken from Za-lubas13 and Zalubas and Corliss.14 The wavelengths ofthe unblended lines are accurate to 4±0.001 A (wave-number: 0.01 cm-1).

Ill. Rotational Analysis of the 0-0 Laser Band

The Second Positive group of N2 is one of the mostextensively studied band systems. It arises from theC3ll B3 lg transition. If the A-doubling is not re-solved one expects two intense branches, one P and oneR, in each subband and two weak branches, Q2 and Q3.At high resolution, one should observe the A-doublingin every branch and at the same time, the intensity al-ternation.

In the present work the single-pulse spectrum pre-sents sixty-eight lines. In a preliminary analysis, fol-lowing the practice set in all previous studies, most ofthese lines were assigned following Dieke and Heath'srotational analysis. A closer look at the relative in-tensities, however, showed some inconsistencies in theassignments of the first Q lines. In order to verify therotational analysis of the first lines and the assignmentsof the new ones, we treated the observed line measure-ments by means of Zare et al. 's program.15 This pro-gram uses a nonlinear procedure that employs all themeasured line positions and iteratively compares theirvalues with those calculated from numerically diago-nalized model Hamiltonian with adjustable constants.This procedure permitted us to correct a few mis-assignments in Dieke and Heath's analysis (Table I) andto determine accurately the molecular parameter vari-ations from the C3ll, to the B3 llg state. In the special

A. Reproductibility of the Laser Spectrum

Although the total intensity of the spectrum may varyfrom one shot to another, the number of lasing lines andtheir relative intensities are quite reproducible undernormal working conditions (a charge voltage of 23 kVand a pressure of 70 Torr).

B. Change on the Spectrum upon Charge Voltage

As expected, 9 no change was observed in the laserspectrum as the applied voltage was increased from 15kV to 25 kV, keeping the N2 pressure constant (70Torr).

C. Pressure Dependence of the Laser Spectrum

This study was carried out at seven pressures (15, 30,45,60, 75,90, and 105 Torr), keeping the charge voltageconstant (23 kV). The spectra in Fig. 4 are given as anexample. A competitive effect between P and R

E E EC ~~~~C C

co, 0)0) (0 I

co co, WI

1-0 0-0 0-1Fig. 2. Low resolution uv laser bands.

3082 APPLIED OPTICS / Vol. 17, No. 19 / 1 October 1978

`4_�-� - __

17

18 2

I

173

1 8 17

16

16

i-L1616

115

1516

1515 14

ill77

14

.' II It'd I 1.4 I 11 *_l P~~~ ~~~ ~~~I I A11 III*_ 14 f 113 12 11

_ __ 1i10,1113 12 3370,821 A

1-1

9

10! 3371,147 A

38

9'.3371,434 A

Pi

Fig. 3. Rotational structure of the C3

1U. B 3llg (0-0) uv laser band of N2.

Fig. 4. Pressure dependenceof the laser spectrum.

45

30

3 1 6 5 472 6 5 -4--7 6 5 4 3

1 October 1978 / Vol. 17, No. 19 / APPLIED OPTICS 3083

19 18

tor r

105

75

I' 11 1 1 11' 11 1111111111 . 1 ;

*1 . I i I I . §§ ^ 11 ''

I 11 4ifil 6-3 7

1111111

mCA4

0m

A A A4 r r

0. 0 0 o - A o - 0

w 0 0_

2 1-1 ~~~~ ~~ ~~ . . .0o 0 0 * 0 0- 0 ao o o

.N0,00000 ^000A00 00

-U)

04-)

0V,

4-) a)

.E r

OC>II a)

- O

44-)

0

.,C

UU

a >)E S.

Cr

c C )

o (a

U)4-)

U) r

a) 0t

C d.,.

ua . 4-

.4-)

2 .4-)

> -A,E CU

Cd>)

S.o iwC erCd 0

C d

o a

C

a) I-

a) ,--c

.__

3084 APPLIED OPTICS / Vol. 17, No. 19 / 1 October 1978

N4

N0C

0m

0-i

z

t

cJ

a)

0

0

.00-

N0.-

,

I

-Z

,b

�-00-000�-00

l

I1�

A

I1�II

I

I -

-I

1�1 1� 1�1

I - I. . .

1� It �,;: .11 1.I I

1: 1� 11�I I -I ;�;q

--

I

GI

2

II

1:SI

n

. . . . . . . . . .

:! n 2 .I. C x C .7

1� 1: 11� 1: 1� 1� 1� It

1� 1! 11 � 1� 1� -�,

z -- .1 �, -1 1. �, A. . . . . . . .

4 �. 1;

I 1% 1.

I I I I :;1� t 1� 1! �., 1� -. .

9.11-11�4 111! 1� -� 1: 1� t 1: I 1�1

- . . . . .

-r. .1

. I

. I

.. zI -

1.

-�z

Y-

O oo o O

I115 i

L-1..II I. I

."6

g I

I

-:z

II I

II

I II

4", I.!! .t

zI I- 6.11.

1�

Table II. Parameter Differences (Values In cm-1 ) C 3fl"( v' = 0)-

8 3ng(v" = 0)

A' - A" = -3.106 4 0.007B' - B = 0.1863 0.0001(DI - D")106 = -0.3 ± 0.4a' -a" = -0.041 0.008aet-eat = 0.293 + 0.007a

-= 0.0pI p = 0.0

q'-q = -0.0Po = 29,671.13 ± 0.01

a The absolute values from ab initio calculations wereC = 0.195 E" = -0.52a' = 0.139 a" = 0.126.

branches can be noticed: at high pressures (70 Torr),only the P-branch lines are lasing, up to J = 20; as thepressure decreases, the following lines disappear: P18,P2 17, P2 18, P3 17, P3 18, P3 19, P3 20, and the P,1, P12,and P117 weaken, while the R13, R14, R15, R16, R3 6appear, and the R,7, R24, R34, and R35 become moreintense.

D. Comments on the A-Doubling ObservationThe A-doubling (0.10-0.20 cm-') has only been ob-

served for six pairs of P, lines: P7, P,8, P,9, P114,P115, and P116. We have observed intensity alterna-tion in the Pee and Pff branches as reported by Massoneet al.6 Since these authors claimed that they saw the

A-doublets when they were operating in an axial modeonly, our results show clearly that the observation of theA-doubling does not depend on the excitation modeused.

V. Interpretation

In order to interpret our spectroscopic results, wehave chosen a model proposed by Patel. 9,20 This au-thor first used this simple model to calculate the gaincoefficient in CO2 and CO lasers; then he gave a gener-alized expression for the optical gain on any kind ofelectronic, vibrational, and rotational laser transitions.'9This expression was deduced from a general formula ofthe gain coefficient given by Bennett2 l:

/ln2\ 1/2 A N1 N2 X2al,2 = _ _ _ g (1)

or 7 ) 47r (l 92 APD

where N, and N2 are the population densities in theupper and lower levels, respectively, g, and g2 the sta-tistical weights of the two levels, X12 the wavelength ofthe transition, and vD its Doppler width. In thisformula it is assumed that the transition is predomi-nantly Doppler broadened. If in addition we make thefollowing assumptions

(1) the molecular wave function may be representedas a product of electronic, vibrational, and rotationalwave functions (Born-Oppenheimer approximation),

(2) the molecule is regarded as a rigid symmetrictop,

(3) Hund's case a holds,

a

Gain distribution

calculated for a=1.2

- slow

h-y4-*4 fast

a I

0

0

rotational relaxation0

Ce

0

a

0o

10 20 30 J

Fig. 5. Gain distribution calcu-lated for a = 1.2 for slow and fast

rotational relaxations.

10 20 30 J

1 October 1978 / Vol. 17, No. 19 / APPLIED OPTICS 3085

., .I I

R2

.~~,

.*

i , .

-

III II

Q3-

k��

II

(4) the rotational populations within a given vibra-tional level are described by a Boltzmann distributioncorresponding to the temperature Trot, Eq. (1) may bewritten

a12 = Qv' USrrN Sj'rot

I--B-hcJ'(J' + 1)-Trot L- kTrot I

V'rot F-B,'hc0Y(' + 1)]exp I kT',0 t I

B,,hcJ'(J" + 1)1exp kTro

[ B,~hcg'(Q" + 1)exp kT'o

with=4irc

3 Se (F 0'0')q 0'0S

3k(27rkTmaulM)1/2

and a (coefficient of inversion) = (B,,Nv)1(BvNv,)where the quantities denoted by a single prime refer tothe upper operating state and those with a double primeto the lower, SJJ" is the Honl-London factor, qv'v" theFranck-Condon factor for the 0-0 band, Se (IV6' ) theelectronic transition moment, Tmol the Maxwell tem-perature, Nv the total population of the vibrationallevel, and Bv, h, c, k, J, Q correspond to the usualquantities.

Also, since we have shown9 that the excitation of theoperating levels is governed by direct electron impact,and the ground state population is constant while thedecay rate of the upper levels is determined by spon-taneous emission, we will assume that Nv, and Nv6 donot depend on the gas temperature.

According to existing data on the radiative lifetimeof the C3 II, state (20 nsec at 70 Torr)9 and the rota-tional relaxation rate (5.10-7 sec at 1 Torr),2 2 twolimiting cases of rotational relaxation can be expecteddepending on the pressure used in the channel:

(a) At low pressure, rotational relaxation cannot takeplace during the time of laser action (slow rotationalrelaxation). In this case, the distribution over the ro-tational sublevels of the excited states reproduces (if weassume a direct electronic excitation from the groundstate) the population distribution of the ground state,thus we have T' t = TmolBv"/Bo and Trot = TmolBv/Bo,where Bo is the rotational constant for the groundstate.

(b) At high pressure, the rotational relaxation is muchfaster than the radiative lifetime, and a Boltzmanndistribution is established over the rotational levels ofevery vibrational level. In that case T' t = Trot =

Tmol.Calculations have been performed in the two cases

with the coefficient of inversion a varying from 0.95 to1.5. The best agreement with the observed intensitydistribution in the spectrum has been obtained for a =1.2 (Fig. 5); we can notice:

P branches: at high pressure (70 Torr), there is nostimulated emission for J > 20 as shown on the spec-trum given in Fig. 3. The line of maximum intensity isP8 , in agreement with our calculations.

Q branches: one observes a single Q line, Q32, whichis indeed the strongest Q line predicted from calcula-tions.

The R branches exhibit an anomalous intensity dis-tribution since there are three predominant lines: R24and R34, which overlap, and R17 (tentative assignmentfor this line). The intensity calculations predict thesame intensity maximum for R,, R2, and R3 at J = 4.Actually the observed R24 and R34 lines are muchstronger than expected while R14 is very weak. Thecalculations also explain that we have seen only a fewR lines since they predict that only 6 or 8 (depending onthe relative rotational relaxation time) should be ob-served (Fig. 5).

The above results are in good agreement with thosepublished by Kaslin and Petrash23 who carried out asimilar study on the 1-0 band of C3llU -> B3llg tran-sition observed at low temperature. Like these authorswe cannot draw any conclusions about the relaxationprocess (fast or slow) operating here.

This work shows therefore that the theoretical modelgiven by Patel to interpret the spectra from CO2 and COlasers can explain the N2 laser spectra as well. Thissimple model may be of help in understanding the gaindevelopment in this type of laser. It explains the ne-cessity of working at as low a temperature as possibleand of avoiding a high repetition frequency of thepulses, since this could lead to a significant increase inthe gas temperature and, therefore, a decrease of thegain in the active medium.

There are still, however, two results which cannot beexplained: some anomalies in the intensities of thelines; the competition effect between the P and Rbranches when the pressure decreases.

We plan to conduct further experiments at low N2pressure and, on the other hand, to test Patel's modelto the hydrogen laser in the near future.

The authors are greatly indebted to R. N. Botter forhis pertinent comments and helpful suggestions on thiswork. They express their thanks to J. Sutton for hiscritical reading of the manuscript. Finally they aregrateful to P. A. Goujon for his help during the experi-ments and to the Tower Staff for their kind hospital-ity.

References1. H. G. Heard, Nature 200, 667 (1963).2. V. M. Kaslin and G. G. Petrash, Pisma 3,88 (1966) [JETP Lett.

3, 55 (1966)].3. T. Kasuya and D. R. Lide, Jr., Appl. Opt. 6, 69 (1967).4. J. H. Parks, D. Ramachandra Rao, and A. Javan, Appl. Phys. Lett.

13, 142 (1968).5. M. Gallardo, C. A. Massone, and M. Garavaglia, Appl. Opt. 7,2418

(1968).6. C. A. Massone, M. Garavaglia, M. Gallardo, J. A. E. Calatroni, and

A. A. Tagliaferri, Appl. Opt. 11, 1317 (1972).7. I. N. Knyazev, V. S. Letockhov, and V. G. Movshev, Opt. Com-

mun. 6, 250 (1972).8. J. 0. Tocho, H. F. Ranea Sandoval, A. A. Tagliaferri, M. Garav-

3086 APPLIED OPTICS / Vol. 17, No. 19 / 1 October 1978

aglia, M. Gallardo, and C. A. Massone, Nouv. Rev. Opt. 5, 319(1974).

9. A. Petit, Note CEA-N-1927 (1976).10. G. H. Dieke and D. F. Heath, Johns Hopkins Spectroscopic Rept.

17, Baltimore (1959).11. F. Launay, in Proceedings of the International Conference on

Image Processing Techniques in Astronomy, Utrecht, March1975 (Reidel, Dordrecht, Holland, 1975).

12. F. S. Tomkins and M. Fred, J. Opt. Soc. Am. 41, 641 (1951).13. R. Zalubas, J. Res. Nat. Bur. Stand. Sect. A: 80, 221 (1976).14. R. Zalubas and C.H.Corliss,,J.'Res Nat. Bur. Stand. Sect.'A: 78,

163 (1974).15. R. N. Zare, A. L. Schmeltekopf, W. J. Harrop, and D. L. Albritton,

J. Mol. Spectrosc. 46, 37 (1973).

16. B. Rosen, International Tables of Selected Constants 17,Spectroscopic Data Relative to Diatomic Molecules (Pergamon,Oxford, 1970).

17. A. Lofthus and P. H. Krupenie, J. Phys. Chem. Ref. Data 6,113(1977).

18. H. Lefebvre-Brion, Laboratoire de Photophysique Moleculairedu CNRS, France; private communication,(1977).

19. C. K. N. Patel, Phys. Rev. A 136, 1187 (1964).20. C. K. N. Patel, Phys. Rev. 141, 71 (1966).21. W. R. Bennett, Appl. Opt. Suppl. 1, 24 (1962).22. L. V. Leskov and F. A. Savin, Usp. Fiz. Nauk. 72,741 (1960) [Sov.

Phys. Usp. 3, 912 (1960)].23. V. M. Kaslin and G. G. Petrash, Zh. Eksp. Teor. Fiz. 54, 1051

(1968) [Sov. Phys. JETP 27, 561 (1968)].

Meetings ScheduleOPTICAL SOCIETY OF AMERICA

2000 L Street N.W., Washington D.C. 20036

30 October-3 November 1978 ANNUAL MEETING OPTICALSOCIETY OF AMERICA, San Francisco Information: J. W.Quinn at OSA or CIRCLE NO. 53 ON READER SERVICECARD

9-10 November 1978 OPTICAL FABRICATION ANDTESTING WORKSHOP, Dallas, Texas Information: J. W.Quinn at OSA or CIRCLE NO. 55 ON READER SERVICECARD

6-8 March 1979 TOPICAL MEETING ON OPTICAL FIBERCOMMUNICATION, Washington, D.C. Information: J. W.Quinn at OSA or CIRCLE NO. 56 ON READER SERVICECARD

2-6 July 1979 NINTH INTERNATIONAL LASER RADARCONFERENCE, Munich, West Germany Information: J. W.Quinn at OSA or CIRCLE NO. 64 ON READER SERVICECARD

7-12 October 1979 ANNUAL MEETING OPTICAL SOCIETYOF AMERICA, Rochester, New York Information: J. W.Quinn at OSA or CIRCLE NO. 54 ON READER SERVICECARD

1 October 1978 / Vol. 17, No. 19 / APPLIED OPTICS 3087