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OPTOGALVANIC DETECTION OF OPTICAL PUMPING

M. Pinard, L. Julien

To cite this version:

M. Pinard, L. Julien. OPTOGALVANIC DETECTION OF OPTICAL PUMPING. Journal de

Physique Colloques, 1983, 44 (C7), pp.C7-129-C7-136. �10.1051/jphyscol:1983711�. �jpa-00223268�

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JOURNAL DE PHYSIQUE

Colloque C7, suppldment a u n O 1 l , Tome 44, novembre 1983 page C7-129

OPTOGALVANIC DETECTION OF OPTICAL PUMPING

M. Pinard and L . J u l i e n

Laboratoire de Spectroscopie Hertzienne de Z'E. N.S., 4 , Place Jussieu, Tour 12 l e r i t a g e , 75230 Paris Ceder 05, France

RQsumd

-

Nous avons d d t e c t d , p a r une mQthode optogalvanique, l e s o b s e r v a b l e s c r Q 6 e s p a r pompage o p t i q u e dans l e s Q t a t s m s t a s t a b l e s du nQon. Come avec une mdtho- de de d 6 t e c t i o n o p t i q u e , des signaux r e l i Q s 2 l ' o r i e n t a t i o n ou P l ' a l i g n e m e n t d l e c - t r o n i q u e ou n u c l Q a i r e peuvent S t r e obtenus. Les mdcanismes r e l i a n t l e s signaux opto- galvaniques 2 des o b s e r v a b l e s non s c a l a i r e s s o n t d i s c u t d s . L'dtude des p r o f i l s des signaux obtenus quand deux f a i s c e a u x de pompage de p o l a r i s a t i o n s moduldes s e propa- g e n t en s e n s opposQs dans l a c e l l u l e montre que l e mdcanisme dominant e s t un e f f e t de pompage du second o r d r e q u i i n d u i t une modulation d e l a p o p u l a t i o n de l ' d t a t mQ- t a s t a b l e .

A b s t r a c t

-

We have used a n o p t o g a l v a n i c method t o d e t e c t o b s e r v a b l e s induced by o p t i c a l pumping i n m e t a s t a b l e s t a t e s of neon. A s w i t h o p t i c a l methods s i g n a l s a r e o b t a i n e d due t o e l e c t r o n i c and n u c l e a r o r i e n t a t i o n o r alignment. D i f f e r e n t mechanisms a r e d i s c u s s e d from which o p t o g a l v a n i c s i g n a l s r e l a t e d t o non-scalar o b s e r v a b l e s may o r i g i n a t e . P r o f i l e s o b t a i n e d from frequency sweeps of two polarisation-modulated c o u n t e r p r o p a g a t i n g pumpbeamsindicate t h e dominant mechanism i s a second-order pum- ping e f f e c t which induces a modulated d e p l e t i o n of t h e m e t a s t a b l e s t a t e .

I

-

INTRODUCTION

The o p t o g a l v a n i c e f f e c t i s now well-known t o be a v e r y s e n s i t i v e method i n l a s e r spectroscopy. A gas d i s c h a r g e i s i r r a d i a t e d a t a wavelength corresponding t o a n op- t i c a l t r a n s i t i o n o r i g i n a t i n g i n an atomic ( o r molecular) l e v e l populated i n t h e d i s - charge ; a n impedance change c a n t h e n be observed r e l a t e d t o changes of atomic i o n i - s a t i o n r a t e s i n t h e d i s c h a r g e . Atomic i o n i s a t i o n i s o f t e n due t o c o l l i s i o n s of e l e c - t r o n s on atomic e x c i t e d s t a t e s A*

A*

+

e- + A +

+

2e- ( 1 )

and o p t i c a l e x c i t a t i o n , which c a r r i e s atoms t o more e a s i l y i o n i s a b l e e x c i t e d s t a t e s , i s u s u a l l y a s s o c i a t e d w i t h a d e c r e a s e of t h e d i s c h a r g e impedance ( a b s o r p t i o n i n c r e a - s e s t h e number of e l e c t r o n s produced).

Because m e t a s t a b l e s t a t e s p l a y a n i m p o r t a n t r o l e i n t h e i o n i s a t i o n p r o c e s s e s , t h e o p t o g a l v a n i c e f f e c t i s p a r t i c u l a r l y l a r g e when t h e absorbing s p e c i e s i s a m e t a s t a b l e atom. Optogalvanic s i g n a l s produced by t h e d e p l e t i o n of m e t a s t a b l e s t a t e s i n neon h a = been e x t e n s i v e l y s t u d i e d . I n a d d i t i o n t o p r o c e s s ( I ) , which has a l r e a d y been r e p o r t e d , Penning i o n i s a t i o n can g i v e an important c o n t r i b u t i o n through t h e p r o c e s s

Ne' + ~ e * + Ne+ + Ne + e- (2)

where Ne* and Ne r e p r e s e n t an atom of neon r e s p e c t i v e l y i n a m e t a s t a b l e s t a t e and i n i t s ground s t a t e . The two p r o c e s s e s g i v e r i s e t o s i g n a l s of o p p o s i t e s i g n s , and f o r small d i s c h a r g e c u r r e n t s t h e l a t t e r p r o c e s s ( 2 ) dominates.

Thus, t h e o p t o g a l v a n i c method has been demonstrated t o b e a s e n s i t i v e method of de- t e c t i n g m o d i f i c a t i o n s of atomic p o p u l a t i o n ~ induced by l i g h t a b s o r p t i o n , b u t one can a l s o t h i n k of u s i n g t h i s method t o d e t e c t non-scalar ( i . e . non-invariant i n r o t a t i o n s ) o b s e r v a b l e s such a s t h e o r i e n t a t i o n o r alignment of a given l e v e l . I t i s indeed w e l l known t h a t , when m e t a s t a b l e atoms a r e o r i e n t e d by o p t i c a l pumping i n a d i s c h a r g e , t h e number of produced e l e c t r o n s i s modified. This e f f e c t has been s t u d i e d i n t h e c a s e

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983711

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JOURNAL DE PHYSIQUE

of the 2 3metastable state of helium [ l ] . ~ ~ It is due to a modification of the Penning cross section resulting from the spin momentum conservation rule. Let us assume, for example, that metastable 23s1 atoms are optically pumped to their sub- level of maximum spin momentum component (MS = + 1) along a given quantisation axis Oz. The Penning collision between two such atoms should be written as

- .

However, such a collision is forbidden since it does not conserve the component along Oz of the total spin momentum. More generally, one understands that the Penning collision probability depends on the relative orientation of the two colliding meta- stable helium. One might think that a similar effect could take place in oriented metastable 3 ~ 2 atoms of neon, although their orientation is not a pure-spin one.

I1

-

DETECTION MECHANISMS OF OPTICAL PUMPING

The mechanisms which may relate non-scalar observables created by optical pumping in a metastable state to the discharge impedance are various. The discharge impedance can be directly related to the atomic alignment when it exists a preferred direction in the discharge. Such an anisotropy may arise either from the electronic motion [2]

or from the atomic diffusion in the cell.

If the discharge is isotropic, two mechanisms may be involved :

(a) In the first one, already mentioned, the ionising collision (2) takes place bet- ween two oriented (or aligned) metastable atoms. We have seen that, due to the total spin momentum conservation in that collision, the ionisation probability is reduced when the atoms have parallel orientations. The number of electrons produced in the discharge then decreaseswhenmetastable atoms are oriented by optical pumping. In the case of aligned atoms the ionisation probability may also vary either for the same physical reason or through a modification of the interaction potential between the two aligned colliding atoms. This mechanism, where the two colliding partners must have interacted with the pumping beam, then allows optogalvanic detection of atomic orientation as well as alignment.

(b) In the second one, the electron density variation is due, through processes (1) or (2), to modifications of metastable-state population arising from optical pumping.

If one considers the theory only to first order in the pumping intensity, optical pumping with a polarisation-modulated beam (of constant intensity) cannot induce a population modulation in the absorbing metastable state. However, it is not true at second order in the pumping intensity, where the population depletion in the meta- stable state is different, for example, for a linearly or a circularly polarised beam. One can then obtain a polarisation-dependant optogalvanic effect associated with atoms which have interacted twice with the pumping beam

".

These possible mechanisms have different physical origins and give optogalvanic effects with different signatures.

(i) If the discharge is anisotropic, the optogalvanic effect can directly detect a non-scalar observable. The signal obtained is proportional to the mean value of this observable and, therefore, to the intensity I of the pumping beam (we only consider here the case of the linear pumping regime).

(ii) If there is not a preferred direction in the cell, the optogalvanic effect pro- ceeds from coupling of two non-scalar observables, of the same tensorial order, cre- ated by the optical pumping. In the case (a), the coupled observables are the two orientations (or alignments) of the two colliding atoms. In the case (b), the orien- tation (or alignment) created by a first interaction between the pumping light and a given atom is coupled, during a second interaction with the same atom, to the ob-

"Such a process, which has been discussed in [3], can be compared with that involved in the polarisation-dependent optogalvanic signal observed by Hannaford and Series

[ 4 ] . In the two cases, the signal does not require anisotropic detection but relies for its detection on the coupling of a non-scalar observable to the total population of the level. This coupling is achieved in their case by stimulated emission (they need partial saturation of the transition) and in our case by a second cycle of op- tical pumping.

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servable of the same tensorial order associated with the absorbed photon. In the two cases, the signal obtained is proportional to the square of the mean value of the orientation (or alignment) ; it thus varies quadratically with the pumping intensity I.

It is then clear that the intensity dependance of the optogalvanic signal allows one to divide the processes which can be involved into two different groups (discharge isotropic or not). Inside each group, other tests permit one to distinguish between processes. For instance, (a) and (b) processes differ by the number of metastable atoms concerned. Velocity selective optical pumping may then be very useful to dis- tinguish (a), where two atoms of different velocities interact, from (b) where only one atom is involved in the optogalvanic effect. In particular, if one uses two counterpropagating pumping beams and detects a crossed effect between these beams, the signal obtained when the laser frequency is swept will be Doppler broadened in the first case and Doppler free in the second case.

111

-

EXPERIMENTAL SET-UP

Pure neon or a mixture of neon and helium is contained in a quasispherical pyrex cell, 12 cm in diameter. The filling pressure (50 mTorr of pure neon in most of the expe- riments) has been chosen to provide a maximum optogalvanic signal. A 50 MHz oscilla- tor produces a weak discharge in the cell by means of two external electrodes, and the laser-induced variations of the discharge impedance are monitored through the correlative changes in the oscillator regime. The optogalvanic signal is obtained by monitoring the grid voltage of the oscillating vacuum tube at the laser beam modulation frequency.

The pumping beam is delivered by a single-mode dye laser which frequency is scanned over atomic transitions of neon. The transitions we used have es~ective wavelengths of 614.3 and 626.6 nm : they relate the two metastable levels 5P2 and 3 ~ 0 (l s5 and

Is3 in Paschen notation), which belong to the Zp53s configuration, to levels of the

~ ~one (respectively to levels 2p6 and Zp5 in Paschen notation). As usual in 5 3 ~ optical pumping experiments, the pumplng beam is expanded before crossing the cell to avoid any optical saturation of the transition. The typical power is then about 1 mW cm-2. Thus, our excitation modifies the orientation and the alignment of the metastable level involved in that transition only. The beam polarisation (or possibly its intensity) is modulated with an electro-optic crystal (for instance at 1.6 kHz) and the optogalvanic signal is monitored through a lock-in d tector at the same fre- quency. The noise associated with this signal is about 8.10-e/ of the tube grid vol- tage for an integration time of 0.3 s.

IV

-

RESULTS

Two different types of experiments have been carried out, using one or two counter- propagating pumping beams.

IV.1

-

Optical pumping with one beam :

In these experiments, the cell was filled with 50 mTorr of pure natural neon and the metastable 3 ~ 2 level of neon was optically pumped using the 614.3 line.

In a first step, the intensity of the pumping beam was modulated so that its effect was to induce a modulated depletion of the metastable state. The optogalvanic signal obtained when the laser frequency is swept through the atomic resonance at

X

= 614.3 nm is represented in Figure l-a. It is very similar to the signal which would be obtained in the same conditions with a fluorescence detectio method. This signal is Doppler broadened so that the two components of 2 0 ~ e and q2Ne present in the cell are not well resolved-SDoppler width 1.3 GHz ; isotopic shift 1.6 GHz). The signal amplitude is about 10 of the grid voltage.

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JOURNAL DE PHYSIQUE

Figure 1

-

(a) Optogalvanic signal obtained with one intensity-modulated pumping beam, when the laser frequency is swept through the atomic resonance at

X

= 6 1 4 . 3 nm.

Two Doppler-broadened components are visible and correspond to the 2 0 ~ e and 2 2 ~ e isotopes present in the cell (pressure 50 mTorr of natural Ne).

(b) Amplitude variation of the signal plotted against the intensity I of the pumping beam (this intensity has been sufficiently reduced so that the pum- ping regime is linear).

The variation of the signal amplitude is plotted against the intensity I of the pum- ping beam in Figure l-b. For sufficiently low intensities, where the optical pumping regime is linear, this amplitude is proportional to I like the depletion of the me- tastable level. We can then conclude that, in our experimental conditions, there is no saturation effect of the optogalvanic signal, which is not surprising because the amplitude of this signal is very small.

Let us also point out that, in our experiment, the depletion of a metastable state produces a decrease of the number of electrons in the discharge (the variation of the tube voltage has a sign opposite to that obtained when one turns the discharge on).

This fact, already reported by many authors, seems to indicate that the Penning collision (2) between metastable atoms is mostly responsible here for the production of electrons in the discharge.

In a second step, the pumping beam intensity has been kept constant but the beam po- larisation was square-wave modulated. We used three possible modulations : (U+, U-) where the beam was circularly polarised alternately left and right hand ; ($,*)

where it was linearly polarised alternately vertically and horizonrally ; and (U+,+) or another similar combination where it was alternately circularly and &inearly po- larised. In these experiments, the cell was set in weak magnetic field B (few hun- dreds milliGauss) either longitudinal, i.e. parallel to the direction of propagation of the pumping beam, or transverse, i.e. perpendicukar to this direction.

Let us first consider the case where the magnetic field was longitudinal (or null).

In that case, the two polarisation modulations (D+, o-) and ($,ff) provided no opto- galvanic signal. A signal was obtained only with a polarisation modulation (@,S) or similar. This result shows that the direction of propagation of the pumping beam is the only preferred direction in our experiment, and explains that no signal could be obtained with the first two polarisation modulations. The optogalvanic signal observed with the (&,S) modulation is reported in Figure 2-a when the laser fre- quency is swept through the

X

= 614.3 nm line. Its amplitude is about 10-4 of the grid voltage, and its profile is very similar to that of the signal of Figure I-a (a stray reflection of the pumping beam inside the cell is responsible for the small peak on the top of the curve).

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(arb. u.) Figure 2 - (a) Optogalvanic signal obtained with a polarisation-modulated pumping beam (alternately linearly and circularly polarised), when the laser frequency is swept through atomic resonance at

X

= 614.3 nm.

(b) Amplitude variation of the signal plotted against the square of the pumping beam intensity (as for Figure 1, the laser intensity is low enough to obtain the linear pumping regime).

We have studied the variation with the pumping beam intensity I of this optogalvanic signal :this variation is shown as a function of in Figure 2-b. We have found that the signal varies quadratically with I, for sufficiently low pumping intensities.

We can thus conclude that, in our experimental situation, the detection mechanism of non-scalar observables (orientation and alignment) is or the (a) or (b) type : no effect of a possible discharge anisotropy appears here.

IV.2

-

Optical pumping with two beams :

In these experiments, two pumping beams from the same laser counterpropagate in the cell, and one only detects a signal which corresponds to crossed effects between the two pumping beams. Such an experiment must clearly distinguish signals proceeding from mechanisms (a) and (b). In the first case, the optogalvanic signal arises from two colliding atoms with different velocities, each one being oriented or aligned by one of the pumping beams : consequently, when the laser frequency is swept, this signal will be broad (its width will be of the order of the Doppler width). In the second case, the signal arises from two interactions of a given atom with the two pumping beams : it will be Doppler free (if we do not take the velocity changing collisions into account).

Two different methods can be used which give the same result : one can modulate the polarisations of the two beams either (D+, 0-1 or (S,") at two different frequen- cies U1 and U2 and detect the signal simultaneously modulated at U1 and U2 : one can also only modulate the polarisation of one beam, (dt, 0-) for example, at frequency a, and use a static polarisation,

a+

or

c,

for the second one. We have indeed seen that no modulated optogalvanic signal appears with only one pumping beam with a modulated polarisation (a', U-) or ($ ,")

.

Any modulated optogalvanic signal obtained

in the same conditions, when a second beam of static polarisation is added, is then necessarily due to a crossed effect between the two beams. In other words, the opto- galvanic signal only depends on the relative polarisation of the two beams (a simi- lar remark is made by ~ Z n s c h et al. [6] who used an analogous experimental arrange- ment).Theoptogalvanic signal is associated only with the atomic orientation when the two polarisations are circular, and with alignment when they are linear.

Two types of experiments have been done. At first, we have used the same cell as abo- ve, filled with 50 mTorr of natural neon : we have thus obtained signals associated

with electronic orientation and alignment in the metastable 3 ~ 2 state. Afterwards, we have replaced this cell by another one which contains 2 1 ~ e and detected signals associated with nuclear orientation and alignment in the metastable 3p0 state.

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JOURNAL DE PHYSIQUE

IV.2.1

-

Detection of electronic observables

-

Figure 3 shows the optogalvanic signal obtained with the first cell when the laser frequency is swept around the

X

= 614.3 nm line when one beam has a static circular polarisation and the other a modulated (a+, 0 - ) polarisation at 1.6 kHz. The signal profile is similar to that obtained in the same cell when one optically detects orientation in an experiment of velocity selective optical pumping.

(

VL 1 GHz

Figure 3

-

Optogalvanic signal due to electronic orientation in the 3 ~ 2 state ob- tained with two counterpropagating pumping beams frequency swept through atomic resonance at

X

= 614.3 nm. One beam has a static circular polarisation and the other a modulated (U+, 6) one at 1.6 kHz. Only crossed-beam pumping effects between the two beams are observed.

The existence in the profile of Figure 3 of a large Doppler-free component shows that process (b) plays an important role in the detection mechanism. This component is associated with atoms of null longitudinal velocity simultaneously interacting with the two pumping beams : for these atoms, the depletion due to crossed pumping effects is different according as the two beams have opposite circular polarisations or not.

The background which appears under the Doppler-free signal may have two origins. As in optical detection of velocity selective optical pumping [ 5 ] [ 7 ] , we may observe through process (b) a signal due to collisions which partially conserve orientation : a metastable atom of longitudinal velocity vz is oriented by one beam, then collides one or several times before interacting with the second beam when its longitudinal velocity is - v,. The background can also be due in part to process (a) where two oriented atoms with different velocities collide.

The same experiment (in a zero magnetic field) can also been carried out with line- arly polarised beams : one then obtains an alignmentisignal. As for orientation, this signal is composed of two parts : a Doppler-free component due to process (b) and a background which can be due to process (a) or (b).

IV.2.2

-

Det ction of nuclear observables

-

The same experiments have also been done on the 'P0 metastable of " ~ e (nuclear spin 7 = 312) using the umping line at

X

* 626.6 nm. The cell we have used was filled with 12 mTorr of 2HNe and 50 mTorr of helium.

In the particular case of nuclear observables, no optogalvanic signal can arise from process (a) : there is no effect of nuclear observables on collision cross cestions.

Only process (b) may play a role.

Figure 4 shows the orientation (4a) and alignment (4b) signals obtained when the laser frequency is swept around

X

= 626.6 nm. One beam has a static polarisation (respectively circular and linear) and the other a modulated one (respectively (a+, a-) and ($,++) at 55kHz.

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1 GHz

Figure 4 - Optogalvanic signals du respectively to nuclear orientations (a) and alignment (b) in the 3 ~ 0 state of "Ne, obtained with two counterpropagating beams frequency swept through atomic resonance at

X

= 626.6 nm. One beam has a static polarisation and the other a modulated one at 55 kHz. Backgrounds arise from colli-

sions of metastable neon atoms on helium present in this cell (12 mTorr of 2 1 ~ e and 50 mTorr of He). In the orientation signal, three direct and three cross over hyper- fine resonances can be seen.

The signal amplitude is about 2.10-5 of the tube grid voltage. Six Doppler-free re- sonances can be seen in Figure (4a) : they are associated with the three hyperfine components of the pumping transition and to the three corresponding cross over re- sonances (the metastable level F = 312 can be connected to the three sublevels F' = 112, 312, 512 of the upper state 2 4 (J = l)).For both observables, the signal profiles look like those obtained under the same conditions by optical detection of velocity selective optical pumping [5] : the resonances have the same sign and the same relative amplitude.

IV.2.3

-

Discussion - In the above experiments, the optogalvanic signals we have obtained for various observables (electronic and nuclear orientation or alignment) have profiles very similar to those obtained with an optical detection method for the same observables. This is not surprising for, if only process (b) plays a role, there is indeed a deep analogy between 3he two types of experiments. Let us consider the case of nuclear orientation of the PO metastable state, where this condition is necessarily fulfilled. A first pumping beam, the polarisation of which is modulated

(a', U-), creates a modulated nuclear orientation for metastable atoms with longi- tudinal velocity v,. In both types of experiments, the second beam which is also circularly polarised (its polarisation may be static or modulated) allows us to de- tect the orientation of atoms having longitudinal velocity

-

v,. In the optical me- thod, this orientation is measured on the second beam absorption, whereas, in the optogalvanic method, the orientation is measured through the population depletion resulting from optical pumping by the second beam. Signals obtained are similar be- cause the measured physical effects (absorption or depletion) are proportional to each other. Both methods then provide signals which have the same properties, and in particular the same profiles when the laser frequency is swept.

Since the similarity between optogalvanic and optical signals is complete in the case where only detection process (b) plays a role, it is then interesting to compare pre- cisely the two types of signals in a situation where the optogalvanic signal may also arise from process (a). We have studied optogalvanic signals associated with elec-

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JOURNAL DE PHYSIQUE

tronic orientation (figure 3) looking for possible discrepancies between the opto- galvanic and optical profiles which might be ascribed to process (a). With the cell filled with 50 mTorr of pure neon and with the same pumping intensity (at

X

= 614.3 nm), we found that optogalvanic and optical signals actually have identical profiles.

As detailed in reference 181, the same result has been obtained in experimental con- ditions where the process (a) efficiency is increased : mixture of Ne and He to re- distribute the orientation over all velocities ; pumping line at 640.2 nm which crea- tes a much smaller population hole in the metastable state 3 ~ 2 . Then we have not ob- served any modification of the Penning ionisation rate due to atomic orientation.

In our experimental conditions, the optogalvanic signal due to non-scalar observa- bles thus arises only from process (b).

V

-

CONCLUSION

We have demonstrated that the optogalvanic method allows one to detect non-scalar observables created by optical pumping in metastable states of neon. Signals can be obtained which are associated with electronic and nuclear orientation or alignment.

We have observed optogalvanic signals arising from a crossed-beam effect between two counterpropagating pumping beams, and shown that the modification of the dis- charge,impedance results from a depletion of the metastable states induced by opti- cal pumping at second order in the intensity. We have studied profiles obtained from frequency sweeps and found that, in these experimental conditions, there is no effect arising from a variation of the Penning collision cross section when the two meta- stable colliding atoms are oriented.

The optogalvanic method using two beams, and the optical method, then give signals which are proportional to each other : in the first case one detects the modification of the atomic population due to the interaction with the second beam, and in the second case one detects the effect of the same interaction on this beam.

Many experiments usually done with an optical detection method can also be perfor- med with an optogalvanic one : velocity selective optical pumping, Hanle effect, etc..

.

REFERENCES

[l] SCHEARER L.D. and RISEBERG L.A., Phys. Lett. 33A (1970) 325 [2] SERIES G.W., Comm. At. Mol. Phys.

2

(1981) 1 9 9

[3] BEVERINI N. and INGUSCIO M., Nuovo Cim. Lett.

2

(1980) 10

[4] HANNAFORD P. and SERIES G.W., J. Phys. B : At. Mol. Phys. 14 (1981) L661 Phys. Rev. Lett. 48 (1982) 1326

Opt. Comm. 41 (1982) 427

[S] PINARD M., AMINOFF C.G. and LALOB F., phy= Rev. (1 979) 2366

[6] HANSCH T.W., LYONS D.R., SCHAWLOW A.L., SIEGEL A., WANG Z.Y. and YAN G.Y., Opt. Comm. 37 (1981) 87

[7] AMINOFF ~ . ~ T a n d PINARD M., S. Physique

43

(1982) 263

[8] JULIEN L. and PINARD M., J. Phys. B : At. and Mol. Phys.

15

(1982) 2881.

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