Population of metastable barium associated with conical emission

15 December 1997

OPTICS COM MUN ICATIONS ELSEVIER

Optics Communications 144 (1997) 315-321

Full length article

Population of metastable barium associated with conical emission G. De Filippo, S. Guldberg-Kj~er, S. Milo~evid ~, J.O.P. Pedersen Niels Bohr Institute, Orsted LaboratoD', Universitetsparken 5, DK-2100 Copenhagen O, Denmark

Received 2 January 1997; revised 1 May 1997; accepted 28 July 1997

Abstract By illuminating barium vapor with a cw broadband laser tuned to the blue of the 6s 1So --, 6p i Pi transition we have observed a red-shifted conical emission. For the same laser detuning we measured a substantial population of the metastable barium levels 5d 3DI. The spatial population distributions appear to be much broader than in the case of zero detuning. The implications of these results on the existing models for conical emission are discussed. © 1997 Elsevier Science B.V. PACS: 42.65.-k; 42.65.Hw; 42.50.Hz Keywords: Conical emission

1. Introduction Since it has been discovered [1] conical emission has attracted a lot of attention as a nonlinear optical phenomenon, associated with the propagation of an intense light beam through a dense medium. Conical emission appears when a laser beam, tuned to the blue of a resonance atomic transition, propagates through a dense atomic vapor. It is characterized by a strong red-shifted light cone in the forward direction defined by a laser beam, and, as described by Pender and Hesselink [2], distinct phenomena are leading to this particular kind of emission. In this work we will report on the special case of a single-photon pump tuned to a single-photon transition in barium. There are several studies on the conical emission near the Ba 6s IS 0 -~ 6p IP l transition [3-8], although most of the work has been performed near the Na 3s ~ 3p transition [9,10] accompained with several theoretical models (see references in Ref. [11]). Most of these models are based on a mixture of four-wave mixing and refraction or include Cherenkov-type emission. However, recent works on Sr point towards serious inconsistencies with the predictions of these models [11]. Recently a comprehensive

i Permanent address: Institute of Physics, HR-10000 Zagreb, Croatia.

model of intense laser light propagation in a fully saturable medium has been presented [12] and found to be in good agreement with experiments on self-focusing and filamentation [13]. Certain experimental conditions lead to beam breakup, which has been proposed [12,13] as a contributing mechanism to cone emission, but a complete model for cone emission is still missing. It is remarkable that all models so far deal with the propagation of intense laser light in a two-level atomic system. At the same time the barium system is well known for the peculiarity that optical excitation to 6p ~.3p~ levels results in the transfer of excitation into lower lying metastable states [14-16]. In this paper we report on the observation of metastable barium atoms populated under the conditions of a near-resonant excitation of the 6 s t S 0 ~ 6ptP~ transition at the same laser detuning where conical emission occurs, and our work thus implies that a two-level model may not be sufficient in a full description that includes both the emitted conical emission and the final population of all atomic levels. Preliminary observation has been made in connection with energy-pooling measurements in barium [17]. In this paper we extend and confirm the earlier results. We use a Ba vapor cell filled with a buffer gas and a broadband cw dye laser tuned to the blue of the 553.5 nm resonance transition. Simultaneously with the observation of a red-shifted cone emission we measure, by means of a barium hollow-cathode lamp, the spatial distribution of

0030-4018/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S 0 0 3 0 - 4 0 1 8 ( 9 7 ) 0 0 4 3 5 - 5

FULL LENGTH ARTICLE

316

G. De Filippo et al. / Optics Communications 144 (1997) 315-321

population density of the metastable levels 5d TD 2, 5d 3D j, and 6p3p2. This paper is organized as follows: The experimental method is described in Section 2. Our results on measurements of metastable state populations and simultaneously on characterization of the conical emission are presented in Section 3. In Section 4 we discuss the physical situation which arises upon the excitation with zero and blue detuning of the laser, and the implications on the propagation of the 553.5 nm light through the medium. Finally conclusions are given in Section 5 together with an outlook for future experiments.

2. Experimental method The experimental arrangement, shown in Fig. 1, has been described in detail in Ref. [17], and thus only a short description will be given here. The barium metal vapor was contained in a cross shaped stainless steel oven of inner radius of 4 cm and a heated region of 10 cm. At our typical working temperature, 865 K, the Ba vapor density was 1.4 × 10 J3 cm -3 determined using the BohdanskiSchins formula [ 18]. The oven was filled with a buffer gas, He or Ar, at pressures up to 100 mbar. Our cell differs from the usually used heat-pipe oven in several ways. For the present experiment the most important difference was that there was no real separation between the barium vapor and the buffer gas. The laser used to irradiate the vapor was a broadband cw dye laser with a bandwidth of approximately 28 GHz. The laser power ranged up to 500 mW. Care was taken to obtain a spatially well defined laser beam, and we used two lenses and an aperture to make a

parallel laser beam of about 2 mm in diameter, A photodiode mounted on a translator in front of the exit window was used to measure the intensity of the fluorescence in the forward direction and to determine the angular spread of the conical emission. The density of metastable atoms was measured by monitoring the transmission of light from an appropriate transition coming from a barium hollowcathode lamp in the direction perpendicular to the incoming laser beam. For that purpose the whole volume of the cell was illuminated by the hollow-cathode lamp. We used a pair of quartz lenses and a periscope to image the light onto the slit of a monochromator and to select the region of the cell from where fluorescence was observed. The same optical path was also used to observe the fluorescence and the conical emission perpendicular to the laser beam. The fluorescence was resolved with a 0.67 m monochromator (McPherson with 1200 g r o o v e / m m grating, blaze 500 nm) and detected by an EMI 9893Q/350B photomultiplier. To determine the spatial distributions of the metastabte states the monochromator was set to the desired wavelength and the transmission of the light from the hollowcathode lamp was recorded by a lock-in amplifier as a function of the laser wavelength. The transmission of the hollow-cathode light from different volumes of barium vapour was then sent into the monochromator by moving the end mirror of a periscope. Thus a set of transmission curves for different positions (y) perpendicular to the laser beam was obtained. Simultaneously to this measurement the conical emission in the forward direction was recorded by a photodiode.

M Ar+L

H.

P

~

SM

I

L

>

MC

Tr ChA

L Fig, 1. Experimental setup, A, amplifier; Ar+L, argon ion laser; BaHCL, barium hollow cathode lamp; BC. barium cell; Ch, chopper; ChA, channel analyzer; DL, dye laser; L, lens; LI, lock-in amplifier; M, mirror; MC, monochromator; P, periscope; PD, photodiode; PM, photomultiplier; SM, step motor: Tr, translator.

FULL LENGTH ARTICLE

G. De Filippo et a l . / Optics Communications 144 (1997) 315-321

317

3. Results 2,0, To determine the spatial distributions of metastable atoms in the levels 5d3D3 , 5d3D2, 5d3Di, 5dID~ and 6p 3p2 we have used the transitions at 611.1 nm (6p' ~P~ -~ 5daD~), 597.2 nm (6p'3p, ~ 5d3D~), 599.7 nm (6p73p 5d D1), 582.6 nm (6p P~ 5d D e ) and 580.~ nm (6d3De ~ 6 p 3 P 2 ) respectively. The reduced absorption cross sections were calculated using the relevant Einstein coefficients from Refs. [19,20]. Unfortunately the ground state spatial density distribution cannot be measured when the laser beam is present using our hollow-cathode lamp since the only useful line is the 6p ~P~ ~ 6s JS 0 transition which is totally absorbed after passing the barium vapor oven. Fig. 2a shows the absorption of the 6p'3P2 ~ 5d3D3 transition at 611.1 nm versus the laser detuning from the 553.5 nm resonance at the 3' = 0 position, i.e. on the laser axis, We observe a substantial absorption, which indicates a substantial population of 5d3D3, when the laser is detuned to the blue side of the resonance, i.e. when the conical emission is produced, as well as when the laser is on the exact atomic resonance. The measured detuning of the laser wavelength to the blue side of the atomic transition is 0.034 rim, corresponding to a frequency detuning of 30 GHz. Thus, the laser bandwidth was just sufficient to resolve the two resonances. As noted below the wavelength of the conical emission is shifted 0.2 nm to the red side of the atomic transition, which is outside the range of Fig. 2a. In Fig. 2b we show a similar scan for y = 0.74 cm, where the absorption of the 611.1 nm transition is now almost exclusively due to the contribution from the conical emission effect. For each scan we have performed a fit of two Gaussians (shown by the solid line) in order to separate the two contributions. For larger vertical displacements, as in Fig. 2b, the absorption appears only for the conical emission resonance, and we have used the absorption curve obtained in this case to determine the width of about 36 GHz. The width of the absorption curve for the atomic resonance is found to be about 28 GHz which is mainly due to the bandwidth of the laser since the Doppler and collisional broadening are about 1 GHz each [15]. These widths were kept constant throughout the fits of all the absorption curves. The separation between the two peaks was determined by the simultaneous observation of the conical emission and the atomic fluorescence maxima. This parameter was also kept constant. From this fitting procedure we obtained the column densities kL at different vertical displacements from the laser beam. We have assumed cylindrical symmetry and have used an Abel inversion procedure [21] to obtain the radial distributions of the population densities. In Fig. 3 we report the spatial distributions of radial population densities N(r)for the 5d3Dl, 5d3D2, 5d3D3,

a)

1,5-

1,0.

0,5.

0,0. i

.

i

.

i

,

"'1

,

1,5.

i

b)

1,0.

0,5.

0,0. b " ~ I

-0,14

•

i

-0.07

Laser

•

i

i

i

0,00

0,07

0,14

detuning

(nm)

Fig. 2. Absorption of the light at 611.1 nm from the hollow-cathode lamp versus laser detuning. The barium vapor temperature was 866 K and helium buffer gas pressure was 11 mbar. The laser power was 220 mW (a) for y = 0. (b) for y = 0.74 crn perpendicular to the laser beam. On the wings of the signals some ripple is observed arising from electronic noise due to the saturation of the dynamical range of the lock-in amplifier.

5d ID 2 and 6 p 3 ~ metastable states in the case of blue-detuning (0.034 nm) and zero detuning. To obtain the distributions, the column densities kL have been divided by the relevant absorption cross sections. It should be stressed that the Abel inversion procedure is not accurate near the axis and that convergence to zero or infinity is an artifact depending on the slope of the function fitting the few experimental data points close to the axis. We note that the spatial population distributions of the 5d 3D~, 5d 3D 2 and 5d 3D 3 metastable levels are much broader in the case of blue detuning of the laser, and that the maximum of the population is not at the center of the laser beam but is reached at about 0.1-0.4 cm from the laser beam, For the population distribution of the 6p3p2 level the opposite effect is observed: the distribution is broader when the laser is resonant with the 6s ~So ~ 6p 1p~ transition (zero detuning). The first observation indicates that the production of red photons which appear in the cone is connected with the transfer of population to the metastable 5d 3Dj levels. To further characterize the conical emission observed in the present experiment we measured the spatial distribu-

FULL LENGTH ARTICLE

318

G. De Filippo et aL / Optics Communications 144 (1997) 315-321 i ~'

i

"

;;: b) ~, ~:',

"

I

i

7

3D2

,'

6

5

-4

."'..

20-

I

:Z 1,5-

J

-,

4~ "P2

~:' ~

3 .~ t,o-~ Z

,~

,,

\',

"-

-

"!'?,i

%

2,,.~o

,

~" \

~p 2

\

...... ~D

2

m,I' ,.'~ ' . ,

%

.

.

.

.

0

I

0,0

0,2

0,4

0,6

0,8

1,0

0,0

0,2

0,4

r (cm)

0,6

0,8

1,0

r (crn)

Fig. 3, Spatial population distributions of the metastable levels for (a) blue detuning and (b) zero detuning of the laser wavelength. The barium vapor temperature was 866 K and the helium buffer gas pressure was 11 mbar. The laser power was 200 roW,

don of the fluorescence perpendicularly to the laser beam. With the laser set at the cone emission resonance the monochromator was tuned over the region around 553.5 nm, We also determined that the fluorescence in this case was red shifted by 0.2 nm, which is in qualitative agreement with the observations performed by Harter and Boyd [22] in a sodium cell. The measured spatial dependence of the fluorescence is shown in Fig. 4, where we also show the fluorescence measured with the laser at zero detuning. The measured profiles could be satisfactorily fitted by Gaussian curves in both cases of zero and blue detuning. I

'"

!

~

I"

I

'

i

'

I

"

The halfwidths were determined to be 0.23 and 0,26 cm, respectively. We see that the intensity of the fluorescence measured in the direction perpendicular to the laser beam increases by an order of magnitude, when the laser is tuned in the blue of the barium resonance transition by 0.034 nm. We note that in addition to the difference in magnitude the curves shown with open circles and triangles also correspond to spectrally shifted emission, Fig. 5 shows the population density of a metastable state in the center of the volume illuminated by the laser versus the laser power. The density of the 5d3D3 state is

"!

16---

14000

14-

12000

:'

\ 12-

0

"-- 10000-

'2

,,~ 800o I,,w -

O

O

e,I

6000 2

~ "~

::

~

4000-

0

2000-

Z

lO-

"

8-

.

6o

4-.

~

~,~.

O

o'

0i

-0,6

,

I

-0,4

'

r"'",'"i"

-0,2

,

0,0

1

0,2

'

[

,

0,4

i

0,6

Position (cm) Fig. 4. The spatial dependence of the fluorescence around 553.5 nm for blue detuning (open circles) and zero detuning (open triangles). The cell temperature was 866 K and the buffer gas pressure was 10 mbar. The laser power was 70 roW.

0

50

100

150

200

Laser power (mW) Fig. 5, Population density of the 5d3D:~ level versus the laser power for blue (open circles) and zero (open triangles) laser detuning, The temperature of the cell was 866 K, the helium buffer gas pressure was 5 mbar.

FULL LENGTH ARTICLE

G, De Fit ippo et aL / Optics Commltnications 144 (19971 315-321

319

Table l Table summarizing cone emission experiments performed on the barium vapor. In the last row the conditions of the present experiment are given. For pulsed lasers the pulse duration is given, A ~'L is the laser bandwidth. HP indicates heat-pipe oven and C stands for cell, the buffer gas used is also indicated. T is the temperature of the cell and N is the atomic density, The cone half-angle is 0, and 6 L and 6CE are the laser detuning to the blue and the red-shifted detuning in the conical emission, respectively. Not all the data were available Ref,

[3] [4] [5] [6] [7] [8] This work

Laser (ns)

Intensity (kW c m - 21

7 15 l0 10 10 0.015 cw

103 5 10 1.2 × 10 ~ 8 × 10 ~ 1.8 )< 107 0.025

A ~L

Set-up

(GHz) 19 1.2 1-3 5 5

HP mode C + Ar HP + Ar HP + Ar HP + Ar HP C + Ar or He

28

monitored through the absorption o f the 611.1 n m transition versus laser p o w e r for blue and zero detuning. Apparently the dependence is linear in both cases, although with a larger slope for the conical emission resonance. From this observation it is possible to deduce that the processes populating this state are o f different origin in the two cases o f excitation. Fig. 6 shows the angular d e p e n d e n c e o f the conical emission on laser p o w e r and in the inset we report the d e p e n d e n c e o f the intensity o f the light in the cone on the laser power. The cone emission can be seen as a halo on a screen mounted after the cell, The cone angle, which we define as the angle between the laser beam and a straight line from the cell entrance to the area o f the halo with m a x i m u m intensity, is measured using the photodiode mounted on the translator and with the laser detuning set to maximize the cone intensity. The transverse map o f the

N

T

0

8L

~Scl."

(cm- 3)

(K)

(dog)

(GHz)

(GHz)

3 x 1015 4 x lO is t0 ~ 10 ~4 0.5-1 × 111u 0.4 X 1016 1.4 × 10 t3

1343 893 1173 1173 1173

2

980 7.5 5-200 47 50

980 3.8 30 45

30

190

1.5-3.5

0.05 2-4

867

intensity o f the cone light allowed us to determine the amplitude o f the cone. Both cone angle and cone intensity show similar saturation behaviour versus laser power. The cone angle reaches 4 degrees at the laser p o w e r o f 200 m W which was used to obtain the results shown in Fig. 3. In Table 1 some o f the results o f the present experiment are summarized.

4. Discussion

For zero laser detuning, the population created in the 6pJP~ level by laser excitation is transferred towards the 5d3D1, 5d 3D2, and 5d LD 2 metastable levels through radiative processes. Collisional mixing then distribute popu-

25-

4,5 20.

4~0 "'"

±

3,5-

I5.

,.~

,.z

3,0

<

6

10,

'7.

2,5

I

r~

5d 3Dj

ea 2,0 Laser

.....

'

d

0

Laser

'

"" !

100

power

(roW)

power i

150

200

(roW)

Fig 6 Half cone angle dependence on the laser power The barium vapor temperature was 866 K and the helium buffer gas pressure was t0 mbar, In the inset the dependence of the intensity of the cone light as a function of the laser power is shown

!

~

6 s 2 Isll

Fig. 7. Sketch of the energy term diagram for the barium atom, showing the allowed transitions (thin arrows) and the laser excitation (thick arrow).

FULL LENGTH ARTICLE

320

G. De Filippo et at./Optics Cmmmmicationx 144 (1997) 315-321

lation among the 5d3Dj levels. Fig. 7 shows the relevant radiative transitions. The other metastable levels 6p 3pj are populated only by collisions of Ba(6p~Pi) with ground state barium or noble gas atoms [23]. It is well known that collisions with noble gas atoms could populate exclusively the 6p3p2 level [24]. Spatially, the metastable levels are produced mainly within the volume defined by the laser beam. From that region the metastable atoms diffuse [25] and are predominantly deactivated through collisions with the wall of the cell or in energy-pooling collisions [17]. Simultaneously a hole in the spatial distribution of the ground state barium atoms is created. Experiments pumping the 6p 1'3P! states have found [15,28,29] that 60-97% of the ground-state atoms are transferred to the metastable states. For the blue detuning of the laser we observe much broader population distributions (widths of about 0.8 cm) of the 5d 3Dj metastable levels, with the maxima displaced between 0.1 and 0.4 cm from the center of the laser beam. Comparing the spatial distributions at r = 0.4 cm, for blue and zero detuning one can see that for blue detuning larger densities of metastable atoms (5d3D2,0 are produced. Thus the ground state population is depleted also outside the volume illuminated by the laser beam. The lifetimes of the 5d3Dj states are very long (greater than 1 s) [26,27] and using He or Ar as buffer gasses, quenching collisions are negligible [25]. Thus the metastables can diffuse out of the region illuminated by the laser. Comparing Fig. 3b and Fig. 4 we note that the metastables even diffuse out to larger distances than the region covered by conical emission. Nevertheless the dramatic difference in the distribution of the metastables in the cases of conical emission resonance and atomic resonance indicates that production of metastables is favoured when the laser is at the conical emission resonance. This rises the question whether cone emission only consists of slightly red shifted emission around 553.5 nm, or if it also includes an infrared stimulated emission which populates the metastable levels. This, however, could not be checked with the photomultiplier available for the present experiment. The other possibility could be that long-range Ba-Ba and Ba-noble gas molecules [30,31] arise in the excitation scheme where especially 1~ (asymptotically connected with 6p~P~)-0g (asymptotically connected with 6s ~So) difference potential gives the contribution to the blue-wing of the 553.5 nm atomic absorption. The expected resonances in the excitation spectrum [32] could not be observed in the present experiment due to the broad-band feature of the laser used in the excitation. A very interesting consequence of the efficient transfer of population towards the metastable states is a strong spatially dependent depopulation of the ground state atoms which consequently influences the propagation of the photons near 553.5 rim. In Ref. [10] the cone half-angle 0 is predicted by a model that includes the effects of phase matching (producing a small cone half-angle 00) and

effects of changes in the refractive index (6n). The laser beam creates a cylindrical region of saturated atoms having refractive index approximately equal to one and surrounded by ground state atoms with anomalous dispersion profile around the resonance frequency. The quantity 6n is the difference in refractive index between the outer and inner regions. Thus a blue-shifted cone does not appear, because this radiation is trapped inside the saturated region, while red-shifted radiation is refracted out of the region with

O=(Oo + 2~n) '/2.

(1)

We can here add that the change of the ground state distribution causes an additional change in the refractive index that can be expressed, outside resonance, according to the following expression [33]: 2rre -~ .(0),r)

= 1+ - ~t

N/( r)f/~ E

-----.

(2)

i.k 092 -- 0)2

Here fik is the oscillator strength, wik the frequency of the transition i -~ k, and Ni(r) is the population distribution of the level i. Eq. (2) can be used to understand qualitatively the behaviour of the refractive index at the wavelength of the red-shifted photons present in the cone. The main contributions to the sum are due to the resonance transition 6s JS 0 --+ 6d ip~ and also to the 6p3pl -+ 6d3D~ transition at 553.586 nm. The second term can, however, be neglected since the oscillator strength for this transition is an order of magnitude smaller than the resonance line [19]. The approximately cylindrical region corresponding to the laser beam is depleted for ground state barium atoms, since also in the case of blue detuning a large part of the population is transferred to the metastable atoms as described above. Using Eq. (2) we note that the refractive index is smaller in the inner than in the outer region where the density of Ba(6s 1So) is larger. This change in refractive index will thus add to the defocusing of the light and to the appearance of a cone as described by Harter et al. [10]. We have to note here that, in spite of the large redistribution of population, the variation of the refractive index is not large enough so that refraction alone can produce the observed cone angles [11]. The change in population density has also consequences at the resonance frequency (zero detuning), because the intensity-dependentpart of the refractive index is proportional to the population density as shown e.g. in Ref. [12]. Contrary to the assumption in Ref. [12] the population is not constant but may have a dramatic spatial dependence. As a cause of the population of the metastabte atoms with cone emission we can suppose a stimulated Raman scattering process [34,35], where the Stokes wave is ending on the metastable states and a subsequent redistribution due to the collisions.

FULL LENGTH ARTICLE

G. De Filippo et al. / Optics Comntunications 144 I 1997) 315-321

5. Conclusions Conical emission appears under a variety of experimental conditions where laser characteristics and medium properties have a crucial role. Table 1 gives the relevant parameters for the existing experiments on barium, We note that the present work is the only one made with a cw laser. Continuous or pulsed operation makes a significant difference concerning the build up of metastable state population, However, even in a pulsed regime significant metastable state densities are achieved after a laser pulse [36]. Shevy and Rosenbluh [37] have measured the time dependence of the conical emission from a sodium vapor, but in this system metastable states are not present, so we encourage the measurement of metastable state population and conical emission in a pulsed experiment. We have shown that simultaneously to the appearance of the conical emission in barium vapor significant transfer of the population into the metastable levels occurs. This depletes the ground state 6s ~So substantially and is questioning the assumption that such a system can be treated as a pure two-le~.el atom with constant population densities in the modelling of the conical emission. Obviously the production of metastable atoms, that are created during the pumping to the blue side of the atomic resonance, have an influence on the propagation of the light. We propose an experiment using a narrow band pulsed laser to study the time evolution of the conical emission simultaneously with the build up of the metastable state population, This could possibly help to clarify the role of metastable state population in the propagation of a laser pulse through a dense barium vapor.

Acknowledgements The project is supported by the Danish Natural Science Research Council. and one of us (SM) is grateful to the Research Council for the financial support during his stay in Copenhagen. We are also grateful to A. Gallagher and J. Huennekens for sending us their results prior to publication and we thank N. Andersen for useful discussions and for lending us most of the equipment used in this experiment,

References [I] Yu.M. Kirin, S.G. Rautian, A.E. Semenov, B,M. Chernobrod, Pis'ma Zh. Eksp. Teor. Fiz. 11 (1970) 340 [JETP Lett. 1 l (1970) 226]. [2] J. Pender. L. Hesselink, IEEE J. Quantum Electron. QE-25 (1989) 395.

321

[3] C.H. Skinner, P.D. Kleiber, Phys. Rev. A 21 (1980) 151, [4] Ph. Kupecek, M. Comte, B, Visentin. J.-P, Marinier, Optics Comm. 56 (1985) 1. [5] W. Chalupczak, W, Gawlik, J. Zachorowski, Optics Comm. 99 (1993) 49, [6] W, Chalupczak. W. Gawlik, J. Zachorowski, Phys. Rev A 49 (1994) R2227. [7] W, Chalupczak, W. Gawlik, J. Zachorowski, Optics Comm. 1II (1994) 613. [8] M.L. Ter-Mikaelian, G,A. Torossian. G.G. Grigoryan, Optics Comm. 119 (1995) 56. [9] U. Domiaty, D. Gruber, L. Windholz, S.G. Dinev, M. Allegrini, G. De Filippo, F. Fuso, R.-H. Rinkleff, Appl. Phys. B 59 (1994) 525, and references therein. [10] DJ. Hatter, P. Namm, M,G. Raymer, R.W. Boyd, Phys. Rev. Lett. 46 (1981) 1192. [11] R.C. Hart, L. You. A. Gallagher, J. Cooper. Optics Comm. 111 (1994) 331. [12] M.L. Dowell, B,D. Paul. A. Gallagher, J. Cooper, Phys. Rev. A 52 (1995) 3244. [13] M.L, Dowell, R.C. Hart, A. Gallagher. J. Cooper, Phys. Rev. A 53 (1996) 1775. [14] A. Kallenbach, M. Kock, J. Phys. B 22 (1989) t691, [15] E. Ehrlacher, J. Huennekens, Phys. Rev. A 47 (t993) 3097, [16] J. Brust, A.C. Gallagher, Phys. Rev. A 52 (1995) 2120. [17] G. De Filippo, S. Guldberg-Kj~er, S. MiloKevid, J.O.P. Pedersen, J. Phys. B 29 (1996) 2033. [18] J, Bohdansky, H.E. Schins, J. Phys. Chem. 71 (1967) 2t5. [191 P. Hafner, W.H.E. Schwarz, J. Phys. B 11 (1978) 2975. [20] L. Jahreiss, M.C.E. Huber, Phys. Rev. A 38 (1985) 2356. [21] M.M. Prost, Spectrochim, Acta B 37 (1982) 541. [22] D.J. Harter, R.W. Boyd, Phys. Rev. A 29 (1984) 739. [23] G. De Filippo, D. Romstad, S. Gutdberg-Kj~er, S, Milo~;evid, J,O,P. Pedersen, Z. Phys. D 39 (1997) 21. [24] W.H. Breckenridge, C.N, Merrow, J. Chem. Phys. 88 (t988) 2329, [25] R.K. Namiotka, E. Ehrlacher, J. Sagle, M, Brewer. D.J. Namiotka, A.P. Hickman, A.D. Streater, J. Huennekens, Phys. Rev. A 54 (1996) 449. [26] 1. Klimovskii, P.V. Minaev, A.V. Morozov, Opt. Spektrosk. 50 (1981) 847 [Opt, Spectrosc. (USSR) 50 (1981) 464]. [27] J. Migdalek, W,E. Baylis, Phys. Rev, A 42 (1990) 6897. [28] J.L. Carlsten, J. Phys, B 7 (1974) 1620. [29] A.F. Bernhardt, Appl, Phys. 9 (1976) 19. [30] A.R. Atlouche, M. Aubert-Frecon, G. Nicolas, F. Spiegelmann, Chem. Phys. 200 (1995) 63, [31] E. Czuchaj, F. Rebentrost, H, Stoll, H. Preuss. Chem. Phys. t96 (1995) 37, [32] S.G. Diner, I.G. Koprinikov, I.L. Stefanov, Appl. Phys. B 39 (1986) 65. [33] W.T. Luh, Y. Li, J. Huennekens, Appl. Phys. B 49 (1989) 347. [34] A.C. Tam, Phys. Rev. A 19 (1971) 1971. [35] A. Curbellier, S. Liherman, D. Mayou. P. Pillet, Optics Comm. 8 (1983) 105, [36] L. Jahreiss, M.C.E, Huber, Phys. Rev. A 28 (1983) 3382. [37] Y. Shevy, M. Rosenbluh, J. Opt. Soc. Am. B 5 (1988) 1 t6.