Resonant multiphoton ionization of caesium atoms by ultra-short laser pulses at 1.06 μm

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Resonant multiphoton ionization of caesium atoms by ultra-short laser pulses at 1.06 µm

L.A. Lompre, G. Mainfray, C. Manus, J. Thebault

To cite this version:

L.A. Lompre, G. Mainfray, C. Manus, J. Thebault. Resonant multiphoton ionization of caesium atoms by ultra-short laser pulses at 1.06

µm.

Journal de Physique, 1978, 39 (6), pp.610-616.

�10.1051/jphys:01978003906061000�. �jpa-00208792�

RESONANT MULTIPHOTON IONIZATION OF CAESIUM ATOMS BY ULTRA-SHORT LASER PULSES AT 1.06

_03BCm

L. A. LOMPRE, G. MAINFRAY, C. MANUS and J. THEBAULT Service de

Physique Atomique,

Centre d’Etudes Nucléaires de

Saclay

BP n° 2, 91190

Gif-sur-Yvette,

France

(Reçu

^le

10 janvier

^1978, révisé le 3 mars 1978,

accepté

^{le 6 mars}

1978)

Résumé. ²⁰¹⁴ L’objet ^{de cet article est} d’étudier l’ionisation à quatre

photons

d’atomes de césium,

en accordant la fréquence ^{du laser} pour qu’il ^se produise ^une excitation résonnante à trois photons ^du

niveau 6F. L’expérience ^a été effectuée en utilisant une impulsion laser de durée 1,5 ns, 50 ps ^et 15 ps, de longueur ^d’onde variable, ^à 1,06 03BC, dans la gamme d’éclairement 108-109 W.cm-2. Le caractère résonnant du _processus d’ionisation

multiphotonique

subsiste, ^{même avec}

l’impulsion

^la plus

courte de 15 _ps. Néanmoins le comportement à la résonance est modifié par ^un effet temporel ^{en bon}

accord avec les prévisions théoriques. ^Le déplacement ^en énergie 0394E de la résonance varie linéairement

avec l’éclairement laser I ; ^{0394E =} 03B1I, ^{avec 03B1 = 2}

cm-1/GW.cm-2.

Ce résultat confirme des mesures

antérieures obtenues avec une impulsion laser monomode de durée 35 _ns, et se révèle en excellent accord avec le calcul du déplacement de la résonance sous l’influence du champ ^laser.

Abstract. ²⁰¹⁴ This paper reports ^the

four-photon

ionization of caesium atoms when the laser

frequency

^{is tuned}

through

^{the resonant} three-photon transition 6S ~ 6F. This experiment ^was performed by using ^a

tunable-wavelength

bandwidth-limited subnanosecond laser pulse ^{at 1.06} 03BCm, in the 108-109 W.cm-2 laser intensity range. Pulse widths of 1.5 ns, 50 _ps, and 15 _ps were used.

The resonant character of the multiphoton ionization process ^was observed, ^even with the shortest

pulse ^{of 15} ps. Nevertheless the influence of a temporal effect is demonstrated according ^to theoretical

predictions. ^{The resonance} shift 0394E of the 6S ~ 6F transition energy ^was found to be linear with the laser intensity ^I within the range 108-109 W.cm-2. 0394E ⁼ 03B1I, ^{with 03B1 = 2}

cm-1/GW.cm-2.

^This

result confirms previous measurements performed ^with

single-mode

^{35 ns laser} pulses ^{and is in} very

good agreement with calculated resonance shifts.

Classification Physics ^Abstracts

32.80K

1. Introduction. ^-

Multiphoton

ionization _pro-

cesses have been the

subject

^{of a} considerable number of theoretical and

experimental

^works

[1].

^Multi-

photon

ionization of atoms

emphasizes

both atomic

properties

and laser

properties, namely frequency, coherence,

^and

polarization.

^In

particular,

^{the multi-}

photon

ionization

probability

^{of an} atom, ^{as a function} of the laser

frequency,

^{exhibits a}

typical

^resonant

character when the _energy of an

integral

^{number of}

photons

^{is close to the} energy of an atomic level

satisfying

^the

parity

selection rules.

Thus,

^{a resonant} enhancement of five orders of

magnitude

^{in the four-}

photon

ionization

probability

of caesium has been observed

by using

^a

single-mode,

tunable-wave-

length, Q-switched Nd-glass

^{laser at} intensities of

108-109 W . cm- 2 [2]. Although

^resonant

multiphoton

ionization

experiments

have been carried out with cw or with

long pulses (10-8 s)

^from

Q-switched lasers,

resonant processes have not yet been studied with _very short laser

pulses (10-11 s). Recently,

^a theoretical

paper

emphasized

^the

importance

^{of the}

pulse

^duration

in a resonant

multiphoton

ionization _process

[3].

^This

model can be

explained

^{in terms of a} characteristic time of the resonant

multiphoton

ionization channel which could be

longer

^{than the}

^10-15

^s time scale of the direct non-resonant

multiphoton

ionization channel.

This characteristic time can be different

depending

^on

the

specific

conditions of the resonant process. It ^can be connected either to the transition from the

ground

state to the resonant state, ^{or to} the transition from the resonant state to the

continuum,

^{or more}

generally

^{to a}

specific

^Rabi

frequency.

^{When a} very short laser

pulse (10- Il s)

^is

used,

^{it can be}

expected

^{that in some}

specific

^{cases, the resonant} process does not have

enough

^{time to take}

place during

^{the laser}

pulse

duration. Thus the

multiphoton

ionization _process would be

governed only by

^the non-resonant process.

The

four-photon

ionization of caesium atoms, when the laser

frequency

^{is tuned}

through

^{the resonant}

three-photon

transition 6S --+

6F,

^{has been}

carefully

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01978003906061000

611

described in the 10- 8 s time scale and _gave evidence of a

typical

^{resonant character}

[2, 4J.

The purpose of the present ^{work is to}

investigate

^{whether or not this}

resonant process is still observable ^{on the 10 -}

9 -10 - Il

s

time scale. It should be

pointed

^out that the simul- taneous influence of resonance and coherence effects is a difficult

problem

which is still far

from _being

resolved at the

present

^time.

Consequently,

^the

investigation

^{of a resonant}

multiphoton

^ionization

process

requires

^a bandwidth-limited laser

pulse

ⁱⁿ order to avoid

having

^{to take into account the sta-}

tistical

properties

of the laser radiation

[5, 6].

^A

bandwidth-limited

pulse

^is

completely

^{devoid of}

intensity

^or

frequency

modulation since its duration is less than or

equal

^to the coherence time.

2.

Expérimental

^{.method. - 2. 1 THE} LASER SYS- TEM. ^- The laser used in the

present experiment

^is

basically

^{similar to the one described in detail else-}

where

[7].

^The

only

difference lies in that the

Fabry-

Perot etalon is now used in transmission instead of reflection as the

fully reflecting

^mirror.

Figure

^{1 shows}

the main elements of the oscillator. The laser rod is

a

Hoya

^LHG-5

neodymium-phosphate glass,

^with

the

lasing wavelength

^{centred on 10 530}

^Á.

^The

Kodak 9740 saturable

dye

^{is in}

liquid

^{contact with the} output mirror which has a reflection coefficient of 0.65.

In order to generate

reproducible

ps

pulses,

^the

laser bandwidth is narrowed

by putting

^one very

highly dispersive prism

^{in the}

cavity.

^This

prism

^{is set}

at the

angle

of minimum

deviation,

^{and the laser beam}

enters and exits at the Brewster

angle.

^This

gives

^laser

radiation which is

highly linearly polarized.

^This

prism

^{reduces the} spectrum ^{to a width of 5}

Á

which

corresponds

^to bandwidth-limited

pulses

^of

5 ps.

As the

pulse

duration is measured

by using

^a 5 ps resolution streak _camera, the shortest

pulse

^which

can be measured with a sufficient

precision

^{has a}

duration of _{15 ps} which

corresponds

^{to a laser}

bandwidth of 1.5

A.

This is achieved

by adding

^a

Fabry-Perot

^{etalon to the laser}

cavity.

^This

Fabry-

Perot etalon consists of two mirrors which have a

reflection coefficient 0.65 and are

separated by

³⁰ gm.

The

pulse

^{duration can be varied}

by changing

^the

thickness of the etalon.

However,

when the thickness of the etalon is increased to

produce pulse

^widths

longer

^{than 0.3} ns, the free

spectral

range of the etalon becomes too small and several

spectral

^{lines are}

allowed to lase.

Therefore,

^{a second}

intracavity

^etalon

has to be used to select a

single

^line.

2.2 GENERAL EXPERIMENTAL ARRANGEMENT. -

Resonant

multiphoton

ionization of caesium atoms was

performed by using

^an

experimental

arrangement identical to the one

employed

ⁱⁿ

previous

^works

[2, 8].

Briefly, by using

^{a Pockels}

switch,

^a

single pulse

^is

selected from the

early

part ^{of the}

pulse

^train gene- rated

by

^the mode-locked

Nd-glass

oscillator. This

single pulse

^is

amplified by

^two

Nd-glass preamplifiers

FIG. 1. ^- Schéma of the tunable-wavelength mode-locked Nd-

glass oscillator. Dl ^and D2 ^{are circular} apertures. ^{Mirror reflection} coefficient R, ^{= 1 and} R2 ^{= 0.65.}

and then passes

through

^a

spatial

filter before

entering

a

three-stage Nd-glass amplifier.

^{The laser}

pulse

^is

focused into a vacuum chamber

by

^a

planocylindrical

lens of 50 cm focal

length.

The atomic

density

^is

no(Cs)

^{= 6 x}

1010 cm -3

in the focal

region.

^{The ions}

resulting

^{from the laser} interaction with the atoms in the focal volume are extracted with a transverse electric field of 500 V . cm-’ and then detected with an

electron

multiplier.

Three laser parameters ^{have to} be measured _very

carefully :

^{focused laser}

intensity, pulse duration,

^and

spectral distribution.

The focused laser

intensity

^is known from surface determinations within the focal volume

by using photometric

measurements

[2, 8].

^{It should be}

pointed

out that the focal surface varies as a function of the

pulse

^{duration. For}

instance,

^{the focal} spot ^area measured with a 1.5 ns laser

pulse

^is twice that for

a 15 _ps

pulse.

This result can be

explained

^{in terms of}

laser aberrations which _govem the focused

intensity

distribution. As is well

known,

laser aberrations arise

mainly

^from the variation of the refractive index of laser rods with

regard

^{to the}

time-averaged

square of the laser electric field. Then a 15 ps laser

pulse, corresponding

^{to a}

length

^{of 0.45 cm} much shorter than laser rod

lengths,

induces smaller aberrations than a 1.5 ns laser

pulse corresponding

^{to a}

length

of 45 _cm,

longer

^{than the laser rod}

length.

The

temporal

characteristics of the

single pulse

^are

measured either

by

^{a streak camera or a}

photodiode

connected to an

oscilloscope, depending

^{on the}

pulse

time scale. Three different

pulse

^{widths were used}

successively :

^1.5 ns, 50 ps and 15

ps. 1.5

^ns

pulses

^are

analysed by using

^a

photodiode (Radiotechnique

XA

10U3)

^{with 150} ps rise

time;

^this

photodiode

^is

connected to a Ferisol OZ 100B

oscilloscope

^{with a}

bandwidth of 2 GHz. 50 _ps and _{15 ps}

pulses

^are

analysed by using

^a 5 ps resolution streak camera of conventional

design.

Detection is achieved either on a

photographic

^{film or on a TV screen}

[7].

The spectrum ^{of the}

amplified single pulse

^{is ana-}

lysed by using

^a diffraction

grating spectrograph

with a

dispersion

^{of 4}

A/mm

^{and a} resolution of 0.1

cm -l

at 1.06 pm. The usual

photographic plate

^is

replaced by

^the cathode of a TV

pickup

^tube

[7].

^This

method

gives

^{a direct} measurement and control of the laser

wavelength

and bandwidth for each laser

shot,

by using

^a storage

oscilloscope

Tektronix 7633.

As is shown in

figure 2a,

^the

pulse

^{train of the mode-}

locked laser has ^a spectrum

(Fig. 2a’)

which consists of

a set

of evenly spaced sharp

^{lines. On the} contrary, ^the

single pulse

selected from the

pulse

^{train has a smooth}

spectrum ^{which no}

longer

^{consists of}

sharp

^{lines. The}

square

pulse

^{shown in}

figure

^2b

corresponds

^{to the}

switching

^of the Pockels cell which selects a

single pulse

^{in the}

pulse

^{train. This} square

pulse

^{has a Fourier}

transform

F(u). Figure

^2b’

shows ( F(u) I2.

^The

^single

pulse

^{shown in}

figure

^2c in time domain has a spectrum which is obtained

by

the convolution of the Fourier transforms of the two functions shown in

figure

^2a

and 2b. Thus the spectrum ^{of the}

single pulse

^{is a}

smooth spectrum ^{as shown in}

figure

^2c’.

FIG. 2. ^- Time and frequency ^{domain of} (a) ^the pulse train of the mode-locked laser, (b) ^the square pulse corresponding ^{to the selec-}

tion process of a single pulse, ^and (c) ^the single pulse.

3.

Experimental

^{results. - Two}

procedures

^are

possible

^to

investigate

^{the resonant}

multiphoton

ionization of atoms. The first one consists of measure- ments of the laser

intensity required

^for

creating

^a

constant number of

ions,

^{as a} function of the laser

frequency

^{in the}

neighbourhood

^{of the resonance}

[2].

The second one consists of measurements of the number of ions formed as a function of the laser

frequency

^{in the}

neighbourhood

^{of the} resonance, for

a fixed laser

intensity.

^{The second}

procedure

^{has been}

chosen in the present ^{work. The}

experiment

^{which we}

analyse

^{here was}

performed

with three différent laser

pulse

durations : 1.5 _ns, 50 ps and 15 ps, with

respective

bandwidths :2 x

10-2 cm-’, 0. 4 cm-’ and 1.4 cm-’.

3.1 1 1.5 ns AND 50 _ps PULSE RESULTS. ^-

Figure

³

shows a

typical

^resonance

profile

^{obtained with a}

bandwidth-limited laser

pulse

^{of 1.5} ns, ^{at a} laser

intensity

^{of 3 x}

10’ W.cm-2.

The width

(FWHM)

of the resonance

profile

^{is 0.2}

cm - ’,

ⁱⁿ

frequency units,

or 0.6 cm -1

expressed

^{in terms of} energy of the resonant

three-photon

transition 65 - 6F. The reso- nance width is much

larger

^than the laser

spectral

width

(0.02 cm -’ ).

^{The 0.6 cm-’ 1 resonance width is}

FIG. 3. ^- Resonance profile ^{due to the resonant} three-photon

transition 6S - 6F in the four-photon ionization of caesium atoms. Laser intensity ^{7=3 x} 10’ W. cm -2. Pulse duration

i = 1.5 ns. Laser bandwidth _y ⁼ 2 x 10-2 cm-1. The arrow

indicates the frequency ^{of the} three-photon transition 6S -+ 6F derived from spectroscopic ^tables.

mainly

^{due to the} unresolved structure of the 6S --+ 6F

transition,

^{with a} contribution of 0.3 cm -1 ¹ for the

hyperfine

^{structure of the}

ground

^{state and 0.1 cm-l}

for the fine structure of the 6F level.

Furthermore,

there is no

significant

^{shift in the}

position

^{of the}

maximum of the resonance

profile.

^{These results are}

in excellent agreement ^with

previous

results obtained with a

single-mode

^{35 ns laser}

pulse [2].

When a 50 ps bandwidth-limited laser

pulse

^is

used,

resonance effects are still observed. Now the width of the resonance

profile

^is

governed by

^{the laser}

spectral

width

(0.4 cm -1). Moreover,

^the

required

^laser

intensity

^is

larger

^{than with 1.5 ns}

pulses

^{and conse-}

quently

^resonance shifts become

significant.

^The

energy shift of the resonance has been found to be linear with the laser

intensity,

ⁱⁿ

agreement

^with

previous

results obtained with

single-mode

^{35 ns laser}

pulses [2].

3.2 15 ps PULSE RESULTS. ^- It is well known that bandwidth-limited

pulses having

^durations

of approxi- mately

5 ps ^can be

produced

^{at the}

beginning

^{of the}

pulse

train of a mode-locked

Nd-glass

^laser.

However, tunable-wavelength

bandwidth-limited

pulses having

a duration _{of 15 ps} are the shortest

pulses

^{which are}

613

consistent with the

stringent requirements

^{of resonant}

multiphoton

ionization

experiments, especially

^a very

good long-term stability,

^{and a}

reasonably

^accurate

measurement of the

pulse shape

^{with the} 5 ps ^reso- lution of our streak camera. For this _reason,

experi-

mental results obtained with bandwidth-limited _{15 ps}

pulses

^{will now be}

given

in detail.

Figure

^{4 shows four}

resonance

profiles

obtained with four different laser intensities. The

analysis

^{of these}

experimental

^results

obtained with _{15 ps} laser

pulses

^can be summarized

by

^the

following

^remarks.

FIG. 4. ^- The variation of the number of atomic caesium ions as a

function of the laser frequency ^{in vacuum in the} neighbourhood of the three-photon transition 6S --+ 6F. Pulse duration T ⁼ 15 ps.

Laser bandwidth _y ⁼ 1.4 cm-1. Laser intensity : (a)

The arrow indicates the frequency position ^{of the} three-photon

transition 6S - 6F derived from spectroscopic ^{tables. The dashed}

line shows the resonance shift for increasing ^{values of the laser} intensity.

- Resonance effects are still observed. As far as

comparison

^with

theory [3]

^is

concerned,

^{one has to}

calculate

the

^value

of the

^parameter

^0,

^{which is defined}

as : 0 ⁼

E2

_r, where

L-’

is a characteristic

frequency,

and i is the

pulse

^width.

According

^{to our}

experi-

mental

values,

^{0 = 0.1 for I = 1.8 x}

108 W.cm-2 corresponding

^{to the}

figure

^4a. This 0 value corres-

ponds

^{to a} time effect which decreases the

amplitude

of the resonance from 105 to 104.

Unfortunately,

^it

would be difficult to measure this relative variation in the resonance

amplitude.

^{As a matter of}

fact,

^the

ion data shown in

figure

^{4 cover the useful} range of . three orders of

magnitude. Plotting

the entire reso- nance

profile

^{over about} five orders of

magnitude

would have

required questionable extrapolations

^due

to the total ionization of all the atoms in the interaction volume for

large

^{numbers of}

ions,

^and

especially

molecular contributions for small number of

ions,

^as

we shall see later on.

Temporal

effects could

only

^be

observed in the

amplitude

^{of the resonance}

profile

^at

much lower 0

values,

i.e. much shorter

pulse

^durations

which are not

experimentally

^available.

In

fact, temporal

^{effects can more}

easily

be observed from another

point

of view. Theoretical

expressions

from recent calculations

[3, 9, 10, 11 ]

^{show that the}

number of ions

N maxres

^{formed at} the maximum of the

resonance

profile

varies with the laser

intensity

^{I as}

^I’

when

pulse

^{widths are}

long enough

^{as in}

[2] (conti-

nuous

regime)

^{and as I" with} 2 n ^{4 when much} shorter

pulses

^{are used.} These calculations show that

NmaxreS

^{oc 14} within the laser

intensity

range

(108 -109 W . cm-2)

^{used in the}

present experiment.

Figure

^{5 shows the}

experimental law

^of variation of the number of ions

Nmaxres

^{as a function of the laser}

FIG. 5. ^- Log-log plot of the variation of the number of ions

Nres ^{formed at the maximum of the resonance} profile ^{as a function}

of the laser intensity. ^{Most of the} points ^{are on a line with a} slope

intensity

^{I. Most of the}

expérimental points obey

^{a 14}

law of variation. The lowest

point

^is

questionable

^due

to

possible

molecular contributions as we shall see

later on.

Thus,

^{it is} shown that

temporal

^{effects do}

play

^{a role in the resonant}

multiphoton

ionization of caesium atoms with _{15 ps}

pulses according

^{to theore-}

tical

predictions.

The

following

remarks will

help

^to avoid confusion

on the

meaning

^{of the} above-mentioned 14

law,

^as

well as saturation effects in the

four-photon

^ionization

of caesium atoms when the laser

frequency

^{is tuned}

through

^{the resonant}

three-photon

transition 6S --> 6F.

First,

^the

slope n

^{observed in}

figure 5,

must not be confused with the usual

slope

measured in

previous

papers such as

[2].

^This

slope corresponds

^{to K = 4 in} non-resonant

four-photon

ionization of caesium atoms.

However,

^{as is well}

known,

^{in the}

vicinity

^{of a} resonance, the

slope

^{K varies}

very

significantly

^{and no}

longer corresponds

^{to the}

number of

photon

^absorbed

by

^{the atom.}

Secondly,

under our

experimental conditions,

^the

one-photon

6F - continuum transition rate is much

larger

^than

the resonant

three-photon

6S ---> 6F transition rate, and is also much

larger

^than the de-excitation rate of the 6F level towards the 6S

ground

^{state. In}

addition,

this

one-photon

transition 6F - continuum is not saturated under our

experimental conditions,

^when saturation is defined as wi »

1,

^{where w is the one-}

photon

ionization rate from the 6F level and i is the laser

pulse

^{duration. wz = 0.17 width 1 =} 15 ps and I = 1.5 x

109W.cm-2.

It should be

pointed

^out

that wi is

roughly

^{the 0 value in ref.}

[3]. Furthermore,

the relation wT » 1 ^can also be

expressed

^as

i/T > 1,

where T is the lifetime of the 6F level under the influence of the laser field. With our

experimental

parameters, ^{T is}

essentially govemed by

^{the one-}

photon

ionization rate from the 6F level.

Thus,

^when

experiments

^{were carried out with a}

long

^laser

pulse

with duration 1 ⁼ 37 ns and a laser

intensity

^of

108 W . cm - 2

as in ref.

[2],

^wi >

1, 1/T > 1,

^{and a}

slope n

^{of about 2.5 is}

observed,

^{while with a laser}

pulse

^{1 =} 15 ps and a laser

intensity

within the range 108-109

W . cm- 2

as in the present

work,

wi

1, ’t 1 T 1,

^{and a}

slope n

^{= 4} is indeed observed.

Lastly,

^{the I4law}

analysed

^{above must not be confused}

with another I’ law which would be

expected

ⁱⁿ

using

a

long

^laser

pulse

^{and a laser}

intensity

^small

enough

^to

have the

one-photon

^{6F - continuum transition}

rate much less than the de-excitation rate of 6F level towards the

ground

^state.

However,

^{it is needless to}

say that no

significant

ions would be formed under these

conditions,

^{the laser}

intensity being

^{too weak.}

- The width of the resonance

profile

^{is 1}

^cm-’

¹

in

frequency units, compared

^to the laser

spectral

width

(1.4 cm -l)

of the bandwidth-limited _{15 ps}

pulses.

The resonance width remains

equal

^to

^{1 cm -}

¹

within the laser

intensity

range 1.8 ^x 108

W . cm- 2-

1.57 x

109 W.cm-2.

Thus the resonance width is

governed by

the laser

spectral

width. This

point requires

^{some comments. Let} the normalized

spectral

distribution function of the laser

intensity

^be

f (v),

with a linewidth

(FWHM)

y. It has been stated in the

literature that the effective linewidth _yK of a resonant

K-photon

transition is _YK ⁼

Ky

^{which seems to be}

inconsistent with our results. It seems better to define the effective linewidth YK for a K-th order _process as :

yK is then smaller than _y.

Moreover,

it should be

pointed

^{out that we define an} effective interaction

time iK

^{for a} K-th order _{process :}

when we consider the normalized

temporal

^distri-

bution function

G(t)

of the laser

intensity

^{with a}

duration

(FWHM)

T ; TK is then shorter than T

[12J.

- One of the most

important

features of the reso-

nant

multiphoton

ionization process is the ^resonance shifts due to atomic level shifts under the influence of the laser field. In

figure 4,

^{the resonance}

position, corresponding

^to the maximum in the number of

ions,

is shifted with respect ^{to the}

frequency position

of the unshifted

three-photon

transition 6S ---> 6F derived from

spectroscopic tables,

^{and indicated}

by

an arrow. The dashed line shows the resonance shift for

increasing

values of the laser

intensity.

Figure

⁶ shows the variation of the resonance

shift

AE, expressed

^{in terms of} energy shift of the

three-photon

transition 6S --->

6F,

^{as a} function of the laser

intensity.

This shift is found to be linear with the laser

intensity

^within the range 108_109

W.cm-2.

AE ⁼ al, ^{with a = 2 + 0.2} cm -1

1 /GW . ^{cm - 2}

ⁱⁿ

good

FIG. 6. ^- Resonance shift, expressed ^{in terms of} energy of the

three-photon transition 6S - 6F, as a function of the laser intensity.

The dashed line is a theoretical result (Ref. [11J). Triangles ^are experimental points derived from a previous experiment ^{with a}

single-mode ^laser pulse (Ref. [2]).

agreement ^{with the}

corresponding

calculations

[9,11J.

The present results obtained with a bandwidth-limited

pulse

^{with a}

spectral

width of 1.4 cm-’ ¹ are in

good

615

agreement ^with

previous

results obtained in investi-

gations

^{of the same resonant} process with a

single-

mode laser

pulse

^{of 35 ns} duration and

10- 3 cm-1

linewidth

[2]. Thus,

^{it seems} that the laser bandwidth is not a fundamental

parameter,

^as

long

^{as a band-}

width-limited

pulse

^{is used. It is also}

important

^to

emphasize

the excellent agreement ^{of the resonance} shift with the calculated values

expressed by

^the

dashed line in

figure

^{6. In} this calculation

[11 ],

^{the shift}

is

mainly

^{due to} the shift of the 6S and 6F level.

Therefore,

^{the resonance shift is}

mainly governed by

the shift of the 6S and 6F level under the influence of the laser field.

It would be of interest to extend shift measurements in

figure

^{6 to}

larger

laser intensities.

However,

^when the laser

intensity

is increased

beyond

^{a definite}

value,

all the atoms in the interaction volume are ionized.

This saturation effect

changes

^{the law of} variation of the number of ions as a function of the laser

intensity,

and induces a

broadening

^{of the resonance}

profile.

Figure

⁷ shows three resonance

profiles

^obtained

under the same conditions as in

figure 4,

except ^now

FIG. 7. ^- Broadening and distortion of resonance profile ^{due to}

saturation effects in the interaction volume. Laser pulse ^{duration :}

15 ps. (a) The laser intensity ^{I = 8.7 x 108 W.cm-2 is small} enough ^{to induce no} significant broadening ^{due to saturation}

effects. The 1 cm-1 ^resonance width is governed by the laser band- width. (b) ^{The laser} intensity ^{/= 1.05 x} 109 W . cm- 2 becomes

large enough ^to broaden the ^resonance width to 1.25 cm -1 due to saturation effects. (c) ^{The laser} intensity ^{1= 1.5 x} 10’ W. cm - ’ induces strong saturation effects and the resonance curve is broaden-

ed to 2.5 cm - 1 .

for a smaller interaction volume.

Figure

^{7a obtained}

with an

intensity

^{/= 8.7 x}

1 Og W . cm -2

shows a

1 cm -1 resonance width

governed by

^{the laser}

bandwidth,

^{as in}

figure

^{4. On the} contrary,

figure

^7b

and 7c obtained with an

intensity

^{I = 1.05 x 101}

and 1. 5

x 109 W.cm-2 respectively

^{show resonance}

widths of 1.25 and 2.5

cm-’, respectively.

^The

broadening

^{of resonance}

profiles

^{due to saturation}

effects in the interaction volume _appears as soon as the laser

intensity

is increased

beyond

^a definite value which

depends

^{on resonance}

detuning

^and

especially

on the

spatial

distribution function of the laser

intensity

in the interaction volume. This effect ^was observed in

previous experiments [2, 4].

^{The broaden-}

ing

^{due to} saturation effects can

greatly

^{alter the effect}

of the

intensity

^{on the} shift and true width of the

resonance curves. Saturation effects have to be care-

fully

^avoided

by using

^small

enough

laser intensities.

Figure

^{4 and}

figure

^{7 showed resonance}

profiles

^for

small

detunings,

i.e. when the laser

frequency

^{is close}

to the

dynamic

^resonance

frequency. Figure

^{8 illus-}

trates a resonance

profile

which extends farther on

both sides of the resonance. This

figure

^{shows a} very

significant

asymmetry ^{in the}

wings

^{of the resonance}

profile,

^{whereas no}

significant

asymmetry appears in the

vicinity

^of the maximum of the resonance

profile.

This asymmetry could be due to the molecular

component

ⁱⁿ the caesium _vapour. Both atomic and molecular caesium ions are observed when the laser

frequency

is less than 9 442

cm - l,

^{whereas no}

signi-

ficant molecular ion is measured in the

longer

^fre-

quency side of the resonance

profile. ^Thé

^{Cs + and}

Cs’

signals

^{are well resolved} and identified

by using

^a

time-of-flight

^mass

analysis.

The collected atomic ions Cs+

(shown by

^starred

points

ⁱⁿ

figure 8)

^are

formed both from a non-resonant

four-photon

^ioni-

zation of atomic

caesium,

^{and from a}

partial

^resonant

dissociation of the

Cs2

^molecules

giving

^{atoms in}

lower excited states

[13],

^{as well as a}

partial

^disso-

ciation of the molecular ions

by

^{the laser radiation}

[14].

The molecular ions can result either from a direct non-resonant

three-photon

ionization of the caesium

molecules,

^{or much more}

likely

^{from a resonant}

FIG. 8. ^- Resonance profile extending ^over both sides of the

resonance. Laser pulse duration : _{15 ps,} laser spectral ^{width :}

1.4 cm-1, resonance width : 1 cm-1. The starred points ^{are influenc-}

ed by the molecular component ^{of the caesium} vapour.

two-photon

excitation of intermediate states of the caesium

molecules,

^followed

by photoionization.

^The

importance

of the molecular component ^can

depend

upon the

relationship

^{of the laser}

frequency

^{to a}

potentially

^resonant intermediate state

of Cs2 [15-16].

Such molecular contributions can dominate the non-resonant

four-photon

ionization of the atoms.

4. Conclusions. ^- A reliable

tunable-wavelength

mode-locked

Nd-glass

laser has been used to inves-

tigate

^{the resonant}

multiphoton

ionization of caesium atoms in the

10-11_10-9

s time scales. This work has

emphasized

^several

important points.

First,

^the

four-photon

ionization of caesium atoms, when the laser

frequency

^{is tuned}

through

^{the three-}

photon

transition 6S --->

6F,

^has

already

been observed in the

10-8

s time scale

[2, 4]

^and gave evidence of a

typical

^resonant behaviour. The present ^{work has} shown that the resonant character is maintained within the

10-9_10-11

s range. The influence of a

temporal

^{effect is} demonstrated in agreement ^with theoretical

predictions [3, 9].

Secondly,

^{the resonance shift}

AE,

^{due to atomic}

level shifts under the influence of the laser

field,

^has

been found to be linear with the laser

intensity

^I

within the _range 108-109 W.cm-2. AE = al, ^with

a ⁼ 2 + ^0.2

cm -’ /GW .

^{cm - 2. This} result is in excellent

agreement

with both theoretical calculations

[9, 11],

and a

previous

result obtained with a

single-mode

^laser

pulse

^{of 35 ns duration}

[2].

^{Thus it seems} that the laser bandwidth is not a fundamental

parameter concerning

resonance

shifts,

^as

long

^{as a} bandwidth-limited

pulse

is used.

Thirdly,

^when

long (1.5 ns)

bandwidth-limited

pulses

^are

used,

^{the width of the resonance}

profile

^is

much

larger

^{than the laser}

spectral

^width

(0.02 cm-1),

and is

mainly

^{due to} the unresolved structure of the 6S --+ 6F transition. On the

contrary,

^when very short

(15 ps)

bandwidth-limited

pulses

^are

used,

^the

width of the resonance

profile

^is

governed by

^{the laser}

spectral

^width

(1.4 cm -1).

These results are valid as

long

^as saturation effects do not appear in the interac- tion volume.

Lastly,

^{there is no} evidence of an asymmetry ^{in the}

vicinity

of the maximum of the resonance

profile,

whereas a very

significant

asymmetry appears in the

wings

^{of the resonance}

profile, probably

^{due to the}

existence of caesium molecules.

Acknowledgments.

^{- The authors wish to} express their

gratitude

^to Professor S.

Feneuille,

^Drs

M.

Crance,

^Y.

Gontier,

^M.

Trahin,

^J. Morellec and P.

Agostini

^for

helpful

discussions.

References [1] LAMBROPOULOS, P., Topics ^on Multiphoton Processes in Atoms.

Advances in Atomic and Molecular Physics, ^{Vol. 12} (1976).

[2] ^MORELLEC, J., NORMAND, D. and PETITE, G., Phys. ^{Rev. A 14} (1976) 300.

[3] ^{CRANCE, M. and} FENEUILLE, S., Phys. ^{Rev. A 16} (1977) ^1587.

[4] ^{GRINCHUK, V. A., DELONE,} G. A. and PETROSYAN, ^K. B., Sov. J. Plasma Phys. ¹ (1975) 172; ^Fiz. Plazmy ¹ (1975)

320.

[5] LECOMPTE, C., MAINFRAY, G., MANUS, C. and SANCHEZ, F., Phys. Rev. A 11 (1975) ^1009.

[6] SANCHEZ, F., Nuovo Cimento B 27 (1975) ^305.

[7] ^{LOMPRE, L.} A., MAINFRAY, G. and THEBAULT, J., ^J. Appl.

Phys. ⁴⁸ (1977) ^1570.

[8] ^{LOMPRE, L.} A., MAINFRAY, G., MANUS, C. and THEBAULT, J., Phys. ^{Rev. A} 15 (1977) ^1604.

[9] CRANCE, M., J. Phys. ^B. (to ^be published).

[10] ARMSTRONG, L., BEERS, ^{B. and} FENEUILLE, S., Phys. ^{Rev. A 12} (1975) 1903.

[11] GONTIER, Y., TRAHIN, M., ^J. Phys. ^{B. 11} (1978) ^L-131.

[12] AGOSTINI, P., BARJOT, G., MAINFRAY, G., MANUS, C. and THEBAULT, J., IEEE Quant. ^{Electron. 6} (1970) ^782.

[13] KLYUCHAREV, A. and DOBROLEZH, B., Opt. Spectrosc. ³⁸ (1975) ^228, Opt. Spektrosk. ³⁸ (1974) ^402.

[14] ^HELD, B., MAINFRAY, G., MANUS, ^{C. and} MORELLEC, J., Phys. Rev. Lett. 28 (1972) ^130.

[15] COLLINS, C. B., JOHNSON, ^B. W., POPESCU, D., MUSA, G., PASCU, ^{M. and} POPESCU, I., Phys. ^{Rev. A 8} (1973) ^2197.

[16] GRANNEMAN, E., KLEWER, M., NYGAARD, ^{K. and VAN DER} WIEL, M., ^J. Phys. ^{B 9} (1976) ^865.