Arnaud Rouzee et al- Laser spatial profile effects in measurements of impulsive molecular alignment

8/3/2019 Arnaud Rouzee et al- Laser spatial profile effects in measurements of impulsive molecular alignment

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INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS

J. Phys. B: At. Mol. Opt. Phys. 38 (2005) 23292335 doi:10.1088/0953-4075/38/14/001

Laser spatial profile effects in measurements ofimpulsive molecular alignment

Arnaud Rouzee, Vincent Renard, Bruno Lavorel and Olivier Faucher

Laboratoire de Physique de lUniversite de Bourgogne, UMR CNRS 5027, BP 47870,21078 Dijon Cedex, France

Received 1 February 2005, in final form 24 May 2005

Published 20 June 2005

Online at stacks.iop.org/JPhysB/38/2329

Abstract

We use a non-intrusive technique based on a polarization scheme to probe the

periodic alignment of the CO2 and N2 molecules induced by a strong laser

pulse linearly polarized. A weak probe field experiences the birefringence

resulting from the alignment of the molecules. By comparing the probe

depolarization signal with the numerical simulation of the time-dependent

Schrodinger equation, it is possible to quantify the alignment of the molecular

sample. The modelling takes into account the spatial profile of the pump

intensity. It allows from the alignment signal to determine the onset of

saturation due to ionization, despite the intrinsic saturation of the alignment

arising for about the same laser intensity.

1. Introduction

In thelast few years, laser-induced molecularalignment hasbecome of great interest in different

domains of application such as chemistry or molecular optics. Oneof the established alignment

techniques is to use a strong non-resonant laser pulse that applies in principle to any molecular

system with an anisotropic polarizability [1]. Within this technique, two cases have to be

considered: the adiabatic [2] and the quasi-sudden regime [3, 4]. In the first case, a relatively

long pulse with respect to the rotational period of the molecule is needed and alignment along

the polarization direction of the field is achieved only during the laser pulse. After extinction

of the latter, molecules return to their initial states. In the second case, the pulse is shorter than

the rotational period and alignment occurs periodically in time at revivals of the rotationalwave packet [5] launched by the laser pulse. This case is of particular interest because the

alignment occurs in field-free conditions that are suitable for most applications. The truly

sudden regime is valid for a pulse duration much shorter compared with the rotational period

of the molecule in its higher rotational state populated during the pulse interaction. Field-

free alignment can be observed by imaging the photo-fragmentation of molecules produced

by an additional strong laser pulse [4, 6, 7]. From the non-isotropic angular distribution,

the degree of alignment is quantified by determining the average value cos2 , where is

0953-4075/05/142329+07$30.00 2005 IOP Publishing Ltd Printed in the UK 2329
http://dx.doi.org/10.1088/0953-4075/38/14/001http://stacks.iop.org/jb/38/2329http://stacks.iop.org/jb/38/2329http://dx.doi.org/10.1088/0953-4075/38/14/001


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2330 A Rouzee et al

the angle between the molecular axis and the polarization direction of the laser field. As

inherent in the imaging technique, molecules are destroyed while the probing process occurs.

The technique employed in the present work makes use of a weak probe that preserves the

molecules [8]. A linearly polarized probe beam experiences the birefringence induced by the

molecular alignment. In the case of linear molecules, the subsequent probe depolarizationprovides an information on molecular alignment. In [8, 9], the spatial dependence of the

electric field for the pump and probe pulse was ignored in the model and an effective value of

(cos2 1/3)2 was extracted by comparing experiments with simulations. In the present

work, we improve the analysis by considering the volume effects in the model and by using

an iterative least-squares fitting of the experimental data for the determination of cos2 .

We present results obtained in CO2 and N2. The numerical simulations are performed for an

adjusted intensity that can directly be compared to the measured intensity. The cos2 value

deduced from the numerical adjustment corresponds to the alignment at the centre of the laser

beam, rather than to a value averaged over the interaction volume. Furthermore, because the

spatial distribution of the laser beams is included in the model, the saturation of the alignment

signal of CO2 observed for large intensities can unambiguously be related to the depletion of

the neutrals through the ionization process.

2. Experimental setup

The experiment is based on a Ti:Sapphire laser chirped pulse amplified system operating at

20 Hz and 1 KHz. The pulse duration is about 100 fs and the wavelength is centred at 800 nm.

The scheme of the experiment is presented in [9]. The incoming beam is split in two parts. The

strong part, vertically polarized, is used as the pump. In order to change the intensity of the

pump, we use a half-wave plate combined with a polarizer. The weak part, used as the probe, is

polarized at 45 with respect to the polarization direction of the pump. A delay line composed

of a corner cube mounted on a motorized linear stage is placed on the probe path in order to

adjust the temporal delay between the pump and probe pulse. Both beams are focused with a

175 mm (300 mm) focal length lens and cross each other in a cell of CO 2 (N2) at a small angle

(2). The measured waist is 30 m (40 m) and 50 m (60 m) for the pump and probe,

respectively. After the cell, the pump is blocked and the depolarization of the probe is analysed

with a polarizer set at 90 with respect to its initial polarization direction. The outgoing signal

field is then collected with a photomultiplier, sampled by a boxcar integrator and displayed

on a computer that is also used to control the delay line. The interaction of the two pulses

takes place in a 0.2 m long static cell at room temperature and under pressure of 0.11 bar of

CO2 or 0.86 bar of N2, which is a compromise to ensure a good signal-to-noise ratio and to

minimize the decay of the signal due to collisions. The spatial overlapping of the laser beams

into the interaction region is adjusted prior to each experimental run by maximizing the signal

amplitude and by checking that the signal shape is not affected by a small displacement around

the position that optimizes the signal. It assumes that an offset


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Laser spatial profile effects in measurements of impulsive molecular alignment 2331

Ep(r,z,t) = E

w0

w(z)exp

2 l n 2

t

p

2exp

r

w(z)

2cos(t)

e p, (1)

where w(z) is the beam radius, w0 is the beam waist (defined at z = 0), E is the peak amplitude

of the pulse, r =

(x2 + y2) is the transverse coordinate, is the angular frequency of thelaser, p is the pulse duration and

e p is an unit vector along the polarization direction. In the

non-adiabatic regime, i.e. p < rot with rot the classical rotational period of the molecule,

the interaction leads to a periodic alignment of the molecules along the vectore p that remains

after the extinction of the pump pulse. Considering the spatial distribution of the electric field,

the magnitude of alignment is different with respect to the position of the molecule within the

laser focus. At the space coordinate (r, z), the state vectorr,z(t) of the molecule is evaluated

by solving the time-dependent Schrodinger equation ihd/dt = H with

H = Hrot p

Ep(r,z,t) (2)

the effective Hamiltonian that describes the non-resonant excitation of the molecular

polarizability, Hrot the rotational Hamiltonian,

p = 1/2

Ep the effective dipole momentand

the polarizability [9]. Higher-order polarizabilities (i.e., hyperpolarizabilities) can be

neglected under the intensity regime investigated in this work. From equation (2), we can

calculate the thermal average value cos2 r,z(t) in each point of space within the interaction

volume and in particular at the focus (r = z = 0), where the alignment is maximum. In the

experiment, the alignment is probed with a second weak pulse, time delayed with respect to

the pump pulse. The birefringence induced by the alignment of the molecular sample changes

the polarization of the probe field and results in a signal field

Es(r,z,t ) Epr(r,z,t )n(r,z,t), (3)

where Epr is the incident probe field envelope, is the time delay, and n = n n is

the birefringence of the medium with n and n the refractive index respectively parallel and

perpendicular to the pump polarization direction. Finally, we can show that the birefringenceis related to the molecular alignment by [10]

n(r, z,t ) N

cos2 r,z(t) 13

. (4)

In this expression, Nis the number density and = is the polarizability anisotropy,

with and the components of the polarizability respectively parallel and perpendicular

to the molecular axis. Because the molecular sample is excited by coherent fields, the total

electric field collected by the detector is obtained by a summation of signal fields (defined in

equation (3)) over the space coordinates

Es(t )

r

z

2 rEs(r,z,t ) dr dz (5)

and, finally, the signal delivered by the detector is

Is( )

+

E2s (t ) dt. (6)

As seen from equations (3)(6), the signal is proportional to the temporal convolution of

(cos2 1/3)2 with the probe intensity, spaced-averaged. By fitting the experimental

data with the numerical simulation, we can deduce the thermal average cos2 at any space

coordinate within the interaction volume.


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-0.1

0.0

0.1

Obs-calc

35302520151050

Pump-probe delay (ps)

-0.6

-0.3

0.0

0.3

0.6

Signal

(arb.units)

Experiment

Theory

Figure 1. Upper graph: signal (experiment) versus pumpprobe delay recorded in CO2 at0.11 bar for a peak intensity of 127 TW cm 2. Numerical simulation (theory) performed for alaser peak intensity of 120 TW cm2. Lower graph: observation calculation.

4. Results and discussion

Experiments have been conducted in CO2 and N2. Figure 1 displays the polarization signal

versus thepumpprobe delay performedat room temperature in CO2. The traceis characterized

by transients equally spaced by Tr/4, where Tr = 1/2B0c 42.7 ps is the classical rotational

period and B0 is the rotational constant in the ground vibronic state. Each peak can be

associated with the alignment of the molecular axis along the direction of polarizatione p of

the pump field (cos2 > 1/3) or to the planar delocalization of the molecular axis in the

plane perpendicular to this direction (cos2 < 1/3). For an isotropic angular distribution

cos2 = 1/3. The nonzero background signal observed between transients is produced by

the permanent alignment of the molecules [4, 8]. In the same figure, we show the numerical

fit of equation (6) based on the solution of the time-dependent Schrodinger equation. The

beam sizes used in the simulation correspond to the measured values (cf section 2). Because

the shape of the transients and the permanent alignment depend both on the laser intensity,

the numerical adjustment is quite accurate. The difference between the calculation and the

observation is shown in the lower graph. The adjusted peak intensity is 120 TW cm2.

Because the calculation accounts for the spatial dependence of the pump and probe fields, this

value is very close to 127 TW cm2, the measured peak intensity. The measurements in N2were performedat higherpressure0.86 bar, in order to compensate for thesmaller polarizability

of N2 as compared to CO2. The results obtained in N2 are shown in figure 2. The transients are

spaced by Tr/4, with Tr = 1/2B0c 8.38 ps. The alternation of small and large transients

results from the difference of spin degeneracy factor between rotational states of odd and

even J-values, respectively equal to 3 and 6. In the same figure, the signal is compared to

the numerical simulation. The latter accounts for a small static birefringence (2% of the

maximum signal) produced by the windows of the gas cell. The agreement between theory andexperiment is found for an adjusted peak intensity of 92 TW cm2, that is about the measured

intensity (90 TW cm2). The residual obscalc is nevertheless not as good as in CO2 for the

following reason. The numerical simulations assume that the laser beams are co-propagating

within the sample. It is known for pumpprobe experiments that crossed beams introduce

degradation of the temporal resolution ensuing broadening of the temporal signal. This effect

is unimportant in CO2 because the transients contain substructures relatively large compared

to N2 and to the pulse duration. In N2, the statistical weight being different for the population


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0.4

0.2

0.0

-0.2

-0.4Signal(arb.units)

-0.1

0.0

0.1

Obs-calc

1614121086420

Pump-probe delay (ps)

Experiment

Theory

Figure 2. Upper graph: signal (experiment) versus pumpprobe delay recorded in N2 at0.86 bar for a peak intensity of 90 TW cm 2. Numerical simulation (theory) performed for a laser

peak intensity of 92 TW cm

2

. Lower graph: observation calculation.

150

125

100

75

50

Ith(TW/cm

2)

1601401201008060

Iexp (TW/cm2)

80

60

40

20

10080604020

slope = 0.93

slope = 0.88

(a) N

(b)2

2

CO

Figure 3. Adjusted peak intensity (Ith) versus measured peak intensity (Iexp). Adjustments aremade over the eight first transients of N2 (a) and three first transients of CO2 (b).

of odd and even J states, the structural shape of the signal is different and the separation

between peaks belonging to a same transient is closer to the pulse duration. This is roughly

accounted for by increasing the pulse duration of the probe pulse from 100 fs to 120 fs in the

simulation of the N2 signal.

We have studied the intensity dependence of the alignment in CO2 and N2. For each

intensity of the pump beam, an iterative least-squares fittings of the temporal traces includingthe three first transients of CO2 (see figure 1), and the eight first of N2 (see figure 2), have been

performed. Figure 3 displays the adjusted intensity Ith versus the measured peak intensity

Iexp between 10 and 165 TW cm2. In this intensity range, the ratio Ith/Iexp is close to 1 for

both molecules. We can compare this value to that obtained with CO2 in a previous work

[9] where volume effects were not included in the calculation. In that work, the effective

intensity introduced in the calculation was compared with the averaged intensity Iav measured

in the experiment. The ratio Ith/Iav was estimated close to 0.7. Assuming that for a Gaussian


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180

160

140

120100

80

60

40

Ith

(TW

/cm2)

0.7 0.6 0.5

< cos2>

35030025020015010050

Iexp (TW/cm2)

(a) (b)

Figure 4. (a) Thermal average of cos2 estimated for CO2 at the beam centre as a functionof the adjusted peak intensity Ith. (b) Same as figure 3(b) but with larger intensities Iexp andmeasurements performed only on the third transient. Discontinuous lines between points includedto guide the eye.

pulse the average intensity is about two times smaller than the peak intensity, it translates to

Ith/Iexp 0.35. Thus, including the volume effect in the calculation leads to a better accuracy

in the determination of cos2 . The agreement between calculation and observation is also

improved.

Further measurements have been performed in CO2 at larger intensities. In this case,

only the third transient ( 32.7 ps) was recorded. The numerical adjustment is therefore

less accurate than using a trace with several transients. Nevertheless, recording only one

transient offers the possibility of acquiring more data sets at different intensities with a better

reproducibility. The results of the numerical simulations are reported in figure 4(b). As it is

shown, a reduction of the ratio Ith/Iexp is observed above 200 TW cm2. At first sight, this

feature could be incriminated to the combined effect of ionization and intrinsic saturation of

the alignment at room temperature. Both arise at about the same laser intensity. Saturation

of the ionization of CO2 occurs around 200 TW cm2 at 800 nm [11], whereas the numerics

predicts the intrinsic saturation of the alignment around 100 TW cm2. Nevertheless, because

the intensity profile of the laser beams is included in the simulation, the discrepancy between

the adjusted and measured intensity can be unambiguously attributed to the result of ionization.

In this context, two scenarios can be considered. (1) Once the neutral molecules have been

ionized, only the resulting ions can eventually produce a probe signal. This would assume that

the ions sample created right after the pump pulse is left in a non-isotropic angular distribution

and therefore can lead to a polarization signal. The latter would be most likely different than

that resulting from the neutrals. So far, we have no evidence that the ions contribute to the

signal observed in this work. The issue of whether or not ions produced from the ionization

of aligned molecules are themselves aligned and measurable should be investigated. (2) The

pump beam could be affected along its propagation through the medium that it ionizes. For

instance, self-defocusing would result in a peak intensity smaller than the one estimated andhence could explain the results of figure 4(b). In CO2, the pump beam geometry measured after

the gas sample above 150 TW cm2 shows a slight alteration of the wave front with noticeable

transverse inhomogeneities that could support this scenario. In both cases, the results of

figure 4(b) confirm that the saturation intensity for ionization occurs effectively around

200 TW cm2. Finally, we show in figure 4(a) the thermal average ofcos2 achieved at the

laser focus. In our experimental conditions (i.e. 100 fs pulse duration, room temperature), the

maximum alignment cos2 0.7 is achieved at a peak intensity of 150 TW cm 2.


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5. Conclusion

In conclusion, we have shown that it is possible to improve the accuracy for the characterization

of field-free alignment by the polarization technique. This is achieved by including in the

theoretical model the spatial profile of the laser beams, which is critical at large laser intensitywhen saturation occurs. It also allows us to observe the limitation of the alignment resulting

from ionization of the neutral molecules by the pump pulse. In addition, we have used an

iterative least-squares fitting procedure to analyse the data. With these improvements, it is

possible to directly compare the calculated intensity to the measured intensity and to extract

the spatial distribution of cos2 . This is of particular importance for experiments that aim

at using samples of aligned molecules.

Acknowledgments

This work was supported by the Conseil Regional de Bourgogne, the Action Concertee

Incitative Photonique from the French Ministry of Research and a Marie Curie European

Reintegration Grant within the 6th European Community RTD Framework Programme. Theauthors would like to acknowledge E Hertz and M Renard for fruitful discussions.

References

[1] Stapelfeldt H and Seideman T 2003 Rev. Mod. Phys. 75 543

[2] Sakai H, Safvan C P, Larsen J J, Hilligse K M, Hald K and Stapelfeldt H 1999 J. Chem. Phys. 110 10235

[3] Ortigoso J, Rodrguez M, Gupta M and Friedrich B 1999 J. Chem. Phys. 110 3870

[4] Rosca-Pruna F and Vrakking M J J 2001 Phys. Rev. Lett. 87 153902

[5] Seideman T 1999 Phys. Rev. Lett. 83 4971

[6] Dooley P W, Litvinyuk I V, Lee K F, Rayner D M, Spanner M, Villeneuve D M and Corkum P B 2003 Phys.

Rev. A 68 023406

[7] Peronne E, Poulsen M D, Bisgaard C Z, Stapelfeldt H and Seideman T 2003 Phys. Rev. Lett. 91 043003

[8] Renard V, Renard M, Guerin S, Pashayan Y T, Lavorel B, Faucher O and Jauslin H R 2003 Phys. Rev. Lett. 90

3601[9] Renard V, Renard M, Rouzee A, Guerin S, Jauslin H R, Lavorel B and Faucher O 2003 Phys. Rev. A 70 033420

[10] Lalanne J R, Ducasse A and Kielich S 1996 Laser-Molecules Interaction: Laser Physics and Molecular Non

Linear Optics (New York: Wiley)

[11] Cornaggia C and Hering Ph 2000 Phys. Rev. A 62 23403

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Arnaud Rouzee et al- Laser spatial profile effects in measurements of impulsive molecular alignment