1. All-Optical Molecular Alignment and Orientation & Attosecond Pulses Generation
through High Order Harmonic Generation
Niccol`o Bigagli∗
Department of Physics & Astronomy, Bates College, Lewiston, ME 04340, USA
Department of Physics, Graduate School of Science,
The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
(Dated: August 20, 2016)
In this document, we report on the results of two experiments: the all-optical alignment and
orientation of OCS molecules towards completely-field-free orientation, and the production of sin-
gle attosecond pulses from argon atoms. For the alignment and orientation experiment, a the
two-color method was employed with a pump-probe setup. The fundamental tone and second har-
monic (λ = 1064 nm and λ = 532 nm respectively) of an Nd:YAG laser (focused intensity of
∼ 1012
W/cm2
) were used as the pump beams and a near infrared Ti:sapphire beam (focused in-
tensity of ∼ 1014
W/cm2
) was used as probe through the processes of photoionization and Coulomb
explosion. Velocity map imaging was used to measure alignment and orientation in terms of, re-
spectively, the cos2
(θ) and cos(θ) parameters, where θ is the azimuthal angle with the vertical
pump polarization. Alignemnt was clearly observed, with best value of cos2
(θ) of 0.579 ± 0.001
for the Nd:YAG fundamental tone (peak power 100 mJ). No unambiguous sign of orientation was
observed, but some data suggests the possibility of its achievement. This points out the need for
further testing and calibration of the setup. Through the exploitation of high harmonic genera-
tion and the employment of Double Optical Gating (DOG), a single attosecond pulse was clearly
generated.
Contents
I. Introduction 1
II. Theorethical Background 2
A. Optical Molecular Alignment 2
B. All-Optical Molecular Orientation 3
C. Semiclassical High Order Harmonic
Generation 4
D. Single Attosecond Pulse Generation 5
III. Experiment 5
A. Experimental Setup and Procedure for
Alignment and Orientation 5
B. Experimental Setup and Procedure for the
Single Attosecond Pulse Production 7
IV. Results and Analysis 8
V. Observations and Discussion 9
VI. Conclusions and Outlook 10
Acknowledgments 11
Appendices 11
A. Chirped Pulse Amplification 11
B. Time Of Flight Mass Spectrometry 11
∗Electronic address: nbigagli@bates.edu
References 12
I. INTRODUCTION
Molecules are the main player in many physical and
chemical processes, and their interactions are what drives
almost all reactions. However, reactions may be strongly
dependent on the position of the molecules themselves.
Understanding molecular stereodynamics (the way in
which the spatial arrangements affect physical and chem-
ical processes) is therefore fundamental for our compre-
hension of several phenomena. For instance, the ellip-
ticity dependence of high harmonic generation has been
shown to be sensitive to molecular alignment [1]. In or-
der to increase and exploit such knowledge, we ought to
be able to control the spatial arrangement of molecules
or to probe the involved ultrafast processes.
An interesting prospect in the light of stereodynamics
is the careful study of molecular alignment and orienta-
tion. This has been seen to be relevant to fields and issues
as diverse as the aforementioned high order harmonic
generation, ultrafast molecular imaging [2], multiphoton
ionization [3–5] or electronic stereodynamics [6]. For
alignment, we mean the arrangement of molecules along
the same line with no distinction between the parallel
and antiparallel configurations. Conversely, orientation
distinguishes between the two possible directions along
the line and preferentially selects one of them. Early
works by Friedrich and Herschbach proposed the employ-
ment of an intense nonresonant laser field for alignment
[7], and combined electrostatic and laser fields for ori-
entation [8, 9]. Since then, the Hiro Sakai Group at
the University of Tokyo has proposed and demonstrated

2. 2
y
x
Alignment
y
x
Field-Free
y
x
Orientation
FIG. 1: Difference between molecular alignment and ori-
entation, with the comparison to the field-free case. The
monochromatic and two-color fields used to attain each ar-
rangement are also shown.
all-optical molecular orientation through strong, nonreso-
nant two-color laser fields [10, 11] and attained laser-field
free three dimensional orientation through a combined
approach exploiting a laser with slow turn on and fast
turn off times [12, 13]. Figure 1 depicts the difference
between alignment and orientation for the linear OCS
molecule, together with the field that may attain them.
Most of the work presented in this report is part of
an effort aimed at the construction of a setup capable
of attaining completely-field-free molecular orientation
through an all-optical method. To do so, an intense non-
resonant two-color laser field with a Gaussian profile and
a rise time of the order of 10 nanoseconds is employed to
adiabatically orient the molecules, and a plasma shutter
composed of an ethylene glycol jet sheet is used to trigger
a rapid turn-off of the field to leave molecules in a field-
free oriented state. We took part in, and report on, the
initial steps of the process, that is on the set up and opti-
mization of the optical path for two-color orientation and
on its operation to check whether this was able to achieve
alignment and all-optical orientation. The plasma shut-
ter was placed on the path, but we were unable to utilize
it during our stay. Test runs showed that our setup is ca-
pable of achieving alignment. It is still unclear whether
orientation was achieved, but there have been promising
signs that point out the need for further investigation.
To observe directly the ultrafast stereodynamical pro-
cesses as, for instance, those involved in the electron dy-
namics, probes of extremely short duration are necessary.
These may be provided by coherent radiation with pulses
of a few attoseconds, first achieved in 2001 [14]. It has
been shown that such attosecond pulses can be produced
in a train (a sequence of a few pulses) by the process of
high harmonic generation [15]. However, the generation
of a train degrades the quality of radiation, so that for ap-
plications a single pulse is desirable. In this work, we also
report on the use of the Double Optical Gating (DOG)
technique to isolate a single attosecond pulse [16].
II. THEORETHICAL BACKGROUND
The processes regulating molecular alignment and ori-
entation and High Harmonic Generation (HHG) may be
understood through both semiclassical and quantum me-
chanical approaches. The semiclassical interpretation is
incapable of giving a complete account of molecular align-
ment and orientation, therefore a full quantum mechan-
ical treatment of these processes is presented in this re-
port. Conversely, although not fully fundamental in na-
ture, a semiclassical picture can accurately predict and
explain most aspects of the production of single attosec-
ond pulses through HHG. Therefore, we limit our treat-
ment of this second phenomenon to such interpretation.
For increasingly more fundamental accounts of HHG we
refer our readers to [17] for the simplified quantum me-
chanical Lewenstein Model and to [18] for a thoroughly
quantum mechanical interpretation.
A. Optical Molecular Alignment
In order to control the spatial arrangement of molecu-
lar species, these must be placed in a region of space in
which a given arrangement is energetically favorable. In
other words, as molecules are quantum mechanical enti-
ties, the isotropy of free space must be disrupted so that
their Hamiltonian will lead to eigenstates with a defined
alignment once the Schr¨odinger equation is solved. For
the alignment of a linear molecule, to which our treat-
ment will be limited, the required anisotropic potential
is created by the interaction between an intense nonres-
onant laser field and the first and second moments (per-
manent dipole moment µ and induced moments, respec-
tively parallel and perpendicular to the principal molec-
ular axis, α and α⊥) of the molecule. Our theoretical
explanation will loosely follow that provided by Friedrich
and Herschbach in [7, 19].
A vertically polarized electric field of the form E(t) =
E0cos(ωt) will entail interaction potentials of the form
Uµ = − µE(t)cos(θ),
Uα = −
1
2
E2
(t)(α cos2
(θ) + α⊥sin2
(θ)),
(1)
where θ represents the azimuthal angle with the po-
larization direction of the laser field. These potentials
are simply given by the interaction between the exter-
nal electric field E(t) and the first two multipole expan-
sion moments of the molecular dipole under an the exter-
nal itself, in which case the polarizabilities are induced.
The theoretical calculation of such polarizabilities is all
but an easy task, but their values need not be exactly
known for experimental applications. All other terms
are assumed to be too small to be relevant [20]. If we
average such time-varying potentials over a laser period
in order to get rid of their time-dependence and there-
fore employ the time-independent Schr¨odinger equation,
provided that the nonresonant condition is satisfied, Uµ
cancels out, and in Uα we can substitute E2
(t) →
E2
0
2 .
Therefore, assuming that the molecule can be treated as
a rigid rotor with angular momentum J and rotational
constant B, the Hamiltonian of the system is given by

3. 3
H = BJ2
−
1
4
E2
0 (α − α⊥)cos2
(θ) + α⊥ . (2)
The Hamiltonian given in 2 can be substituted in the
time-independent Schr¨odinger equation, which has been
seen to reduce to a so called spheroidal wave equation in
cos2
(θ),
d
d(cos(θ))
(1 − cos2
(θ))
d
d(cos(θ))
−
M2
1 − cos2(θ)
+
+ λ ˜J,M + c2
cos2
(θ) S ˜J,M = 0,
(3)
where S ˜J,M and λ ˜J,M are respectively the eigenfunc-
tions and eigenvalues, to be found numerically,
c =
α
α⊥
− 1
α⊥E2
0
4B
is a dimensionless parameter characterizing the field-
induced molecular anisotropy and the quantum numbers
M and ˜J carry their usual meaning, where the tilde on
˜J represents the field-free rotor state adiabatically corre-
lated with the found eigenstate. A detailed study of the
solutions of 8 is presented in the aforementioned works
by Friedrich and Herschbach, and shows that they consist
of so called pendular states, labelled by M and ˜J, librat-
ing with a potential energy symmetric about θ = 90◦
with clear minima at θ = 0◦
and θ = 180◦
. Therefore,
the value of cos2
(θ) ˜J,M , the expectation value of the
square of the cosine of the azimuthal angle for the spe-
cific state, on which the system’s Hamiltonian is directly
dependent as shown by equation 2, is the perfect observ-
able to quantify the degree of alignment. Aligned states
will, in fact, have cos2
(θ) ˜J,M > 0.5. The individual ex-
pectation values of cos2
(θ) ˜J,M are evaluated through
the Hellmann-Feynman theorem in [19], showing that
cos2
(θ) ˜J,M increases with higher induced dipole, hence
for higher external field intensities.
For a sample of molecules in the gaseous state with
a given temperature distribution, the ensemble average
of cos2
(θ) is all that can be measured. However, since
the energy of the molecules depends on the cosine squared
parameter, we can readily determine such ensemble aver-
age at a temperature T for a rotational partition function
Zrot as
cos2
(θ) =
˜J
e
−
˜J( ˜J+1)B
kBT
Zrot
˜J
M=− ˜J
cos2
(θ) ˜J,M . (4)
This is what is experimentally measured. It is
also important to mention that perfect alignment (i.e.
cos2
(θ) = 1) is quantum mechanically unattainable.
Unbroken Symmetry: Phase = π/2 Maximum Asymmetry: Phase = 0
Potential (a.u.)
0 π
θ
Potential (a.u.)
0 π
θ
a) b)
FIG. 2: Total interaction potential of a linear molecule in a
two-color field for different phase differences. In image a), for
a phase of φ = π
2
, we have a perfectly symmetric potential,
while in inamge b), for φ = 0, asymmetry is maximized. Any
intermediate phase difference will give a partial asymmetry.
B. All-Optical Molecular Orientation
In order to achieve molecular orientation, the verti-
cal symmetry of the potential responsible for the spatial
control of the molecules must be broken. One way in
which this can be done is by the employment of a verti-
cally polarized intense nonresonant two-color laser field,
as proposed and demonstrated by the Hiro Sakai Group
[10, 11]. In this case, the radiation is formed by the su-
perposition of two pulses, one with twice the frequency
of the other, taking the form
E(t) = E0(t)[cos(ωt) + γcos(2ωt + φ)], (5)
with γ ≤ 1 the relative field strength and φ a necessary,
tunable phase difference. Such a field leads, in a linear
molecule, to the same interaction potentials with the per-
manent dipole and polarizabilities shown in 1. However,
in this case the third order moment in the molecule’s mul-
tipole expansion, the hyperpolarizability β (more specifi-
cally β and β⊥, respectively parallel and perpendicular
to the principal molecular axis) needs to be considered.
This leads to an extra interaction potential between the
molecule and the external field of the form
Uβ = −
1
6
E3
(t)[(β − 3β⊥)cos3
(θ) + 3β⊥cos(θ)].
(6)
It is now important to notice the relevance of the phase
difference φ on the degree of asymmetry of the potential.
Figure 2 shows the total potential as a function of the
azimuthal angle θ after a cycle average, which cancels out
Uµ as in the one-color case, and is given by
U(θ) = −
1
4
α cos2
(θ) + α⊥sin2
(θ) E2
0 (t) + γE0(t)
2
−
1
8
β cos3
(θ) + β⊥cos(θ)sin2
(θ) cos(φ)γE3
0 (t).
(7)
From figure 2 and equation 7 we can see that the
asymmetry (and hence orientation) is maximized for a

4. 4
phase of φ = 0, while φ = π
2 retrieves the pure align-
ment situation. Assuming therefore for the rest of our
treatment a simpler, orientation-optimal electric field
E(t) = E0(t)[cos(ωt) + cos(2ωt)], the time-independent
Schr¨odinger equation with Hamiltonian H = BJ2
+U(θ)
(following equation 2) can again be given in terms of the
cos(θ) parameter as
d
d(cos(θ))
(1 − cos2
(θ))
d
d(cos(θ))
−
M2
1 − cos2(θ)
+
+ λ ˜J,M + a2
1cos(θ) + c2
cos2
(θ) + a2cos3
(θ) S ˜J,M = 0,
(8)
where a1 =
β⊥E3
0
8B and a2 =
(β −3β⊥)E3
0
8B . Therefore,
in the orientation case we see how both cos(θ) and
cos2
(θ) play a role in the determination of eigenstates
and eigenvalues. These can again be evaluated through
the Hellmann-Feynman theorem and the ensemble aver-
ages of their expectation values for individual eigenstates
is found for an arbitrary gaseous sample by mimicking
equation 4. These will be the observables of our ex-
periment, allowing us to determine whether the sample
of molecules has been oriented or aligned respectively.
Since in a field-free case with completely random orien-
tation a value of cos(θ) = 0 is expected, an ensemble
of oriented molecules should result in cos(θ) > 0. In
[10] a detailed analysis of the dependence of cos(θ) on
several experimental parameters is presented. Worth of
mention is the positive correlation between orientation
degree and laser power and the enhancement of orien-
tation for low temperatures around 1 K. Even in this
case, perfect orientation (i.e. cos(θ) = 1) is quantum
mechanically unattainable.
C. Semiclassical High Order Harmonic Generation
Whenever atoms or molecules are exposed to high in-
tensity electromagnetic radiation, they may produce high
frequency harmonics of the external field. This process,
named High Harmonic Generation, can be classically
modelled by the so called three-step process, depicted
in figure 3 [21]. The three steps are: (i) ionization, (ii)
propagation and (iii) recombination. In this interpreta-
tion, the original unperturbed atomic or molecular po-
tential well is modified by the incident laser field, which
may lead to strong-field multiphoton ionization through
the tunneling of an electron in the well whenever the field
is at its maximum value. The electron in the continuum
state then feels itself the influence of the same external
field, which entails a motion in the polarization plane of
the radiation governed by the classical motion
r
U
r
Tunneling
Recombination
Photon Emission
a) b)
c) d)
e-
e-
e-
e-
r r
U
U U
FIG. 3: Three Step Model of HHG. In a) the electron is con-
fined in the unperturbed molecular potential well. In b) an
external laser field modifies the potential so the electron can
tunnel into a continuum state (step 1). Between b) and c)
the laser field accelerates the electron at first away from the
molecule and then back in its proximity (step 2). In the case
of recombination, in d) the kinetic energy acquired in the ac-
celeration in the continuum is liberated as a high frequency
photon (step 3).
x =
qE0
meω
[−cos(ωt)] + v0xt + x0,
y = α
qE0
meω
[−sin(ωt)] + av0yt + y0,
vx =
qE0
meω2
sin(ωt) + v0x,
vy = −α
qE0
meω2
cos(ωt) + v0y,
(9)
where E0 is the external field’s amplitude, ω its an-
gular frequency, α a polarization parameter, and x0, y0,
v0x and v0y are given by the initial position and velocity
respectively (usually all taken to be 0 right after tunnel-
ing). For linearly polarized light (α = 0), it is clear that
within the first laser period the electron will be acceler-
ated away from the ion to then return in its vicinity at a
time t with a nonzero acquired kinetic energy, given by
(assuming tunneling at t0 = 0)
K(t) = 2Upsin2
(ωt), (10)
with Up = E0
2ω
2
the ponderomotive energy of the elec-
tron in the field. When the electron approaches the par-
ent ion in this manner, there is a nonzero probability
that it will recombine returning to its original place in
the well. In this case, the energy acquired in the field
will be released in the form of a high frequency photon
with energy
Eγ = K(t) + Ip, (11)
where Ip is the ionization potential of the original atom
or molecule.

5. 5
Time
Attosecond Pulse
FIG. 4: Train of attosecond pulses generated by a temporally
Gaussian laser pulse enveloping three optical cycles.
Quantum mechanical considerations further explain
some other key features of HHG. One of these is the
presence of selection rules dictated by symmetry, ruling
what harmonics will be produced. For all species, only
even-order harmonics are observed. Furthermore, further
selection rules ought to be considered for some molecules
[22], specifying more the order of produced harmonics.
D. Single Attosecond Pulse Generation
The photon produced through HHG, with the rela-
tively high energy given by equation 11, will potentially
have an extremely short wavelength of the order of a few
tens of nanometers, and therefore a period of ∼ 100 as.
Therefore, since the generated radiation will be consti-
tuted of single photons, ultrashort coherent pulses of the
duration of a single optical cycle will be attained.
If a temporally Gaussian laser pulse with a femtosec-
ond duration (the shortest attainable by current com-
mon lasers) is employed for the HHG process, this will
generally envelope at least a few optical cycles. There-
fore, as shown in figure 4, HHG will take place several
times, with ionization happening at each peak with high
enough intensity and recombination three quarters of a
cycle later. This will result in a train of attosecond pulses
in the temporal domain, each exhibiting a relatively large
wavelength bandwidth. Given our purpose of attaining a
clear attosecond pulse for imagining purposes, a train of
peaks is to be avoided. In fact, this creates an interfer-
ence patter in the wavelength domain given the Fourier
transform relation between temporal and wavelength do-
mains, deteriorating the quality of the radiation.
To produce single attosecond pulses, the procedure of
Double Optical Gating (DOG) is employed [15, 16]. For
this, the technique of polarization gating (PG) [23] is
supplemented by the addition of a weak second harmonic.
Given a pulse inducing HHG, PG exploits the observed
polarization dependence of HHG to reduce the region of
the pulse that is fertile for HHG [1, 24]. In fact, given
the three step model, HHG takes place predominantly
when the radiation is linearly polarized. In the case of
elliptically polarized light, the added polarization direc-
tion will make the electron move in two dimensions, so
that it will not return in the vicinity of the parent ion
and will not be able to recombine. In practice, this is
achieved through the use of two counter-rotating circu-
larly polarized fields focused on the same position. They
will ensure that the pump polarization is linear only for
a fraction of its duration, hence producing less attosec-
ond pulses. Instead, the addition of a second harmonic
simply enhances the relative intensity of the central peak
of the attosecond train, so that this will be predominant.
In fact, the pulse’s intensity depends on the external field
strength.
III. EXPERIMENT
A. Experimental Setup and Procedure for
Alignment and Orientation
A pump-probe setup is employed to align and ori-
ent a sample of carbonyl sulfide (OCS) molecules. The
optical path is presented in full detail in figure 5.
For pumping, the fundamental tone and second har-
monic of an Nd:YAG laser are used, with wavelengths
of λ1 = 1064 nm and λ2 = 532 nm respectively. Both
their spatial and temporal profiles are Gaussian, and
the pulse duration is of T1 ≈ 12 ns for the fundamen-
tal and T2 ≈ 8.5 ns for the second harmonic. The
Nd:YAG power can be set in a range [50 mJ, 200 mJ]
for the fundamental tone, resulting in a focused inten-
sity of ∼ 1012
W/cm2
. The power of the second har-
monic is roughly 15% that of the fundamental tone. The
intensity and pulse duration ensure the adiabatic align-
ment and orientation of the molecules, while avoiding the
risk of triggering ionization processes. The second har-
monic is produced through a non-linear barium borate
(β-BaB2O4) crystal, and the two beams can be sepa-
rated and recombined arbitrarily. They can be employed
separately for alignment or together with varying phases
or rise-time delays for both alignment and orientation.
Rise time delay is adjusted through an interferometer,
while the phase difference through a fused silica plate.
In fact, the plate’s refractive index, n(λ), is wavelength
dependent and, due to the different refraction, so is the
path travelled by the two beams when the plate is in-
clined. Hence, varying the plate’s inclination introduces
a small delay between the two harmonics, in terms of
a phase difference. A Ti:sapphire laser with wavelength
λT i:Sa ≈ 800 nm is used for the probing process. The
beam pulses are spatially and temporally Gaussian, with
a pulse duration of TT i:Sa ≈ 35 fs. This ensures a focused
intensity of ∼ 1014
W/cm2
, which ionizes the molecules
through photoionization and Coulomb explosion. The re-
quired high powers are achieved through Chirped Pulse
Amplification (CPA), detailed in appendix A.
The overlap of the three beams employed is checked
through the insertion of a glass plate before the ionization

6. 6
Ti:Sa
Nd:YAG
M
M
MM
M
M
M
M
M
M
M
M
M
M
M M
M
M
M
M
M
M M
M
M
M
M
M
MM
M
M
M
S
S
S
HM
HM
Polarizers/Waveplates
Array
PD
PD
HWP
CL
Achromatic CL
Chamber Valve
Delay
Platform
DL CL
Achromatic CL
Alcohol Sheet
Achromatic DL
Dichroic M
Glassplate
CLF
BS
BSInterferometer
FSP
M - Mirror
BS - Beam Splitter
S - Shutter
PD - Photodetector
CL - Converging Lens
DL - Diverging Lens
HM - Height Mirrors
HWP - Half Wave Plate
F - Filter
FSP - Fused Silica Plate
- High Power Ti:Sa
- Low Power Ti:Sa
- Nd:Yag Fundamental
- Nd:Yag First Harmonic
- Low Power Nd:Yag
HWP
HWP
HWP
CL DL Pinhole
FIG. 5: Optical path for the molecular alignment and orien-
tation experiment.
region of our setup, which reflects ∼ 10% of the beams’
power to a series of lenses and ultimately to a photodi-
ode. Through the use of a 10 µm pinhole, the focused
profiles of the three beams (with diameters of 30 µm)
are scanned in three dimension. Using the Ti:Sa as a ref-
erence, the paths of the two Nd:YAG harmonics can be
modified individually by specific mirrors, and their foci
in a coupled manner through the two achromatic lenses.
Figure 6 shows the overlapped profiles of the Ti:Sa and
Nd:YAG first harmonic at the focus of the former beam.
The overlap is the pivotal parameter of the whole exper-
imental setup, and therefore particular care ought to be
employed to ensure it is optimized. In fact, we want to
make sure to probe the region where alignment and ori-
entation are taking place and to correctly superimpose
the two Nd:YAG harmonics to break the field symmetry.
As the foci of the two Nd:YAG beams did not coincide in
the propagation direction, a trade-off position had to be
employed with the Ti:Sa focus in between them, closer
to the less powerful second harmonic.
The actual experiment took place in the vacuum cham-
ber sketched in figure 7, subdivided itself into three sub-
chambers. The OCS sample gas is seeded in helium, and
injected into subchamber (i), with a pressure of the or-
der of ∼ 10−4
Pa, through an Even-Lavie valve [25]
with pulses of ∼ 20 µs. Supersonic cooling and the use
of a skimmer to separate subchambers (i) and (ii) gen-
erate a molecular beam constituted of mainly the lower-
lying rotational states [25], which are more easily aligned
or oriented given their lower temperature (cfr. sections
II A and II B). In subchamber (ii), with a pressure of
∼ 10−6
Pa, molecules are initially let drift. A 10 cm
electrostatic deflector is placed in this region, giving the
possibility of spatially separating in one dimension given
rotational states through a vertically varying and hori-
zontally homogenous electric field. The deflector exploits
the Stark effect to separate high- and low-field seeking
eigenstates spatially [26]. The gas then enters the in-
−30 −20 −10 0 10 20 30
−50
0
50
0
0.5
1
1.5
2
Horizontal Pinhole Position
Ti:Sa and YAG Beams Overlap
Vertical Pinhole Position
LaserIntensity(a.u.)
FIG. 6: Sample image of the beam profiles of Ti:Sa (red)
and Nd:YAG fundamental tone (blue) acquired through the
pinhole used for the beam overlapping procedure. The ap-
proximately Gaussian spatial profile can be observed clearly.
(i) (ii) (iii)
FIG. 7: Vacuum chamber setup, comprising three sections:
(i) injection and selection, (ii) interaction and drift, and (iii)
detection. The image also shows the needed laser polariza-
tions. Image Credit: Prof. Hirofumi Sakai
teraction region of the chamber. Here, the three laser
beams are focused on the same point of the molecular
beam and alignment, orientation and ionization through
photoionization/Coulomb explosion take place. The ion-
ization process conveniently preserves the angle at the
time of probing. In fact, our setup ensures that the ions
will mostly be ejected along the direction of the molecu-
lar axis, therefore retaining the angle with the vertical of
the parent molecule. A time of flight (TOF) mass spec-
trometer then separates the product ions through a set
of electrodes with a potential difference of 6 kV and a
30 cm drift tube. A detailed expalination of TOF mass
spectrometry is given in appendix B. The TOF does
not modify the azimuthal angle retained by the ion ei-

7. 7
-25
-20
-15
-10
-5
0
5
0,5 1 1,5 2 2,5 3 3,5
Signal(a.u.)
Time of Flight (µs)
TOF Mass Spectrometry Data
H+
C+++
/He+
O+++
H2
O+++
C++
O++
O2
+++
S+++
C+
O+
/S++
H2
O+
CO+
OCS++
S+
/O2
+
/SO2
++
OCS+
OCS+
SO2
+
FIG. 8: Spectral profile of the ions produced by the Ti:Sa
laser. We focused our attention to the singly charged sul-
fur, assuming that the contributions to the peak from the
singly charged molecular oxygen and sulfur dioxide, with sim-
ilar mass-to-charge ratios, were negligible. Two peaks were
unidentified, while the two OCS+
peaks are given by differ-
ent sulfur isotopes.
ther, as the acceleration and drifting are perpendicular
to the plane of alignment and orientation. Through the
exploitation of the spectrometer, we employ the S+
ion to
measure alignment and orientation. The observed spec-
tral profile for the gas in the chamber is shown in figure
8.
In subchamber (iii) (pressure of ∼ 10−7
Pa), the de-
gree of alignment and orientation is measured through
two-dimensional velocity map imaging (VMI) [27]. This
experimental technique employs electrostatic lenses to
create a direct correspondence between ion velocity and
detection position, so that the initial molecular angu-
lar distribution can be retrieved. A microchannel plate
(MCP) detector is employed as a two-dimensional detec-
tor, which then lights up a phosphor screen. The spatial
distribution of the S+
ions is recorded through a CCD
camera. Since, as explained above, the azimuthal angle
of the ion is the same as that of the parent molecule, the
S+
angular distribution represents that of the original
OCS molecules.
The polarization of the three laser beams is fundamen-
tal for the outcome of the experiment. In fact, alignment
and orientation take place along the polarization direc-
tion of the pump beams, as seen in sections II A and II B.
It is along this direction that the isotropy of free-space is
broken. Therefore, these ought to be vertically polarized
to the maximum degree possible for a correct use of VMI.
This is ensured through the use of frequency-specific half-
wave plates (so to modify independently the polarization
of each harmonic), polarizers and a removable power me-
ter. Instead, the vertical polarization of the Ti:Sa beam
was kept to a minimum. In fact, the photoionization
and Coulomb explosion processes eject the ions with an
added kinetic energy along the polarization direction of
the laser. Therefore, a non-zero vertical polarization will
affect the degree of alignment. Hence, ideally the probe
ought to be completely horizontally polarized. This in-
troduces a velocity distribution in the TOF data, but its
effect is only a slight broadening of the peak in our mass
spectrometry data. However, as we see from figure 8, we
are far from the resolution limit of the spectrometer, so
this will have no effect on our experiment. Within our
setup, it is observed that the Ti:Sa beam is slightly ellip-
tically polarized. It is therefore impossible to eliminate
all effects of probing on the alignment and orientation
degrees, as we will see in section IV.
Our experiment consisted in measuring the degrees
of alignment and orientation under different conditions.
Test runs were made with only the Ti:Sa probe employed.
Then, the alignment due to the two Nd:YAG harmonics
was measured separately to check the dependence of the
process on the pump power. Finally, the two harmonics
were superimposed for alignment and orientation. Since
neither the relationship between the fused silica plate
inclination and the micrometer controlling it nor that
between inclination and phase difference between har-
monics were known, a calibration was attempted. The
variation in molecular orientation for different microme-
ter positions was therefore checked. Three different step
sizes were employed, to try to understand the aforemen-
tioned relationships. These were 500 µm (large), 25 µm
(medium), and 5 µm (small).
B. Experimental Setup and Procedure for the
Single Attosecond Pulse Production
In order to produce single attosecond coherent radi-
ation, a 5 fs Ti:Sa laser beam is used to induce high
harmonic generation in argon gas. To generate the 5 fs
beam, a ∼ 40 fs, λ = 800 nm laser with a bandwidth of
∆λ = 50 nm is initially employed. Frequency chirping
is induced in the radiation through the use of a neon
hollow fiber, which ensures that the beam is straight
and, through a third order non-linear process, separates
temporally the composing wavelengths and increases the
bandwidth to ∆λ = 200 nm. Then, through a chirped
mirror, the process is reversed and a 5 fs, λ = 800 nm
pulse is attained. This process effectively reduces the
number of optical cycles in the pulse from ∼ 14 to ∼ 3.
As seen in section II C, this in turn diminishes the num-
ber of as pulses in the train. The beam is then introduced
in a vacuum chamber and focused with an intensity of
5·1014
W/cm2
on an Ar beam, injected through an E-L
valve. Figure 9 shows the optical path inside the cham-
ber. The produced radiation has a central wavelength
of λ ≈ 30 nm and is constituted of a pulse containing a
single optical cycle, therefore reaching the required du-
ration of ∼ 100 as. An aluminium filter is then used to
absorb the pump, while letting the attosecond pulse go
on to a diffraction grating, which separates spatially the
composing wavelengths before they reach a CCD camera.
In this way, the wavelength spectrum of the pulse can be
monitored to check whether a single pulse or a train of
pulses are produced, as they show respectively a single

8. 8
Ar Injection
Vacuum Chamber
M
M M
M
SFocusing
Mirror
Toroidal
Mirror
Aluminium
Filter
Diffraction
Grating
CCD
Focus Point
FIG. 9: Experimental setup inside the vacuum chamber for
the production of attosecond pulses through high harmonic
generation. The solid red line represents the 5 fs pump, the
dashed purple line the attosecond pulse.
broad peak or several resolved peaks in the wavelength
domain.
For the isolation of a single as pulse through the DOG
procedure, a second pump beam identical to the previous
one (not shown in figure 9) is employed, and their foci
are overlapped on the same point of the Ar beam.
IV. RESULTS AND ANALYSIS
For the alignment and orientation experiment, the
CCD image was analyzed directly. In fact, since as ex-
plained in section III A the probing mechanism does not
affect the angular distribution of the molecules, their az-
imuthal angle can be calculated directly from the incident
position of the S+
ion on the MCP, captured through the
CCD camera. Figure 10 a) shows an image gathered
through the CCD camera, as well as the angle θ that was
calculated for each data point. As we can see, the CCD
performance is not symmetric about the y-axis, there-
fore, in order to not skew the data, only the right half
of the acquired signal was analyzed. Figure 10 b) shows
the density plot for the data used. Then, a histogram
was plotted for the angular distribution to have a visual
reference to check whether alignment or orientation had
been achieved. Figure 11 shows one of such histograms
plotted with 180 bins with a width of 1◦
. Lastly, for a
quantitative picture on the attainment of alignment and
orientation, cos(θ) was calculated for each data point
and then averaged, or first squared and then averaged
to get cos2
(θ) . Uncertainties for both quantities were
calculated as standard errors. Several acquisition runs
took place for all beam configurations, and the gathered
values were combined as averages. In figure 11 the mea-
sured parameters relative to the presented data are also
given. The cos2
(θ) values are also presented in table
I for the two days in which the experiment focused on
molecular alignment. The separation between different
days is needed for two reasons. At first, the power of
the Nd:YAG was changed between days, so the relative
100 200 300 400 500 600
0
50
100
150
200
250
300
350
400
450
Original CCD Distribution
x position
yposition
a) b)
θ
x position
yposition
Half CCD Density Plot
−200 −150 −100 −50 0 50
50
100
150
200
250
0
5
10
15
20
25
30
35
FIG. 10: Signal acquired through the CCD camera. Image a)
shows the position of the individual ions detected as well as
the angle relevant to our analysis. Image b) shows a density
plot of the data used.
0 20 40 60 80 100 120 140 160 180
0
200
400
600
800
1000
1200
YAG Fundamental Histogram
θ (Deg)
NumberofDataPoints
<cos2
(θ)>=0.579±0.001
<cos(θ)>=0.016±0.002
FIG. 11: Histogram for the angular distribution given by the
Nd:YAG fundamental tone pump, together with the calcu-
lated degrees of alignment and orientation.
improvement, or lack thereof, of alignment for different
pumping configurations may only be considered within a
given day. Secondly, only data taken with the same over-
lap of the foci may be compared effectively. We may only
ensure that the overlap is the same for a given day, as
this needs to be optimized again before every run. The
power used for the first day was 100 mJ and 15 mJ for
the fundamental and second harmonic of the Nd:YAG
laser respectively. For the second day, powers of 130 mJ
and 18 mJ were employed.
Day Probe Only Fundamental 2nd
Harmonic Full Nd:YAG
1 0.561 ± 0.001 0.579 ± 0.001 0.561 ± 0.001 0.571 ± 0.001
2 0.555 ± 0.001 0.579 ± 0.001 0.558 ± 0.001 0.576 ± 0.002
TABLE I: Molecular alignment degree: cos2
(θ) with dif-
ferent pump beam configurations.
For the orientation measurements, figure 12 a) shows
the variation of the cos(θ) parameter for large microm-
eter increments, while figure 12 b) shows the variation for

9. 9
3.5 4 4.5 5 5.5 6
0
0.01
0.02
0.03
Cosine with Phase Changes − Large Steps
Micrometer Position (mm)
‹cos(θ)›
3.5 4 4.5 5 5.5 6
0.57
0.575
0.58
0.585
Cosine Squared with Phase Changes − Large Steps
Micrometer Position (mm)
‹cos2
(θ)›a)
2.95 3 3.05 3.1 3.15 3.2 3.25 3.3 3.35
−0.02
−0.01
0
0.01
0.02
Cosine with Phase Changes − Medium and Small Steps
Micrometer Position (mm)
‹cos(θ)›
2.95 3 3.05 3.1 3.15 3.2 3.25 3.3 3.35
0.54
0.55
0.56
0.57
Cosine Squared with Phase Changes − Medium and Small Steps
Micrometer Position (mm)
‹cos2
(θ)›
b)
FIG. 12: Variations of orientation with fused silica plate incli-
nation given by a) large and b) medium and small micrometer
increments. The alignment variation is given as a reference
for the lasers’ power fluctuations. Black ellipses mark the
possible data points showing the possibility of orientation.
medium and small increments. The variation of cos2
(θ)
is also plotted as a reference. In fact, the lasers employed
are very unstable because of the high powers involved in
the experiment. Hence, their intensity varies largely, and
this affects the orientation of the molecules. A varia-
tion in the measured cos(θ) value could be due to such
power fluctuations instead than a phase variation. The
cos2
(θ) measurement is used as a reference for such
fluctuations. In fact, this should be unaffected by the
phase difference, hence variations in its value may only
be due to power differences. Therefore, we may infer that
we are in the presence of orientation whenever the distri-
bution of cos(θ) in the presented graphs deviates from
that of cos2
(θ) . The set Nd:YAG power (notwithstand-
ing fluctuations) was 130 mJ and 18 mJ respectively for
the first and second harmonics for the large increments,
and 140 mJ and 20 mJ for the medium and small step
sizes.
The attainment of a single attosecond pulse was
λ≈30 nm
λ≈30 nm
a)
b)
FIG. 13: Wavelength distribution of the generated attosec-
ond pulse. Image a) presents the results without DOG, while
image b) shows the observed distribution with DOG.
checked through the CCD camera in which a linear, bijec-
tive map between horizontal position and pulse’s wave-
length distribution was given by the diffraction grating.
Images were acquired when only one pump beam was
employed for HHG and when both pump beams trig-
gered DOG. The comparison of the wavelength profiles
was used to evaluate whether a single pulse or a train
of pulses had been generated. Figure 13 shows the
data taken. Image a) represents the signal when only
one pump beam is employed, while for image b) the two
beams are superimposed to utilize DOG.
V. OBSERVATIONS AND DISCUSSION
Our experimental setup clearly attained the goal of
aligning molecules through the use of a nanosecond non-
resonant intense pump beam, as shown in table I.
In fact, although we observe that the probing process
skewed the data as, given the nonzero vertical polariza-
tion of the Ti:Sa beam, values of cos2
(θ) > 0.5 were
observed when no pumping was taking place, the val-
ues gathered for all fundamental Nd:YAG and all com-
bined first and second harmonic pumping, as well as
one instance of second harmonic pumping, were higher
than the cases in which only probing was employed.
The higher cos2
(θ) can therefore be ascribed to the
Nd:YAG influence. The only data point which shows
no enhanced alignment when the pumping takes place
is given by the 15 mJ second harmonic. Since in this
case cos2
(θ) Ti:Sa = cos2
(θ) 2nd , we may suggest as an
explanation that the power of the pump was simply not
enough to align molecules. Moreover, for both days of the
experiment we observe the expected hierarchy in degree
of alignment cos2
(θ) Ti:Sa ≤ cos2
(θ) 2nd < cos2
(θ) 1st
mimicking the power hierarchy. The allowed equality in
the former relation is given by the expressed possibility
that the second harmonic’s power is too low to trigger

10. 10
alignment. The only result that is not readily explainable
is the fact that the alignment due to the combined laser
fields seems to be lower than that due to the fundamen-
tal alone. In fact, the addition of the second harmonic
should increase the total power of the radiation and en-
hance alignment. One explanation for this behavior could
be that, during our procedure, almost 40 minutes passed
between the measurements with the fundamental alone
and those with the combined fields. In this time, the
overlap of the pump and probe beams could shift consid-
erably, giving the observed results.
The orientation data, instead, allows for less clear-cut
results. In fact, the majority of measurements gives a
cosine value of cos(θ) ≈ 0.016, which is also the value
given when only probing or a single pump color are em-
ployed (therefore, when no orientation is expected). The
non-zero cos(θ) values in these latter instances are
probably to be ascribed to the observed uneven perfor-
mance of the CCD camera, which altered the data. How-
ever, when two colors are employed, the measured degree
of orientation should improve. This is not necessarily ob-
served for most data points. However, there is no clear
understanding of the phase between the two colors for
our data points, as the fused silica plate was not cali-
brated. In fact, the calibration data show two instances
(for micrometer positions of 3.125 mm and 3.250 mm)
in which orientation is enhanced in a way that deviates
from the power fluctuations of the pump beams (cfr. fig-
ure 12). This is a sign that orientation may have been
achieved. Moreover, as orientation is more difficult to
trigger than orientation, the power of the pump lasers
may have been too low or the overlap of the three beams
may not have been good enough.
Finally, the single attosecond pulse generation exper-
iment was thoroughly successful. As we can clearly see
from figure 13, the DOG procedure determined the iso-
lation of a single attosecond pulse. In fact, in image a)
the observed distinct peaks are a sign that HHG is giving
a train of pulses, while the unique broad peak in image
b) shows how, through DOG, a single as peak was gen-
erated.
VI. CONCLUSIONS AND OUTLOOK
Overall, our experiments were largely successful.
Molecular alignment was clearly attained with different
setups, and the expected relationship between cos2
(θ)
and pump power was observed. The only feature of align-
ment that requires further study is its lower degree seen
for molecules under the two-color field than under the
Nd:YAG fundamental alone. As mentioned earlier, the
imperfect overlap of the three foci or its shift with time
due to the lasers’ instability may explain this behavior.
This may be checked by running experiments with the
two setups closer in time. The overall degree of align-
ment can also be improved to get closer to the unattain-
able cos2
(θ) = 1 limit. This can be done by improving
the overlap of the three beams or by increasing the power
of the lasers. Both these results are achievable, for in-
stance, via the substitution of the two achromatic lenses
in our setup with two sets of frequency-specific lenses,
one for each harmonic. On a first level, this will decou-
ple the foci of the two Nd:YAG harmonics, so that the
three beams could be fully overlapped even in the lasers’
propagation direction and no trade-offs will be necessary
as in the present setup. Moreover, the achromatic lenses
are the optical element that limits the power of the pump
beams. In fact, the glue holding together their two com-
ponents (needed for the achromaticity) is easily burned
by our laser intensities.
Further study is instead needed to understand whether
our setup is able to achieve molecular orientation. On
a first level, higher laser powers and a better overlap
for the three beams may again be the key to trigger a
higher, more easily identifiable, degree of orientation. In
this respect, the same considerations made for molecular
alignment apply. Instead, specific to orientation, the cali-
bration of the fused silica plate should be continued. The
small increments in the micrometer reading were seen to
have possibly shown orientation. The process should be
carried on with a larger range checked on the micrometer
and even finer increments. This might better reveal the
relationship between the micrometer reading, the plate’s
inclination and phase difference, fundamental for the ori-
entation experiment in order to reach an optimal phase.
Some improvements to the experiment that apply to
both molecular alignment and orientation can also be
identified. On the side of the optical elements, the over-
lap process and all other optimization procedures could
be made easier through computer-controlled or even au-
tomatic feedback systems. Moreover, as we can see from
figure 10, the data is affected by considerable noise lev-
els given by leftover molecular species in the chamber.
Their presence can be also noted from the recorded TOF
data. The high noise hides the signal of the S+
ions, and
therefore decreases the observed degrees of alignment and
orientation. The removal of such background, either di-
rectly from the chamber or through a subtraction algo-
rithm, has the potential of leading to better results, and
is currently under development.
If it is demonstrated through the proposed improve-
ments that our setup is capable of achieving orientation,
the plasma shutter ought to be made operational. In this
way, our final objective of completely field free molecular
orientation may be pursued. To do so, the position of the
ethylene glycol sheet ought to be optimized at the focus
of the Ti:Sa beam needed to trigger plasma formation,
and the appropriate delay time ought to be found. All
the proposed improvements to the setup will ultimately
be instrumental for such a delicate aim.
In terms of the extremely successful attosecond pulse
production experiment, the main improvement that
could be made regards the understanding and removal
of the interference pattern on the wavelength spectrum,
which can be observed in figure 13. This is certainly

11. 11
due to some interaction between the beams within the
chamber, and its nature may probably be identified eas-
ily. Moreover, it would now be extremely interesting to
start employing the produced attosecond pulses for their
proposed purpose, that is as probes for ultrafast molec-
ular or electronic phenomena, as the electrons’ motion
within semiconductors. They could also be used to ob-
serve the electrons’ motion during alignment and orien-
tation, which could ideally link the two performed exper-
iments.
Therefore, important progresses were made through
our project towards the overall objectives of the Hiro
Sakai Group. Our setup was able to clearly achieve
molecular alignment and there were promising signs of
orientation. However, there is considerable room for the
improvement of the experiment, as our limited time did
not allow a full optimization of all components and details
of the elaborate experiment. This means that improved
alignment and clear orientation may be achieved reason-
ably soon, so that the plasma shutter for completely-
field-free orientation may be included as well. Once this
is done, one last far-reaching aim may be pursued: the
use of aligned/oriented molecules as waveplates to modify
the polarization of as pulses and increase their potential
as probing radiation.
Acknowledgments
I would like to thank all the members of the Hiro Sakai
Group for their guidance and help in all parts of the ex-
periment, from its theoretical components to its imple-
mentation: my gratitude goes to professor Dr. Hirofumi
Sakai, assistant professor Dr. Shinichirou Minemoto, vis-
iting research scientist Dr. Hiroki Mashiko, doctoral stu-
dent Md. Maruf Hossain, and master student Wataru
Komatsubara. I would also like to thank specifically my
fellow UTRIP student Holly Herbert from Trinity Col-
lege Dublin for being an outstanding lab partner and
sharing this project and experience with me. My par-
ticipation in this project was made possible through the
FUTI Global Leadership Scholarship and the Hoffman
Research Support Grant, awarded me respectively from
Friends of UTokyo, Inc. and the Hoffman Foundation.
APPENDIX A: CHIRPED PULSE
AMPLIFICATION
The amplification of ultrafast lasers (with pulses of
femtosecond duration) is technically troublesome. In
fact, the compression of high energy in short pulses can
induce extremely high powers and therefore beam distor-
tion and optical damage in the components involved in
the required amplification process [28]. The technique of
Chirped Pulse Amplification (CPA) is able to overcome
such limitation by applying the amplification process to
longer pulses. In our explanation of CPA, we will fol-
low the treatment given in [28, 29]. The principle of
chirped pulse amplification is based on the employment
of a stretcher and a compressor respectively used to elon-
gate the temporal duration of a low-energy femtosecond
pulse and then to recompress it to its original duration.
The stretching process exploits the relatively broad spec-
tral bandwidth inherent to ultrashort pulses to introduce
a wavelength chirping, usually through dispersion in a
given material. Devices employed vary from diffraction
gratings to optical fibers. The compressor operates in a
similar, reverse fashion, restoring the original duration
of the pulse. Between the stretcher and the compressor
an amplification process takes place. This may employ
all available techniques for laser amplification, resulting
in an increase in the pulse energy by ∼ 8 ± 2 orders of
magnitude. However, given the longer duration of the
pulse, this energy will result in peak powers that will not
damage or distort the amplification medium nor other
optical elements. After the recompression, the amplified
energy will remain unaffected, resulting in the required
high peak powers. In this way, the only optical elements
that need to be able to withstand the high powers of the
short pulse are only those in the compressor. The high ef-
fectivity of the CPA method in achieving highly energetic
ultrashort laser pulses is therefore given by the separa-
tion it operates between the short pulse generation and
the amplification process needed to achieve high powers.
APPENDIX B: TIME OF FLIGHT MASS
SPECTROMETRY
Time of Flight mass spectrometry is an experimental
technique employed to determine the composition of a
given gaseous sample through the identification of the
molecules and atoms composing it. To do so, it exploits
the fact that the acceleration that an electric field im-
presses on a point charge is dependent on its charge-
to-mass ratio. By ionizing the species composing the
sample - usually through an electron discharge or pho-
toionization/Coulomb explosion processes - in the extrac-
tion region and accelerating them for a fixed length in a
constant electric field, molecules or atoms with different
mass-to-charge ratio are given different velocities. Then,
a drift tube is used to separate temporally such species by
allowing them to travel at the aforementioned different
velocities. Finally, a detector (usually a MCP detector)
records the arrival times of the ions. Such times are then
fitted to recover the relationship between arrival time and
charge-to-mass ratio, so that information on the makeup
of the sample can be retrieved.
More systematically, a force F = qE will be exerted
on an ion formed in a region with a constant electric field
E, entailing a potential energy at the ionization position
r before the end of the extraction region (where the zero
potential energy is set) of

12. 12
U = −
0
r
F · dr = qEr. (B1)
By energy conservation, at the beginning of the drift
tube, where the E field goes to zero, we will have K =
1
2 mv2
= qEr, so that the ions will have a mass-to-charge
ratio dependent velocity
v = 2Er
q
m
. (B2)
If we let the length of the drift tube be d and the time
employed by an ion to get to the detector be ttof, it is
readily derived that
ttof =
d
v
=
m
q
d
√
2Er
= k
m
q
, (B3)
where the constant k simply combines all parameters
involved, so that no specific knowledge on the experi-
mental apparatus is required to perform TOF mass spec-
troscopy. Finally, to directly retrieve information on the
individual species, we may rewrite
m
q
= k t2
tof, (B4)
so that a linear fit on the square of the time-of-flight
data can be employed.
All this treatment assumed the lack of an initial veloc-
ity distribution in the acceleration direction. In practice,
ions are generally extracted with a nonzero velocity in
such direction. This will result in broader peaks in the
time-of-flight spectrum, which may lead to unresolved
data when extremely high precision is needed. In most
applications, the initial velocity distribution is not ex-
tremely troublesome and is neglected altogether.
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