Download All-Optical Alignment and Orientation of Neutral Molecules

All-Optical Alignment and Orientation of
Neutral Molecules & Attosecond Pulse
Generation
Holly Herbert
Department of Physics, Trinity College Dublin,
College Green, Dublin 2, Ireland
Summer of 2016
Abstract
The central body of this report, labelled section I, focuses on the research conducted in the area of Molecular Alignment and
Orientation, with section II addressing the research conducted in the area of Attosecond Pulse Generation. As detailed in section I,
the alignment of a sample of gasous OCS molecules was achieved through the application of an intense single colour non-resonant
laser field of frequency ω. The degree of alignment was probed via coulomb explosion of the sample molecules and subsequent
measurement of the directions of the ejected fragment ions. The alignment parameter hcos2 θ i, where θ is the angle between the
molecular axis and the polarisation axis of the applied field, was calculated to be 0.5791±0.001, which had increased from the
background value of 0.54 beyond the margins of experimental error. Molecular orientation of the same sample was attempted via the
addition of a second colour laser field of frequency 2ω, with the degree of orientation probed in the same manner. The orientation
parameter hcosθ i was calculated to be 0.017±0.001, which did not increase from the background value of 0.016 beyond the margins
of experimental error. Thus no conclusive evidence was found to verify the achievement of molecular orientation. The relationship
between the degree of orientation achieved and the relative phase between the two applied laser fields was also investigated, with no
conclusive evidence drawn to support that variations of the relative phase have any impact on the achieved degree of orientation.
As detailed in section II, 40fs laser pulses outputted by a standard TiSap laser were temporally reduced to 5fs pulses through the
employment of a hollow core fibre compressor and used to generate a pulse train containing 4 attosecond pulses via High Harmonic
Generation from a sample of gaseous Argon. Double Optical Gating was then successfully employed in order to isolate a single
attosecond pulse from this train.
Section I - All Optical Molecular Alignment and Orientation
Introduction
symmetric top molecules.
There are however a number of flaws associated with
such traditional techniques. Firstly, brute force orientation
requires extremely strong electrostatic fields, the presence
of which often alters the chemical and physical properties
of the molecules involved, thus presenting a large barrier
to the accurate study of chemical and electronic steroedynamics using samples of oriented molecules. Hexapole
focusing involves the spatial separation of the original
sample based on rotational state, and thus provides samples of oriented molecules with densities too low for
further experimentation. Finally, both techniques rely
exclusively on the interaction between the electrostatic
field and the permanent molecular dipole moment and
thus are not applicable to non-polar molecules.
In recent years, almost all molecular alignment and
orientation techniques have turned to the employment of
laser fields. The alignment of neutral iodine molecules
[9] as well as many other molecular species [10] has been
demonstrated by Sakai et al. via the application of a
strong, non-resonant, linearly polarised laser field. This
technique relies on the interaction between the laser field
and the induced dipole moment of the molecules, and
results in the alignment of the molecular axis along the
The manipulation of molecules via the application of external fields has found itself to be, and indeed remains,
one the most thriving areas of research in Physics. The
potential to exert control over the translational and rotational degrees of freedom of molecules has wide ranging
applications that span the breath and depth of Science,
from allowing the investigation of chemical [1] and electronic [2] stereodynamics, to enabling the creation of
molecular movies [3-5]. The resulting samples of aligned
or oriented molecules offer fantastic prospects for novel
experiments with complex molecules, for example High
Harmonic Generation [6], and overall, for a large range
of experiments in Chemistry and Physics, a high level of
control over the external degrees of freedom of molecules
is hugely beneficial.
Many different molecular orientation techniques have
been realised over the years. Brute force orientation [7]
and hexapole focusing [8] were two of the first techniques
developed. By Brute force orientation, a strong electrostatic field orients molecules with large dipole moments,
and by hexapole focusing, inhomogeneous electrostatic
fields, created by a hexapole focuser, orient state selected
1
All-Optical Alignment and Orientation of Neutral Molecule & Attosecond Pulse Generation
polarisation direction of the applied field. However, this
method is incapable of discriminating between the parallel and anti-parallel configurations of the molecule, and
so may not be used in order to achieve orientation.
Many modern orientation techniques have been based
on the proposal [11-12] that a combination of electrostatic
field and intense non-resonant laser field may result in an
enhanced degree of molecular orientation compared to
that achieved by traditional methods. Techniques based
on this combined field approach have been employed
by the Sakai group, as well as many others, in order to
demonstrate both 1[13,14] and 3[15] dimensional molecular orientation. While this approach does facilitate an
enhanced degree of orientation when compared to the
brute force method, it remains inapplicable to non-polar
molecules due to the dependence of the approach on the
interaction between the electrostatic field and the permanent molecular dipole moment, and also in depending
on this interaction, the technique does not lend itself
to development towards a method capable of achieving
orientation in the absence of applied fields.
With these issues in mind, the Sakai group proposed[16] and demonstrated [17] a novel technique for the
achievement of all optical molecular orientation i.e. orientation in the absence of an electrostatic field. This technique, based on what is referred to as the two color laser
field approach, does not rely on the permanent dipole
moment of the sample molecules, nor on any resonant
process and also offers an enhanced degree of orientation compared to traditional techniques. The mechanism
underpinning the technique is based on the interaction
between the laser field and the molecular anisotropic
polarisability as well as the anisotropic hyperpolarisability. This technique offers numerous advantages, from
enabling the control of the achieved molecular orientation through the variation of the relative phase between
the two colours, to the applicability of the approach to almost non polar molecules. This method also lends it self
to development towards a technique capable of achieving
orientation in the completely field free regime, as has
been suggested by Sakai et al. [18].
ment of a molecular axis to one hemisphere relative to the
other, i.e. the external field preferentially selects either
the parallel or anti-parallel configuration. The inversion
symmetry of the distribution is broken, and the molecules
are often described as behaving as single headed arrows.
Molecular orientation is achieved through the application
of a vertically asymmetric field, as illustrated by figure
1(c).
Figure 1: (a)
(b)
(c)
(a): Absence of external field- Random distribution
(b): Application of vertically symmetric field- Alignment
(c): Application of vertically asymmetric field- Orientation
Basic Theory
Traditional techniques designed for the achievement of
molecular orientation involved exploitations of the Stark
effect; the interaction between the permanent dipole moment of a molecule and an applied electric field. The
permanent dipole moment ~µ of any molecule is given by
~µ = ∑ qi~ri ,
(1)
i
where the vectors ~r j give the positions of charges qi
and the sum extends over both the electrons and nuclei in
the molecule. The potential energy of a neutral molecule
with permanent dipole moment ~µ, placed in an electric
field ~E, is given by
Ustark = −~µ · ~E = −µhcosθ i E = µe f f E,
(2)
where θ is the angle between the molecular dipole
moment and the lab-fixed axis, as defined by the direction
of the applied field ~E. When the applied field is spatially
inhomogeneous, the molecule experiences a force given
Alignment versus Orientation
by
In the absence of any external fields, a sample of linear
~F = − dU = µe f f dE ,
(3)
dx
dx
molecules will be randomly distributed in space, as illustrated by figure 1(a). Molecular alignment refers to where µe f f depends explicitly on hCosθ i, which is a functhe confinement of a molecular axis to a laboratory-fixed tion of the rotational state of the molecule. This force
axis, as defined by the direction of an applied electric allows the spatial separation of a molecular sample based
field. The molecular fixed axis may align parallel or anti- on rotational state and is exploited by the Hexapole focusparallel with respect to the lab-fixed axis. This implies ing technique in order to generate state selected samples
that the molecular ensemble will remain inversion sym- in which all molecules are oriented at a single angle θ
metric, and the molecules are often described as behaving with respect to the lab-fixed axis. It is worth noting that
as double headed arrows, in that neither the parallel nor molecules possess vibrational, rotational and electronic
anti-parallel configuration is preferentially selected by the degrees of freedom, each with its own characteristic enexternal field. Molecular alignment is achieved through ergy scale. Interactions of an external electric field with
the application of a vertically symmetric field as illus- a molecule are unlikely to perturb the electronic or vitrated by figure 1(b).
brational structure of the molecule, only the rotational
In contrast, molecular orientation refers to the confine- structure.
All-Optical Alignment and Orientation of Neutral Molecule & Attosecond Pulse Generation
In terms of Brute force orientation, spatially homogenius electrostatic fields are employed in order to align
molecules via the interaction between the applied field
and the permanent molecular dipole moment ~µ. In general for linear molecules, the permanent dipole moment
will lie along the molecular axis. Under the influence of
an applied electric field, the dipole moment and so molecular axis will precess about the lab-fixed axis in a manner
analogous to a magnetic moment precessing about an
applied magnetic field. The molecular axis in this way is
confined to a small range as it swings to and fro about
the field direction, and such a state of the molecule is
referred to as a pendular state in which the molecule
may be considered, on average, to be aligned with the
direction of the applied field. Both the hexapole focusing
and brute force alignment methods allow the achievement of modest orientation and rely on the interaction
between the field and the permanent dipole moment of
the molecule.
In attempts to improve the degree of alignment and
orientation achieved, attention has been turned to the
employment of laser fields. When considering the interaction of a laser field with a molecule, a number of points
should be noted. Firstly, for an electromagnetic wave, the
relation between electric and magnetic field strength is
given by
~E = c~B,
(4)
a linear molecule placed in an electric field of the form
E~(t) = E0 (t)Cos(ωt), is given by
Ĥ = B~J 2 − ~µ · ~E,
(5)
where B is the rotational constant of the molecule, ~J
is the angular momentum operator and B~J 2 represents
the unperturbed Hamiltonian of a linear molecule, approximated as a rigid motor. Upon the application of
an electric field ~E, a molecule generally responds by redistributing its internal charge, leading to the formation
of an induced dipole moment, µ~ind . Provided that the
applied field is small, the induced dipole moment of a
molecule takes the form
µ~ind = α~E,
(6)
where α is the molecular polarisability. Thus in the presence of an electric field ~E, the total dipole moment of a
polarisable molecule becomes
µ~tot = ~µ + µ~ind = ~µ + α~E,
(7)
and the Hamiltonian of the system becomes
Ĥ = B~J 2 − (~µ + α~E) · ~E
(8)
Due to the fact that the electric field changes direction
every half optical cycle, the interaction with the permanent dipole moment averages to zero over one full optical
thus justifying neglecting the interaction of the magnetic cycle and the −~µ · ~E term is dominated by the interaction
field component with the molecule, as it is smaller than of the laser field with the induced dipole moment of the
the interaction with the electric field by a factor of the molecule. Averaged over one optical cycle, the interaction
speed of light. It should be noted that the laser field may term takes the form
interact with the sample molecules in either the adiabatic
1
or non-adiabatic regime. This report focuses on tech−µ · E = − E2 ([α para − α perp ]cos2 θ + α perp ),
(9)
2
niques involving adiabatic interactions, i.e. techniques
1
in which the duration of the applied laser pulse is far
= − E2 (∆αcos2 θ + α perp ),
(10)
2
larger than the rotational period of the sample molecules.
Finally, laser-based alignment and orientation techniques where α para and α perp are the components of the polarisare greatly enhanced by the cooling of the initial rota- ability parallel and perpendicular to the molecular axis retional energy of the sample molecules, and the majority spectively and θ is the polar angle between the molecular
of methods assume a high degree of rotational cooling axis and polarisation axis of the laser pulse. Provided that
prior to the application of the alignment or orientation the polarisability is anisotropic, i.e. that α para − α perp 6= 0,
technique.
this interaction may be exploited in order to achieve
Molecular alignment may be achieved through the ap- molecular alignment. The induced dipole moment is
plication of a vertically symmetric, strong, non-resonant the same in both directions along a linear molecule and
laser field of frequency ω. In order to understand the its interaction with the laser field creates a symmetric
mechanism underlying this technique, it is necessary to double potential well. If α para < α perp , equation 10 shows
consider the manner in which the laser field interacts minima around θ=0, π, thus creating a potential miniwith the molecule. A molecule may be treated as a spatial mum for the molecules along the polarisation direction
distribution of charge, and thus may be characterised by of the laser field. The eigenstates of the molecules in the
a multipole expansion; a series in which the first term is presence of the electric field are referred to as pendular
referred to as the monopole, the second as the dipole and states in which the molecular axis liberates around the
so forth. The various terms in the expansion are referred polarisation direction. Provided that the electric field is
to as moments of the charge distribution. The monopole turned on adiabatically, the pendular states consist of
corresponds to the total charge, which, for the purposes linear superpositions of the field free rotational states.
of aligning neutral molecules, is zero, and as a result The anisotropy of the molecular polarisability does not
the multipole expansion will be dominated by the dipole distinguish between the two ends of the molecule, with
moment. The interaction energy associated with a dipole both the parallel and anti-parallel configurations equally
moment ~µ in an electric field ~E is given by U = −~µ · ~E, probable, and so this technique may not be employed in
as mentioned in equation 2. Thus, the Hamiltonian for order to achieve orientation.
All-Optical Alignment and Orientation of Neutral Molecule & Attosecond Pulse Generation
When orientation is sought, a vertically asymmetric
interaction potential is required in order for one configuration of the molecule to be preferentially selected over
the other. There exist two central methods by which this
is achieved
• The combined electrostatic and intense non-resonant
laser field approach
• The two colour intense non resonant laser field approach
In the combined field approach, the application of a static
electric field modifies the double potential well created by
the laser field alone, effectively resulting in one well being
lowered in energy with respect to the other. With one of
the wells corresponding to θ=0 and the other to θ=π, one
orientation will be preferentially selected over the other
depending on the manner in which the symmetry of the
potential is broken.
In the two colour laser field approach, as pioneered by
the Sakai group, a second laser field is employed such that
the superposition of the two colours yields an asymmetric
electric field and thus asymmetric potential. The total
electric field takes the form
E(t) = E0 (t)[Cos(ωt) + γCos(ωt + φ)],
(11)
where E0 (t) is the electric field amplitude, γ is the ratio
of amplitudes and φ is the phase difference between the
two colors. ω represents the frequency of the fundamental tone, and 2ω represents the frequency of the second
colour.
The Hamiltonian of the system makes clear the underlying physics of this technique. The key lies in the addition
of the hyperpolarisability term to firstly, the expression
for the induced dipole moment of the molecules in the
presence of the laser field, and secondly to the Hamiltonian itself. As stated in equation 6, the induced dipole
moment of a molecule is linear in the applied electric field
strength ~E, provided that the field is small. Including the
next higher order term in the expression for the induced
dipole moment yields
with respect to the polarisation axis, and the hyperpolarisability interaction is responsible for the asymmetry of
the potential, which allows the achievement of orientation. The polarisability interaction takes the same form
as mentioned in equation 10, with the hyperpolarisability
interaction taking the form
1
− β E~2 · ~E = − [( β para − 3β perp )cos3 θ + 3β perp cosθ ] E3 ,
6
(15)
where β para and β perp are the hyperpolarisability components parallel and perpendicular to the molecular axis,
respectively. In order to maximize the asymmetry of the
potential to enable the selection of one configuration over
the other, the hyperpolarisability interaction should be
maximized. To achieve this, the parameter to be maximized is
h E3 i =
(16)
where φ is the relative phase between the two colours.
Maximal asymmetry is thus achieved by setting the relative phase difference equal to 0 or π. Figure 2 below
illustrates the dependence of the asymmetry of the potential on the relative phase difference. With a phase of π2 ,
the symmetry of the single laser field induced potential is
maintained, and no orientation should be achieved. With
a completely random phase, the potential starts to change
shape however not in a drastic manner. Finally with
a phase of π, the potential becomes strongly vertically
asymmetric, allowing the preferential selection of either
the up or down orientation of the molecules as desired.
In this manner, the extend to which the symmetry of the
potential is broken is completely dependent on the phase
between the two colors, and thus the degree of orientation
may be controlled by varying the relative phase.
Unbroken Vertical Symmetry : Phase = π/2
Potential (a.u.)
0
µ~ind = α~E + β~E2 ,
3
γE0 3 cosφ
4
θ
π
Slight Vertical Asymmetry : Random Phase Maximum Vertical Asymmetry : Phase = 0
Potential (a.u.)
0
θ
π
Potential (a.u.)
0
(12)
where β is the molecular hyperpolarisability. The interaction term −~µ · ~E to be added to the Hamiltonian in this
case becomes
Figure 2: Illustration of the dependence of the interaction potential
−~µ · ~E = −(~µ + α~E + β E~2 ) · ~E,
(13)
yielding a Hamiltonian of the form
~2 ) · ~E
Ĥ = B~J 2 − (~µ + α~E + β E
(14)
As before, the B~J 2 term represents the unperturbed rotational Hamiltonian of the molecule and the interaction
with the permanent dipole moment averages to zero over
one optical cycle. Thus, the polarisability interaction is responsible for the creation of a double potential well, preferentailly selecting neither configuration of the molecule
on the relative phase between the two colours
It is important to notice that the polarisability interaction, responsible for molecular alignment, depends explicitly on the term cos2 θ, with the hyperpolarisability
interaction depending explicitly on cosθ. The angle θ between the molecular axis and the polarisation direction
of the applied laser field is an experimentally measurable
parameter, and the calculation of hcos2 θ i and hcosθ i for a
given distribution of molecules allows the quantification
of the experimentally achieved degree of alignment and
orientation respectively.
θ
π
All-Optical Alignment and Orientation of Neutral Molecule & Attosecond Pulse Generation
Experimental Set up
The Lasers
There was need for three laser beams in this experiment. Each beam was generated using either a Nd:YAG
or TiSap laser, both of which employed chirped pulse
amplification*1 .
1- Nd:YAG fundamental tone: needed to achieve molecular alignment
•
•
•
•
•
Vertically polarised pump pulse
λ= 1064 nm (IR)
Focus intensity= 1012 W/cm2 .
Pulse Duration=12 ns
Spatial and temporal gaussian profile*2
Central Features of the Optical Set Up
• Two separate paths for the TiSap and Nd:YAG beams
• Each path contained a series of optical elements (mirrors, lenses) in order to guide each beam to the central interaction chamber
• Half wave plates were inserted into both paths in order to ensure the horizontal polarisation of the TiSap
beam and the vertical polarisation of both harmonics
comprising the Nd:YAG beam
• A fused Silica plate was inserted into the path of the
Nd:YAG beam only and was used to vary the relative
phase between the two harmonics
The Chambers
Neutral OCS seeded in helium gas was used as a sample.
The
set up, as illustrated in figure 4, consisted of three
2- Nd:YAG second Harmonic: needed to break the symdifferentially
pumped vacuum chambers, with pressures
metry of the fundamental to achieve molecular orienta−4
−6
of 10 , 10 and 10−7 respectively, as viewed from left
tion
to right.
• Generated through second order harmonic generation in a non-linear crystal (BBO) by the fundamental
tone
• Vertically polarised pump pulse
• λ= 532 nm (green vis)
• Focus intensity= 1012 W/cm2
• Pulse Duration= 8.5 ns
• Spatial and temporal gaussian profile
3- TiSaphire: needed to probe the achieved degree of
alignment or orientation via coulomb explosion of the
Figure 4: Schematic representation of the involved vacuum chambers
sample molecules
and detection system
•
•
•
•
•
Horizontally polarised probe pulse
λ= 800 nm
Focus intensity= 2 × 1014 W/cm2
Pulse Duration= 35 fs
Spatial and temporal gaussian profile
The Beam Paths
Figure 3: Schematic representation of the optical set up
• Seeded OCS gas was pumped into the first chamber
via an Evan Lavie valve
• Supersonic expansion of the gas allowed cooling below 1K
• A skimmer was appropriately positioned in order
to pass only the coldest molecules into the second
chamber
• Within this chamber, the three laser beams were spatially overlapped and focused to a point which lay
both directly in the path of the OCS beam, and between a set of electrodes
• At this point, the Nd:YAG beam(s) aligned or oriented the OCS molecules, depending on whether the
single or two colour approach was being employed
• In the presence of the Nd:YAG pulse, the TiSap probe
pulse dissociated the OCS molecules via coulomb
explosion
• The fragment ions were accelerated towards a TOF
drift tube by the surrounding electrodes, allowing
the temporal separation of the fragment ions based
on their charge to mass ratio
• The ejected ions reached an MCP, the anode of which
was formed by a phosphor screen
• The MCP was appropriately gated in order to image
singly ionised sulfur, S+
All-Optical Alignment and Orientation of Neutral Molecule & Attosecond Pulse Generation
• Once struck by an ion, the phosphor screen fluo- TOF Mass Spectrometer
resced, and was imaged by a CCD camera which
The TOF mass spectrometer played the central role within
outputted 2D distributions of S+ ions at the instant
the detection system of enabling the imaging of singly
of coulomb explosion
ionised sulfur, S+ , only. This piece of apparatus allowed
the temporal separation of the different fragment ions
The Detection System
present in the interaction chamber and facilitated the
identification of the time at which each species impacted
In order to investigate the achieved degree of alignment
the phosphor screen, referred to as the time of flight
and orientation, a detection system consisting of a TOF
(TOF). This identification allowed the MCP to be gated
mass spectrometer, MCP, Phosphor screen and CCD camsuch that the outputted 2D distributions were captured
era was employed. The detection system functioned by
for S+ only.
imaging the fragment ions ejected from OCS molecules
The manner in which the TOF mass spectrometer funcupon interaction with the TiSap probe pulse. The TiSap
tioned
may be understood in a number of simple steps.
14
probe pulse had an intensity of 10 W/cm2 , exceeding
Firstly, upon coulomb explosion, the fragment ions were
the ionisation threshold of OCS molecules. In this high
accelerated towards the TOF drift tube by the electrostatic
intensity regime, there were two central mechanisms via
field generated by the surrounding electrodes, gaining
which the fragmentation of the OCS molecules could
energy W
occur
W = qEr,
(19)
• Photodissociation; The breaking of molecular bonds
upon photon absorption
• Coulomb explosion; A two step process involving
ionisation, followed by bond breaking due to the
repulsion between the molecular components of the
same charge
In the process of Coulomb Explosion, by the conservation of angular momentum, the fragment ions were
ejected and recoiled along the molecular bond axis, thus
maintaining the angle θ between the vertical polarisation
axis of the Nd:YAG and the molecular axis. Imaging OCS
molecules at the instant of Coulomb Explosion allowed
the extraction of the angle θ from the 2D distributions,
and so enabled the quantification of the achieved degree
of alignment and orientation by allowing the calculation
of the alignment and orientation parameters, hCos2 θ i and
hCosθ i, respectively. It was decided that for this experiment, the Coulomb Explosion channel described by equations 17 and 18 would be focused on, with all generated
2D distributions representing singly ionised Sulfur only.
where E is the electric field strength, q is the charge of
the fragment ion and r is the distance from the point of
ejection to the TOF drift tube. Assuming zero kinetic
energy in the direction of motion prior to acceleration,
the velocity of the fragment ion upon reaching the TOF
drift tube was given by
r
v=
2qEr
m
(20)
Within the TOF drift tube, no fields were present and
the fragment ions were allowed to drift, in a presumed
frictionless environment. Assuming that the TOF drift
tube had a length L, the time taken for the respective
fragment ions to reach the phosphor screen was governed
exclusively by the charge to mass ratio and given by
tto f =
L
=L
v
r
m
=k
2qEr
r
m
q
(21)
Connecting the MCP to a digital Oscilloscope allowed
the observation of the signal illustrated in figure 5 below.
OCS+ → OCS2+ + e−
(17) The displayed x axis represents time, with each peak
corresponding to a different characteristic TOF, and so
2+
+
+
OCS → S + CO
(18) to a different ionised species present in the interaction
chamber.
The polarisations of the Nd:YAG and TiSap probe
pulses were pivotal in terms of maintaining the angle
θ during the imaging process. Once ejected, the fragment
ions were subject both to the electrostatic field accelerating them towards the TOF mass spectrometer, and also
to the field of the TiSap pulse, accelerating them along
the direction of polarisation. It was thus necessary that
the TiSap pulse was polarised in the horizontal direction,
normal to the detector plane and parallel with the axis of
propagation of the ions. In this manner, any change in
the trajectory of the ions due to the presence of the TiSap
pulse would not effect the projection of the angle θ onto
the plane of the detector. In addition, any overestimations
of the achieved degree of alignment due to the presence Figure 5: Time of flight signal as outputted by the digital oscilloscope
connected to the MCP
of the TiSap pulse were avoided.
All-Optical Alignment and Orientation of Neutral Molecule & Attosecond Pulse Generation
In an ideal situation, this plot would show signals corre• t= 2µs: Voltage applied to MCP is increased from
sponding only to species ejected from the fragmentation
1kV to 2kV for the purpose of gating for S+
of OCS, however due to imperfect pumping of the vac• t=49.2ms: Evan Lavie Valve is pulsed, injecting OCS
uum chambers, many other species were also present.
into chamber. It is desired that this happens 0.8ms
The raw TOF data did not enable the direct linking of a
before the emission of the TiSap pulse, however since
peak to an ionised species as the displayed TOFs were
the TiSap acts as the master signal, the operation of
not absolute. In order to overcome this problem, a list
the pump valve had to be timed in this manner.
was generated with all of the possible molecular species
• t=50ms: Next pulse is emitted from the TiSap laser
present in the chamber and their corresponding charge to
mass ratios. Of all of the species present, it was obvious
Experimental Method
that singly ionised hydrogen had the smallest charge to
mass ratio and so shortest TOF, with singly ionised OCS There were three central aims in this experiment;
having the longest TOF by the same argument. Know• To achieve and probe the alignment of OCS
ing the TOF and charge to mass ratios associated with
molecules, requiring the temporal and spatial overthe first and final peaks yielded a pair of simultaneous
lap of the Nd:YAG fundamental and TiSap probe
equations of the form
pulses
r
m
• To achieve and probe the orientation of OCS
+ b,
(22)
tto f = k
q
molecules, requiring the temporal and spatial overlap of the Nd:YAG fundamental, second harmonic
where the constant b was added to take into account the
and TiSap pulses
fact that a time t=0 did not correspond to a TOF of zero.
• To demonstrate the dependence of the degree of
Solving the pair of simultaneous equations for k and b
achieved orientation on the relative phase between
gave the relation
the two harmonics generated by the Nd:YAG, rer
quiring the adjustment of the fused Silica plate
m
tto f = 0.4(
) + 0.16,
(23)
q
Spatial Overlap of the Three Beams
which was manipulated to give
It was pivotal to the achievement and detection of molecular alignment and orientation that accurate spatial overlap
m
(
) = 2.5(tto f ) − 0.4
(24) of the three beams was attained. A number of steps were
q
employed in order to achieve this
Thus, the TOF associated with each peak provided infor• A glass plate was inserted into the path of both the
mation on the charge to mass ratio of the ionised species
Nd:YAG and TiSap beams, directly before entering
responsible. Comparing the theoretically calculated value
m
the interaction chamber and directly after transmisof q with the list containing all of the possible species
sion through the major lens responsible for focusing
and their respective charge to mass ratios allowed the
within
the chamber
mapping of a specific ionised species to each peak. Hav•
The
plate
was positioned such that the beams were
ing identified the peak associated with S+ , the MCP was
incident at roughly 45◦
appropriately gated via a home built high voltage power
• As governed by Fresnel’s laws, roughly 90% of the
supply such that all outputted 2D distributions reprebeam intensity was transmitted to the chamber, with
+
sented S only.
roughly 10% reflected through an angle of 90◦ . It
was the reflected beam only that was further worked
Relative Timings
with
•
The focus length of the major lens was known and
Molecular alignment and orientation are achieved while
allowed the rough estimation of the focus point of
the Nd:YAG pulse is present only, with the molecules
the three beams. A sheet of paper was employed
returning to their field free states in the time period beand moved into the path of the beams to verify this
tween pulses. Thus it was necessary that the coulomb
position
explosion of OCS molecules occurred while the Nd:YAG
• Some distance behind this focus point, a second fopulse was also present. To facilitate this, the Nd:YAG and
cusing lens was used in order to re-focus the beams
TiSap pulses were temporally overlapped prior to the beonto a photodiode
ginning of the experiment via electronic synchronisation.
• A sheet of foil containing a pinhole with a diameter
The TiSap pulse was then treated as the master signal,
on the order of micrometers was mounted on an
and all other components of the set up were timed with
automated stand and inserted into the beam path at
respect to this. Each time a pulse was emitted from the
the estimated focus position. The stand could also
TiSap laser, the clock on the MCP was reset to t=0.
be adjusted manually
• t=0: TiSap pulse is emitted
• A two-person, systematic approach was employed in
• t=100ns: TiSap pulse reaches the interaction chamber
order to pass each beam through the pinhole
r
All-Optical Alignment and Orientation of Neutral Molecule & Attosecond Pulse Generation
spatial overlap was seen to drift with time and had to
be rechecked prior to beginning of each experiment
7
x 10
Ti:Sa and YAG Beams Overlap
2
1.5
Laser Intensity (a.u.)
• Person 1 was positioned on eye level with the beam*,
while Person 2 was positioned behind the pinhole,
manually controlling its motion in the x any y directions
• Person 1 observed the position of the beam on the
foil which contained the pinhole
• Person 2 adjusted the position of the pinhole in the
x direction, until alerted by Person 1 that the beam
had fallen outside of the boundary of the foil
• Person 2 then adjusted the position of the pinhole
in the y direction by one increment of the manual
control knob
• This process was repeated, and in this manner, the
beam was systematically scanned across the entire
area of the foil, until it was seen that light had passed
through
• This approach was applied firstly to the second harmonic of the Nd:YAG alone such that the beam being
worked with could be seen
• The TiSap beam was added afterwards, and in order
for the photodiode to differentiate between the two
beams, their temporal overlap was removed
• The light passing through the pinhole was detected
by the photodiode and the signals were displayed on
a digital oscilloscope
• By interpreting the oscilloscope output, further manual adjustments of the x, y and z positions of the
pinhole were made in order to maximize the signals
• Optimum spatial overlap of the three beams required
that the position of the pinhole overlapped exactly
with the focus position and so finer adjustments of
the pinhole position in the z direction were needed
• The photodiode was connected to the PC where,
through the programme LABVIEW, the motion of
the pinhole in the z direction was controlled and the
beam profiles were imaged
• Despite the employment of achromatic lenses, the
three beams did not focus to exactly the same point,
and so the focus of each beam was found separately
• As the z-position of the pinhole approached the focus
position, the beam signal was maximized, and the
beam profile became increasingly gaussian
• The z-position at which each beam displayed maximum intensity was located and the pinhole was
placed at a position deemed to be in the centre of the
individual focus points
• In order to attain perfect spatial overlap, the manual
adjustment of one or two pivotal optical elements
within the set up was necessary
• As these element were adjusted, the profiles of the
beams were imaged, as illustrated in figure 6
• Via the interpretation of the outputted beam profiles,
the directions in which the elements needed to be
adjusted could be reasoned, and spatial overlap was
achieved
• Finally, the TiSap and Nd:YAG pulses were temporally overlapped, the glass plate was removed and
the set up was fully prepared for use
• Due to slight instabilities in the laser systems, the
1
0.5
0
50
0
Vertical Pinhole Position
−50
−30
−20
30
20
10
0
−10
Horizontal Pinhole Position
Figure 6: Overlapping beam profiles, as imaged by the photodiode
*It was ensured that while on eye level with the Nd:YAG
second harmonic beam that the power had been reduced,
and that goggles designed to protect specifically against
light in the 500nm range were worn
Investigation of the Relative Phase between
the Two Harmonics
In order to investigate the relationship between the
achieved degree of orientation and the relative phase
between the fundamental and second harmonic, a fused
Silica plate was employed. Due to the wavelength dependence of the refractive index, the fundamental and second
harmonic produced by the Nd:YAG laser spent different
periods of time within the fused Silica plate. The variation of the angle of inclination of the plate with respect
to the beam resulted in the variation of the relative phase
between the two harmonics, thus shaping the interaction
potential seen by the molecules. It was known that orientation would be optimised for a relative phase of 0 or π,
however the relative phase between the two harmonics
at the instant of generation was not known, nor was the
relation between adjustment of the inclination of the plate
and the induced phase difference.
In this experiment, the angle of inclination of the fused
Silica plate was varied via the manual adjustment of a
micrometer screw gauge present upon the apparatus. For
each new screw gauge position, orientation of the OCS
molecules was attempted via the application of both the
fundamental and second harmonics, and the corresponding 2D distributions were outputted. From the distributions, the value of the orientation parameter hcosθ i was
calculated in order to deduce whether the adjustment of
the screw gauge had resulted in the reduction or enhancement of the achieved orientation.
All-Optical Alignment and Orientation of Neutral Molecule & Attosecond Pulse Generation
Results and Analysis
The raw data collected in all experiments comprised 2D
distributions of S+ ions at the instant of coulomb explosion. From such a 2D distribution, as illustrated in figure
7, the alignment parameter hcos2 θ i and the orientation
parameter hcosθ i were extracted. Each point on the distribution corresponded to one impacting S+ ion. The
centre of the distribution was outputted by LABVIEW,
and using this center, the x and y positions of all points
within the distribution were found. Using these positions
and the formula for Cosine,
Figure 8: 2D distribution of S+ ions in presence of the TiSap probe
pulse only
Cosθ = p
x
x2
+ y2
,
(25)
the average value of cos2 θ and cosθ were calculated for the
distribution, thus yielding the alignment and orientation
parameters respectively. This analysis was carried out
using matlab, and allowed the quantification of the degree
of alignment or orientation achieved.
Peaks may be noticed at values of θ=0 ,π and the values
of hcos2 θ i and hcosθ i were calculated to be 0.541±0.001
and 0.004±0.003 respectively. The value of the alignment
parameter was thus larger than the expected value of 0.5
by an amount that was non-negligible, and the blame for
this discrepancy was placed on the imperfect horizontal
polarisation of the TiSap laser. In an attempt to reduce
the value of hcos2 θ i to 0.5, the polariser responsible for
ensuring the horizontal polarisation of the TiSap beam
was adjusted and the 2D distributions of the S+ ions were
captured for each adjustment. From each 2D distribution,
the value of hcos2 θ i was calculated and the position of the
polariser corresponding to the value of hcos2 θ i nearest
to 0.5 was selected for the duration of the experiment.
Figure 8 corresponds to the distribution with the polariser
in this optimum position. Since it was not possible to
reduce the value of hcos2 θ i to 0.5, it was decided that
0.54 would be taken as a background value, and that in
order to conclude the achievement of alignment upon the
addition of the Nd:YAG pulse, an increase in the value of
the alignment parameter beyond this would be needed.
Alignment
In order to achieve the alignment of OCS molecules, the
Nd:YAG fundamental tone was applied. Figure 9 illustrates the analysed data corresponding to this situation.
Figure 7: 2D distribution of S+ ions as imaged by the CCD camera
Bar charts were generated with each bin corresponding
to a given angle θ with respect to the vertical, and the
height of each bin representing the relative number of
S+ ions detected at this angle. Ideally, in the absence of
the Nd:YAG pulse, such a bar chart should be completely
flat, yielding no peak at any particular value of θ. The
calculated values of the alignment and orientation parameters for the distribution should be 0.5 and 0 respectively,
as the OCS molecules should be randomly distributed
+
in space. Figure 8 illustrates the chart generated in the Figure 9: 2D distribution of S ions in presence of the Nd:YAG
fundamental
tone
and
TiSap probe pulse
presence of the TiSap pulse only.
All-Optical Alignment and Orientation of Neutral Molecule & Attosecond Pulse Generation
Both YAG Harmonics
450
400
Number of Data Points
Peaks may be noticed at values of θ= 0, π. These
peaks have clearly been enhanced with respect to the
background image generated while the sample was in
the presence of the TiSap pulse only. This is obvious
upon the comparison of figures 8 and 9. The enhancement of the peaks corresponds to an enhanced number
of S+ ions detected at the angles θ= 0, π, and was due
to the successful alignment of the OCS molecules with
the vertical direction. The value of hcos2 θ i was calculated
to be 0.579 ±0.001 which clearly increased beyond the
background value of 0.54, outside of the bounds of experimental error, allowing the conclusion that alignment had
been achieved.
The value of hcosθ i was calculated to be 0.016±0.001.
An increase in this parameter was not expected upon the
addition of the Nd:YAG fundamental pulse only. It was
thus decided that in order to conclude the achievement of
orientation upon the addition of the second harmonic, an
increase in the value of the orientation parameter beyond
this value of 0.016±0.001 would be needed.
The relationship between pulse intensity and the
achieved degree of alignment was also investigated. The
second harmonic was constantly maintained at a lower
power than the fundamental, generally in the region of
20mJ, with the fundamental in the region of 130mJ. Figure 10 illustrates the analysed data corresponding to the
situation in which the second harmonic only was applied.
350
300
250
200
150
100
50
0
0
20
40
60
80
100
θ (Deg)
120
140
160
180
<cos2(θ)>=0.567±0.002
<cos(θ)>=0.017±0.004
Figure 11: 2D distribution of S+ ions in presence of both Nd:YAG
harmonics and TiSap probe pulse
The value of hcosθ i was calculated to be 0.017±0.001,
which did not increase above the background value of
0.016, outside of the bounds of experimental error. Thus,
in this experiment, it could not be concluded that orientation was achieved.
Investigation of the Relative Phase between
the Two Harmonics
Figure 10: 2D distribution of S+ ions in presence of the Nd:YAG
second harmonic and TiSap probe pulse
In order to investigate the effect of the relative phase
between the two harmonics on the achieved degree of
orientation, the inclination of the fused Silica plate with
respect to the beam was varied. 2D distributions in the
presence of both Nd:YAG harmonics were generated for
different positions of the micrometer screw gauge, and
so different angles of inclination of the plate. From each
2D distribution, the values of hcos2 θ i and hcosθ i were
extracted. The values of hcosθ i were used to investigate
whether or not the achieved degree of orientation had
been improved. Due to the fact that varying the relative
phase between two harmonics should have no effect on
the achieved degree of alignment, the values of hcos2 θ i
were used as a reference, such that random fluctuations
due to laser system instabilities could be differentiated
from true increases in the orientation parameter.
The value of hcos2 θ i was calculated to be 0.558±0.001
which increased from the background value of 0.54, outside of the bounds of experimental error. Thus it was
concluded that alignment had been achieved via the application of the second harmonic. However, this value of
hcos2 θ i was less than that achieved by the application of
Figures 12 and 13 illustrate the values of hcos2 θ i and
the fundamental tone, thus verifying the dependence of
hcosθ i corresponding to different positions of the micromalignment on the intensity of the applied pulse.
eter screw gauge. The screw gauge was uncalibrated, in
that it was unknown by how much the relative phase
Orientation
between harmonics would change for a given adjustment
When the orientation of the OCS molecules was sought, of the screw gauge. Figure 12 illustrates the values of
both the fundamental and second harmonic of the the alignment and orientation parameters as the screw
Nd:YAG were applied. Figure 11 illustrates the analysed gauge was adjusted in 0.5mm increments, with figure 13
data corresponding to this situation.
illustrating the same situation for increments of 0.025mm.
All-Optical Alignment and Orientation of Neutral Molecule & Attosecond Pulse Generation
between relative phase between the two harmonics and
the achieved degree of orientation.
Section II
Introduction
The ability to probe and to image dynamical electronic
and molecular processes on shorter and shorter timescales
has lead to the development of the area of Attosecond
Figure 12: hcos2 θ i and hcosθ i values for 0.5mm increments of the Physics. It is predicted that the control of a single, isolated
attosecond pulse will allow the investigation of a vast
screw gauge
range of processes previously taking place on timescales
too small to imagine, from the motion of electrons within
their orbitals and indeed within semiconductors, to the
processes at play in photosynthesis. The controlled production of single attosecond pulses has, in very recent
years, been achieved [19] and since then has inspired the
development of technology towards many noble applications, for example the use of single attosecond pulses for
the generation of live bio-images as an alternative to Xray
imaging. However, the generation of isolated attosecond
pulses places stringent requirements on the driving laser,
making the technology accessible to only a small number
of laboratories across the world. In 2008, a method of
isolation of single attosecond pulses known as Double
Optical Gating was proposed [20] and is investigated in
this experiment.
2
Figure 13: hcos θ i and hcosθ i values for 0.025mm increments of the
screw gauge
It was hoped that figures 12 and 13 would show at least
one clear peak as the inclination of the fused Silica plate
was varied, indicating that a relative phase between harmonics of 0 or π had been achieved. However, in figure
12 no increase in the value of hcosθ i which could not be
written off as a random fluctuation by comparison with
the corresponding hcos2 θ i value was seen. It is possible
that this was due to the step size being too large, such
that phase shifts introduced between the two harmonics
were completely random and generally hit on values that
were not optimum in terms of facilitating the achievement
of orientation.
In figure 13, there were two instances at which the
value of hcosθ i was seen to increase, and which could
not be written off as a random fluctuation by comparison
with the corresponding hcos2 θ i value. This suggests that
it is possible that the step size taken on the screw gauge
was again too large to allow the observation of clear, gradual peaks in the values of hcosθ i, and that potentially, an
optimum relative phase somewhere close to 0 or π happened to be hit on in the instances circled in figure 13.
This would suggest that upon better calibration of the
micrometer screw gauge, the variation of the inclination
of the plate could be used to enhance the probability of
achieving orientation. This data does not however provide any conclusive evidence supporting the relationship
Theory
High Harmonic Generation
High Harmonic Generation (HHG) is a non-linear process which involves the illumination of a target material
by an intense laser pulse and results in the emission of
harmonics of the incident laser beam by the material.
Although inherently quantum mechanical in nature, this
process is often understood using the semiclassical three
step model.
1 An electron within an atom is confined to the region
of space surrounding the nucleus by the attractive
Coulomb potential. An incident light pulse modifies
this potential such that tunneling through the barrier
is facilitated and the electron tunnels out into the
continuum in a process known as tunnel ionisation.
2 The electron is accelerated along the direction of the
laser field and follows a trajectory that leads first
away from the atom, and then back.
3 Upon returning to the vicinity of the ion, the electron
recombines and rids itself of the excess energy that it
gained during its acceleration by emitting harmonic
radiation.
All-Optical Alignment and Orientation of Neutral Molecule & Attosecond Pulse Generation
Figure 14: Three step model of High Harmonic Generation
The success of this process strongly depends on
the intensity and the polarisation of the incident light
pulse. The relationship between HHG and incident intensity is obvious, with higher intensity beams increasing
the probability of ionisation. With respect to the polarisation dependence, it has been shown [21] that linearly
polarised light facilitates HHG, with elliptically polarised
light reducing the success and finally with circularly polarised light permitting no HHG. This can be understood
by considering that the trajectory followed by the ionised
electron is determined by the direction of the incident
light field. In this manner, circularly polarised light yields
a trajectory that does not lead the electron back within
the vicinity of the ion, thus preventing recombination
and elliptically polarised light creates a trajectory that, by
the same logic, dramatically reduces the probability of
recombination.
Attosecond Pulse Generation
When atoms are driven by laser pulses containing multiple optical cycles, a train of attosecond pulses is generated
[22] through repeated HHG.
One attosecond pulse is generated every half cycle of the
incident laser pulse, as illustrated in figure 15. Each half
cycle enables HHG through the 3 step model. Beginning
at position 1, the applied light field modifies the coulomb
potential well confining the electron to the atom and the
electron tunnels into the continuum. The electron is then
accelerated away from the atom, until it reaches position
2. At this point, the direction of the light field reverses
and the electron is accelerated back towards the ion. At
position 3, the electron recombines with the ion and emits
a pulse, with a duration on the order of attoseconds. The
generated attosecond pulse train contains pulses temporally separated by a half period of the incident light
field. Such pulse trains have limited experimental use,
and isolated attosecond pulses are instead desired.
Figure 15: Illustration of the manner in which attosecond pulses are
generated
Isolation of Single Attosecond Pulses via
DOG
DOG is an approach used to control the HHG process
so that a single attosecond pulse may be generated using
multiple cycle pulses. This technique employs a combination of Polarisation Gating and Two Colour Gating.
• Polarisation Gating
Two counter-rotating, circularly polarised pulses
with an appropriate time delay are spatially overlapped in order to generate a single pulse that is
linearly polarised for a small portion of its duration,
and circularly polarised for the majority. Since HHG
is only realised using linearly polarised incident light
fields, only a small portion of the incident pulse is
capable of generating an attosecond pulse. As a
result, the number of attosecond pulses within the
generated train is reduced.
• Two Colour Gating
A weak second harmonic field is added to the Polarisation Gating field in order to modulate the pulse
shape. When appropriately modulated, this addition can reduce the number of attosecond pulses
generated by reducing the intensity of the light field
constituting the incident pulse at the beginning and
ending of its duration. These parts of the pulse thus
become incapable of generating attosecond pulses.
The central part of the incident pulse wavepacket
may simultaneously be enhanced in the same manner. This method utilises the dependence of HHG on
incident pulse intensity.
Experimental
There were two major parts to the experimental set up.
Firstly, pulses of appropriate temporal duration for use in
attosecond pulse generation needed to be produced and
secondly, these incident pulses needed to be guided to
the target medium and the generated attosecond pulses
needed to be detected.
All-Optical Alignment and Orientation of Neutral Molecule & Attosecond Pulse Generation
Production of Incident Pulses of Appropriate
Duration
The TiSap laser was used to generate pulses with the
following characteristics;
•
•
•
•
•
λ= 800nm
Temporal duration=40fs
Length of one optical cycle =τ = 800nm
= 2.6fs
c
40
≈ 14
Number of optical cycles/pulse = 2.6
Number of attosecond pulses generated/pulse≈28
A pulse train containing 28 attosecond pulses is experimentally useless and difficult to reduce to a single isolated
pulse using DOG. It was decided that a pulse with a temporal duration of 5fs was most appropriate. Within one
5fs pulse, there are two optical cycles and thus potentially
four generated attosecond pulses, which can much more
easily be reduced to a single pulse by DOG. In order to
generate a 5fs pulse from a 40fs pulse, a hollow core fibre
compressor in combination with chirped mirrors*3 was
employed. A hollow core fibre compressor is used to
spectrally broaden high energy input fs pulses by nonlinear interaction with a noble gas of adjustable pressure
inside a hollow fibre. Chirped mirrors then compress the
pulse after the fibre and the increased spectral width supports shorter pulse durations than the input pulses. The
combination of the the hollow core fibre compressor and
chirped pulse mirrors act to take a 40fs pulse, broaden its
frequency spectrum, and then compress it temporally, to
a duration far smaller than that which would have been
supported before spectral broadening, 5fs in the case of
this experiment.
Attosecond Pulse Generation and Detection
A schematic of the experimental setup from the point
after which the 5fs pulses were produced is illustrated in
figure 16. Argon gas was employed as the sample onto
which the 5fs pulses were focused in order to generate
the attosecond pulses via HHG. The set up included the
following components;
• Vacuum chamber containing Argon gas
• Toroidal focusing mirror, used to focus the incident
5fs TiSap pulses to a point within the vacuum chamber
• Aluminium membrane, used to screen 800nm light
from continuing any further within the set up. The
CCD camera was preferentially sensitive to visible
light, making it necessary to screen all light which
was transmitted through the sample of Argon gas
without inducing the generation of attosecond pulses
• Diffraction grating, used to disperse the different
wavelength components of the generated attosecond
pulses for analysis
• CCD camera, used for imaging the dispersed attosecond pulses
Figure 16: Schematic representation of the Experimental set up following the production of the 5fs pulses
Results
It is understood that a 5fs pulse incident on the sample of Argon gas should result in the generation of an
attosecond pulse train containing four pulses, provided
that the hollow core fibre compressor and chirped mirror
combination were successful in reducing the duration
of the incident pulse from 40fs to 5fs. Each attosecond
pulse within the train will have a wavelength of 30nm
and the pulses will be temporally separated by 1.3fs, half
an optical cycle of the incident 800nm light. The CCD
image illustrated in figure 17 displays the detected and
outputted intensity versus wavelength spectrum corresponding to this situation.
Figure 17: Wavelength versus intensity spectrum in the absence of
Double Optical Gating
Four peaks are clearly visible, as was expected. The
reason for the set of four peaks at four different values of
wavelength, despite our knowledge that each attosecond
pulse is generated with a wavelength of 30nm, may be
roughly understood by considering the four generated
attosecond pulses to have undergone interference in the
time domain. The pattern outputted appears as if a single
30nm beam was incident on four ’slits’, giving rise to four
peaks in the wavelength domain. Three generated attosecond pulses by this logic could be equivalent to three slits
and three peaks in the wavelength domain, and so forth.
Naturally, this is purely an analogy, however it facilitates
the understanding that four peaks in the wavelength domain corresponds to a generated attosecond pulse train
consisting of four pulses.
Figure 18 illustrates the spectrum detected and outputted when DOG was employed. In this case, a single broad peak, centered at 30nm is visible. This illustrates the situation for which only one attosecond pulse is
present, and so only one ’slit’ in this interference model
is present. It may thus be concluded via the comparison
of figures 17 and 18 that the employment of DOG was
All-Optical Alignment and Orientation of Neutral Molecule & Attosecond Pulse Generation
successful in isolating a single attosecond pulse.
Figure 18: Wavelength versus intensity spectrum in the presence of
Double Optical Gating
Discussion and Conclusions
In section I, the alignment of neutral OCS molecules was
achieved via the application of the fundamental tone
(λ=1064 nm) generated by an Nd:YAG laser with a peak
power in the region of 130mJ. The value of the alignment
parameter, hcos2 θ i, was calculated to be 0.579±0.001,
which increased above the background value of 0.54, outside of the bounds of experimental error. The application
of the second harmonic generated by the Nd:YAG laser
(λ=532nm) with a peak power in the region of 20mJ
also resulted in the achievement of alignment, with the
value of hcos2 θ i calculated to be 0.558±0.001. This value
increased by an amount substantially less that that resulting from the application of the Nd:YAG fundamental
tone, and thus the dependence of the degree of achieved
alignment on the intensity of the incident pulse was verified.
Orientation of neutral OCS molecules was attempted
via the application of both the Nd:YAG fundamental and
second harmonics. The value of the orientation parameter,
hcosθ i, was calculated to be 0.017±0.001, which did not
increase above the background value of 0.016 outside of
the bounds of experimental error. Thus it could not be
concluded that orientation was achieved. It was thought
that since the relative phase between the two harmonics
was unknown, a relative phase which did not facilitate the
achievement of orientation could have been responsible
for this failure.
Variations of the relative phase between the two harmonics with the aim of locating the inclination of the
fused Silica plate which resulted in a relative phase of 0
or π were unsuccessful. Varying the relative phase between the two harmonics was not seen to improve the
degree of orientation achieved, thus eliminating a relative
phase between harmonics corresponding to a symmetric
interaction potential as the cause for the failure of the
achievement of orientation.
Since it was unknown by how much a single adjustment
of the micrometer screw gauge controlling the inclination
of the fused Silica plate would change the relative phase
between the two harmonics, adjusting the inclination of
the plate in order to locate a relative phase of 0 or π was
difficult. This lack of calibration of the plate potentially
led to the adjustments made consistently being too large,
meaning that from one adjustment to the next, completely
random jumps in induced relative phase were made. The
data generated did, on two instances, yield values of the
orientation parameter which could not be written off as
random fluctuations. Potentially in these two instances,
a relative phase close to 0 or π was achieved, with all
other measurements corresponding to relative phases
which happened to be more in the region of π2 , yielding
symmetric interaction potentials which did not facilitate
orientation. This is however a very optimistic manner of
viewing the results.
In order to improve the probability of achieving orientation in the future, it would be beneficial to include a
stark state selector within the set up such that only the
coldest rotational states of the OCS molecules are permitted into the interaction chamber. The power of the beams
should be further increased, as it has been verified that
the degree of alignment achieved depends on the incident power. In addition, the 2D distributions contained a
large amount of noise, which if removed, may allow the
recovery of more promising results.
In section II, 40fs pulses were successfully reduced to
5fs pulses via the employment of a hollow core fibre compressor and chirped mirrors. The produced 5fs pulses
were used to generate an attosecond pulse train consisting
of four pulses via HHG from a sample of gaseous Argon.
Double optical gating was then successfully employed in
order to isolate a single attosecond pulse from the train.
In the future, it is hoped that the two areas of research
may be linked and that samples of aligned molecules may
be used as birefringent wave plates in order to control
the polarisation state of the generated attosecond pulses.
Due to the nature of the process, all generated attosecond pulses are linearly polarised, and it is hoped that
upon aligning molecules at 45◦ to the vertical and passing
the attosecond pulses through the aligned sample, that
circularly polarised pulses may be produced.
Acknowledgments
The author would like to thank Professor Hirofumi Sakai,
Assistant Professor Shinichirou Minemoto, Mr. Md.
Maruf Hossain and Mr. Wataru Komatsubara for their
acceptance into the group, their guidance, patience and
for all of their help in the lab! The author would also
like to thank Dr. Hiroki Mashiko for his insight into the
area of Attosecond Pulse Generation, the ILO office for
the fantastic organisation of the UTRIP programme, the
Graduate School of Science Scholarship for the financial
support as well as Mr. Niccolò Bigagli for the long hours
of company in the lab as well as for all of the figures used
in this report.
Appendix
*1 Chirped Pulse Amplification (CPA)
With the advent of the mode locked laser came the ability
to experimentally realise ultrashort laser pulses. Associated with such pulses are high elecric field strengths and
All-Optical Alignment and Orientation of Neutral Molecule & Attosecond Pulse Generation
peak powers;
E
τ
Where E is the energy of a single pulse and τ is the
pulse duration. As a result, attempting to amplify such
pulses often yields optical damage of the gain medium
through which the pulses propagate. In order to avoid
such damage, an amplification technique aimed specifically at ultrashort pulse amplification was developed and
is referred to as Chirped Pulse Amplification.
The idea behind this technique is to manipulate the ultra
short pulses in a reversible manner, such that the pulses
are temporally stretched prior to being introduced to the
gain medium and temporally compressed after exiting
the gain medium.
In this way, the ultra short pulses are never introduced to
the gain medium and damage to the apparatus is avoided.
The most common approach for the reversible stretching
and compressing of ultra short pulses is the employment
of a pair of diffraction gratings. Due to the broad spectral
bandwidth of ultra short pulses, the stretcher operates by
introducing dispersion of these components. The time delay of the different spectral components within the pulse
gives rise to a long, chirped optical pulse, with a far lower
peak power as a result. The compressor operates on the
same principle, with dispersion that closely matches that
produced by the stretcher, but opposite in sign.
Thus, the ultrashort pulses generated by a mode locked
laser will first undergo temporal stretching, amplification
to high energies in the gain medium, and finally compression, ideally to the original pulse duration. Damage to the
laser amplifier is avoided, and this method of ultrashort
pulse amplification was employed by both the TiSap and
Nd:YAG lasers in our experiments.
Ppeak =
*2 Gaussian Pulse
In all conducted experiments, it is assumed that the employed pulses have a spatial and temporal Gaussian profile. Under this assumption, the pulse intensity takes the
form
I (r, t) = I0 exp[−
4ln2t2
( FW HM)
2
]exp[−
2r2
],
ω2
(26)
where FWHM is the full width at half maximum height.
Integrating the Intensity over space and time yields the
energy of the pulse,
Z +∞
exp[−
4ln(2t2 )
Z +∞
2r2
]dr,
ω2
−∞
−∞
( FW HM)
(27)
which clearly requires a standard Gaussian integral to
solve, yielding
√
FW HM π πω 2
√
E pulse = I0 (
).(
)
(28)
2
2 ln2
I0
E pulse ≈
]dt × 2π
2
I0 πω 2 FW HM
2
γexp[−
(29)
*3 Chirped Pulse Mirror
A chirped mirror is effectively an extended version of a
dielectric mirror, which is made to reflect only a single
frequency of light. It is composed of transparent materials, uniformly layered at a quarter of the wavelength
of the light that the mirror is designed to reflect. The
chirped mirror is designed in a similar way, but with
the aim of reflecting a wider range of frequencies. This
is achieved by creating the mirror using many layers of
different depth. For example, there may be N layers with
a specific depth designed to reflect one wavelength, another N layers with a slightly greater depth, designed to
reflect a slightly greater wavelength and so forth for the
range of wavelengths for which the mirror is designed to
reflect. Because light reflected from the deeper layers of
the mirror will have traveled a further distance than those
reflected from the surface layers, the mirror can be used
to change the relative timings of wavefronts of different
wavelengths. This can be used to disperse a pulse of light
of different wavelengths which all arrive at the same time,
or indeed to tighten a pulse of light in which different
wavelengths arrive dispersed in time.
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