1 Molecular Movies from Molecular Frame Photoelectron Angular
17
collision takes place. Evidence for the occurrence of multiple/late re-collisions was
explicitly observed in [14]. The late re-collisions correspond to trajectories where
the electron, after being pulled out of the atom in a particular half-cycle, misses
the ion on the first, or even second re-collision opportunity, so that the scattering
event that leads to a substantial change in the electron momentum only occurs on
the second, or even third re-collision opportunity.
The hologram in Fig. 1.6 can on the one hand be viewed as a ‘static’ measurement
with the potential to determine a molecular structure. Since, however, this measurement is completed within the pulse duration of the mid-infrared ionization laser, it
can be easily extended to the monitoring of time-dependent structural changes in
molecules, provided that the mid-infrared laser sources can be constructed with a
pulse duration that is commensurate with the time-dependent molecular structural
changes of interest. With the availability of 30–50 fs mid-infrared laser pulses these
two requirements can readily be reconciled. At the same time, a single hologram
such as shown in Fig. 1.6 already contains time-dependent information on ultrafast
electron dynamics, due to the way that the time of ionization and the time of the
re-collision with the ion directly determine the final momentum. This is very similar to the operating principle of the attosecond streak camera, that is commonly
used in attosecond science to characterize attosecond laser pulses and to record
time-dependent events on the attosecond timescale [55, 56]. In this manner, the
holography experiment allows to obtain information on the ionization dynamics
and ultrafast ‘hole dynamics’ in the molecular ion left behind that is on the subor few-femtosecond timescale.
In order to arrive at the interpretation of the side-lobes in Fig. 1.6 in terms of
a holographic interference between a signal and reference electron wave, a number of numerical methods were used. The side-lobes are reproduced when the
time-dependent Schrödinger equation (TDSE) is solved in the single active electron (SAE)-approximation [57], but this does not provide any physical insight yet.
A deeper understanding can be obtained when using methods that are based on the
strong-field approximation (SFA), which has already been invoked in the explanation of many strong-field phenomena [58]. In the SFA, one assumes that prior to
ionization the laser field has a negligible interaction with the electron compared to
the interaction of the electron with the atomic or molecular ion core, and that after
ionization, which is assumed to occur by means of a tunneling process, the situation
is reversed, i.e. the motion of the electron is then entirely governed by the interaction of the electron with the laser field. These assumptions allow one to explain,
for example, the high-energy cut-off that is observed in HHG [19]. SFA in its simplest form cannot explain the holographic interferences that are observed in Fig. 1.6,
since it does not include the Coulomb interaction of the electron with the ion from
which it as extracted and the changes in the electron momentum that are induced by
electron-ion recollisions that occur under the influence of the oscillatory laser field.
A suitable method to include the Coulomb interaction into SFA was introduced by
Bauer and Prophuzhenko [59, 60], making use of the fact that within an SFA framework strong field ionization can be numerically evaluated using the application of
a saddle-point method [61], which regards ionization resulting in a given final momentum (p z , p x ) as arising from a finite number of distinct ionization events, which
17
collision takes place. Evidence for the occurrence of multiple/late re-collisions was
explicitly observed in [14]. The late re-collisions correspond to trajectories where
the electron, after being pulled out of the atom in a particular half-cycle, misses
the ion on the first, or even second re-collision opportunity, so that the scattering
event that leads to a substantial change in the electron momentum only occurs on
the second, or even third re-collision opportunity.
The hologram in Fig. 1.6 can on the one hand be viewed as a ‘static’ measurement
with the potential to determine a molecular structure. Since, however, this measurement is completed within the pulse duration of the mid-infrared ionization laser, it
can be easily extended to the monitoring of time-dependent structural changes in
molecules, provided that the mid-infrared laser sources can be constructed with a
pulse duration that is commensurate with the time-dependent molecular structural
changes of interest. With the availability of 30–50 fs mid-infrared laser pulses these
two requirements can readily be reconciled. At the same time, a single hologram
such as shown in Fig. 1.6 already contains time-dependent information on ultrafast
electron dynamics, due to the way that the time of ionization and the time of the
re-collision with the ion directly determine the final momentum. This is very similar to the operating principle of the attosecond streak camera, that is commonly
used in attosecond science to characterize attosecond laser pulses and to record
time-dependent events on the attosecond timescale [55, 56]. In this manner, the
holography experiment allows to obtain information on the ionization dynamics
and ultrafast ‘hole dynamics’ in the molecular ion left behind that is on the subor few-femtosecond timescale.
In order to arrive at the interpretation of the side-lobes in Fig. 1.6 in terms of
a holographic interference between a signal and reference electron wave, a number of numerical methods were used. The side-lobes are reproduced when the
time-dependent Schrödinger equation (TDSE) is solved in the single active electron (SAE)-approximation [57], but this does not provide any physical insight yet.
A deeper understanding can be obtained when using methods that are based on the
strong-field approximation (SFA), which has already been invoked in the explanation of many strong-field phenomena [58]. In the SFA, one assumes that prior to
ionization the laser field has a negligible interaction with the electron compared to
the interaction of the electron with the atomic or molecular ion core, and that after
ionization, which is assumed to occur by means of a tunneling process, the situation
is reversed, i.e. the motion of the electron is then entirely governed by the interaction of the electron with the laser field. These assumptions allow one to explain,
for example, the high-energy cut-off that is observed in HHG [19]. SFA in its simplest form cannot explain the holographic interferences that are observed in Fig. 1.6,
since it does not include the Coulomb interaction of the electron with the ion from
which it as extracted and the changes in the electron momentum that are induced by
electron-ion recollisions that occur under the influence of the oscillatory laser field.
A suitable method to include the Coulomb interaction into SFA was introduced by
Bauer and Prophuzhenko [59, 60], making use of the fact that within an SFA framework strong field ionization can be numerically evaluated using the application of
a saddle-point method [61], which regards ionization resulting in a given final momentum (p z , p x ) as arising from a finite number of distinct ionization events, which