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Correlated multielectron dynamics in
mid-infrared laser pulse interactions
with neon atoms
Qingbin Tang,1,2 Cheng Huang,1 Yueming Zhou,1 and Peixiang Lu,1,∗
1 Wuhan
National Laboratory for Optoelectronics and School of Physics, Huazhong University
of Science and Technology, Wuhan, 430074, China
2 College of Physics and Electronic Engineering, Xinyang Normal University, Xinyang,
464000, China
∗ [email protected]
Abstract: The multielectron dynamics in nonsequential triple ionization
(NSTI) of neon atoms driven by mid-infrared (MIR) laser pulses is investigated with the three-dimensional classical ensemble model. In consistent
with the experimental result, our numerical result shows that in the MIR
regime, the triply charged ion longitudinal momentum spectrum exhibits
a pronounced double-hump structure at low laser intensity. Back analysis
reveals that as the intensity increases, the responsible triple ionization
channels transform from direct (e, 3e) channel to the various mixed
channels. This transformation of the NSTI channels leads to the results
that the shape of ion momentum spectra becomes narrow and the distinct
maxima shift towards low momenta with the increase of the laser intensity.
By tracing the triply ionized trajectories, the various ionization channels at
different laser intensities are clearly identified and these results provide an
insight into the complex dynamics of the correlated three electrons in NSTI.
© 2013 Optical Society of America
OCIS codes: (020.4180) Multiphoton; (260.3230) Ionization; (270.6620) Strong-field process.
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1.
Introduction
Detailed understanding of the correlated multielectron dynamics driven by the strong laser field
is essential to extend our knowledge on laser-matter interaction and the concepts of attosecond
physics to many-body microscopic systems [1]. Due to the strongly correlated electron-electron
behavior, nonsequential double or multiple ionization (NSDI, NSMI) of atoms by the intense
laser pulse have attracted continuously increasing attention [2–16] since the observation of the
dramatically enhanced double ionization (DI) yields [17]. The experiments on the ellipticity
dependence of the DI yield [18, 19], especially the differential measurements of recoil ion and
emitted electron momenta [1, 8, 20], provide strong evidences that the recollision mechanism
is dominantly responsible for the NSDI and NSMI process [21]. According to this recollision
scenario, an electron is ionized by the laser field, and then is driven back by the oscillating field
and interacts with its parent ion, leading to the release of one or more electrons. Further analyses
of the recoil ion momentum distributions [20,22], the photoelectron energy distributions [23,24]
and the correlated electron spectra [1, 5, 8, 25] provide more detailed information about the
ionization process.
For nonsequential triple ionization (NSTI), though intensity-dependent ion yields [26, 27] as
well as ion momentum distributions [28–30] have been measured, the understanding of strongfield NSTI mechanisms remains restricted. For instance, a recent experiment [30] has measured
the momentum distributions of Ne3+ by the 795-nm pulses at the intensity range from 1015 to
2 × 1016W /cm2 . The various triple ionization (TI) channels at different laser intensities have
been identified by tracing the intensity-dependent evolution of the recoil-ion momentum spectra. The authors speculated
and (0-1-3) processes are responsible for spectrum
that the (0-3)
with the maxima at ±4 Up and ±2 Up , respectively. While, at the transitional intensities
such as I = 3PW /cm2 and I = 6PW /cm2 [see Figs. 1(e) and 1(h) in [30]], the responsible
processes for TI remains obscure. Theoretically, an accurate description of NSDI or NSMI
needs full quantum theory. However, because of the enormous computational demand, fulldimensional solution of the time dependent schrödinger equation has only been performed on
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9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.021433 | OPTICS EXPRESS 21435
NSDI of helium by 400 nm laser pulses [31], and in the long-wavelength regime, it seems impossible to extend this quantum-mechanical calculation to NSTI that involves three correlated
electrons in the foreseeable future. Thus, the efforts aimed to provide a detailed picture of NSTI
have been recently concentrated on the development of classical approaches [15, 32–37]. However, due to the variety of the possible pathways, including different combinations of sequential
(S) and nonsequential (NS) ionization steps [30, 33, 35, 38] as well as the possibility of recollision excitations in certain intensity regime, up to now, the understanding of strong-field TI
mechanisms remains fragmentary.
The wavelength of the laser pulses in those previous studies are mainly in the near-infrared
(NIR) region (λ ≤ 1μ m). With the advance of ultrafast laser technology, the mid-infrared (MIR)
laser pulse (1μ m<λ ≤ 10μ m) have become available [39]. Recently, the interaction of atoms
and molecules with MIR laser fields has drew much attentions and some new phenomena and
applications have been observed and proposed [40–43]. For example, an unexpected spike-like
structure at the low energy region of the above-threshold-ionization (ATI) spectra in the MIR
regime has been experimentally observed [40, 41]. In the study of high-harmonic generation
(HHG), it has shown that the MIR laser pusle not only produces much more energetic harmonic photons but also reduces harmonic chirps [43], which is beneficial for attosecond pulse
generation. The strong-field NSDI and NSTI of atoms and molecules by the MIR pulses has
also attracted experimental attention [44, 45]. In [45], the momentum distributions of Ne3+ and
Ar3+ by the 1300-nm pulses at the intensity I = 0.4PW /cm2 have been measured. The authors
reported that the shapes of longitudinal momentum distributions for the Ne3+ and Ar3+ all exhibit a clear double-hump structure that is different from those at NIR wavelength [29,30]. This
result indicates that in the MIR regime, the responsible dynamics of correlated multielectron
for TI process is different from that in the NIR regime.
In this paper, the correlated multielectron dynamics in strong-field NSTI of neon atoms
driven by 1600-nm laser pulses is investigated with a three-dimensional (3D) full classical
ensemble model [13, 15]. The numerical result shows that the triply charged ion momentum
spectrum exhibits a pronounced double-hump structure at the low laser intensity, which is well
consistent with the experimental result [45]. Back analysis reveals that at low laser intensity,
the direct (e, 3e) ionization channel is dominantly responsible for NSTI, where one electron
ionizes firstly, then it is driven back by the laser field to recollide with the parent nucleus and
kicks out the other two electrons immediately. While for moderate intensity, besides the (e, 3e)
channel, there is a mixed ionization channel where the first and second electrons are ionized
through a recollision-induced (e, 2e) process and the third electron is excited after recollision
and then released by laser field near the subsequent field maximum. Furthermore, the two TI
channels are contribute significantly to NSTI at moderate intensity. For the high intensity, the
combined sequential and nonsequential (S/NS) ionization channel where the two electrons are
released sequentially and the third electron is ionized through a recollision with the second
electron plays a dominant role in NSTI. Consequently, the shape of the ion momentum spectra
becomes narrow and the distinct maxima shift to the low momenta as the intensity increases.
2.
The full classical ensemble model
The full classical ensemble model has achieved success in understanding of NSDI and NSTI
[13–15, 35] and it has been described in detail in [13, 35]. The evolution of the three-electron
system is determined by the classical equation of motion (Atomic units are used throughout the
paper if not stated otherwise.)
d 2 ri
= −E(t) − ∇[Vne (ri ) + ∑ Vee (ri , r j )],
dt 2
i= j
(1)
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9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.021433 | OPTICS EXPRESS 21436
where the subscript i is the electron label which runs from 1 to 3. E(t)= ẑ f (t)E0 sin(ω t) is the
electric field, where the ẑ is the laser polarization direction and f (t) is the pulse shape which
has two cycles turn-on, six cycles at full strength and two cycles turn-off. In our calculation, the
wavelength is 1600nm. The nucleus-electron and
are represented
electron-electron interaction
by a 3D soft-Coulomb potential Vne (ri ) = −3/ (ri )2 + a2 and Vee (ri , r j ) = 1/ (ri − r j ) + b2 ,
respectively. The soft parameter a is employed to avoid autoionization, which sets the lower
limit of a. There is also an upper limit for a, which is determined by the condition that there
is a classically allowed region for the three electrons with the total energy of the ground-state
energy of the target. For the targets investigated in this paper, the lower and the upper limits of
a are about 0.945 and 1.06 a.u., respectively. Here, similar to [13,14], the screening parameter a
is set to be 1.0 a.u. Note that a small change of the parameter a has little impact on the statistical
results presented in our paper. The parameter b is included to avoid the coulomb singularity in
our calculations. It could be set to equal any other small value (including zero). In our work, we
set b=0.1 a.u. To obtain the initial value, the ensemble is populated starting from a classically
allowed position for the neon atom with ground state energy of −4.63 a.u., i.e., the sum of
the first, the second and the third ionization potential of neon. The available kinetic energy
is distributed randomly between the three electrons randomly in momentum space. Then the
electrons are allowed to evolve a sufficient long time in the absence of the laser field to obtain
stable position and momentum distribution [13, 14]. After the laser pulse is turned off, if three
electrons have positive energy, we define triple ionization.
3.
Results and discussions
In Fig. 1, we present momentum distributions of the triply
charged ions as a function of the
laser intensity. The data in Fig. 1 are plotted in units of Up in order to account for the intensity dependence of the drift momentum received by the recoil ion [30], where the Up is the
ponderomotive energy. Figures 1(a), 1(c) and 1(e) illustrate two-dimensional ion momentum
distributions for 0.5PW /cm2 , 1PW /cm2 and 2PW /cm2 , respectively. Here, the horizontal axis
shows the longitudinal (parallel to the laser polarization direction, i.e., z axis) ion momentum
and the vertical axis corresponds to the transverse (along x axis) momentum. For all intensities, the transverse momenta are concentrated around zero. The longitudinal momenta, instead,
exhibit two clear maxima at non-zero values, which indicates NSTI channels dominate TI at
present intensities [22]. An important feature of these spectra is that the width of the spectra
becomes narrow with the increase of the intensity. The longitudinal momentum distributions,
i.e., the projections of data of two-dimensional ion momentum spectra onto the horizonal axes,
could illustrate this feature more clearly [see the right column of Fig. 1].
For 0.5PW /cm2 , Fig. 1(b) displays the longitudinal momentum distributions of triply
charged ions. The Ne3+ spectrum is essentially identical to the distributions reported in [45] for
TI of Ne at the intensity of 0.4PW /cm2 with the wavelength of
1300 nm. The spectrum exhibits
a clear double-hump structure, with two-defined peaks at ±4 Up and almost no ions produced
2
with zero longitudinal momentum are observed.
When the intensity increases
to 1.0PW /cm
2
and 2.0PW /cm , the two peaks move to ±2 Up [see Fig. 1(d)] and ±1.2 Up [see Fig. 1(f)],
respectively. This indicates that the peaks shift to the low momenta with the increase of the laser
intensity. In addition, comparing Figs. 1(b), 1(d) and 1(f), one can find that the valley of the ion
longitudinal momentum distributions becomes shallow as the intensity increases. These results
indicate that in the MIR regime, the responsible microscopic electron dynamics for NSTI at
different intensities are different and complex.
Tracing back the temporal evolution of TI trajectories allows us to unveil the microscopic
multielectron dynamics of atomic TI, and thus provides an intuitive way to identify the different ionization channels. In present intensity regime, we find that there are three main NSTI
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0.6
0
0.4
−0.5
0.2
−1
−6
0
2
4
6
0
0
1
0.1
0.8
0.6
0.4
−0.5
0.2
−4
−2
0
2
4
6
−6
−4
−2
0
2
4
6
−4
−2
0
2
4
6
−2
0
2
4
6
0.05
0
0
1
0.1
0.8
0.6
0
0.4
−0.5
0.2
−4
−2
ion
Pz
0
2
1/2
/ (Up)
4
6
0
−6
(f)
(e)
0.5
−1
−6
Counts (arb. u.)
(c)
0
1
0.05
(d)
0.5
−1
−6
Pion
/ (Up)1/2
x
−2
Counts (arb. u.)
1/2
/ (Up)
ion
Px
−4
Counts (arb. u.)
(b)
0.8
0.5
1
0.1
1
(a)
ion
Px / (Up)
1/2
1
0.05
0
−6
−4
Pion
/ (Up)1/2
z
Fig. 1. The two-dimensional (the left column) and the longitudinal (the right column) momentum distribution of Ne3+ ions. The laser intensities are (a) and (b) 0.5PW /cm2 , (c) and
(d)
1.0PW /cm2 , (e) and (f) 2.0PW /cm2 , respectively. The distributions are plotted in units
of U p . The ensemble size are 15 million (0.5PW /cm2 ), 10 million (1.0PW /cm2 ) and
6 million (2.0PW /cm2 ). For the two-dimensional momentum distributions, the horizonal
axis denotes the longitudinal momentum (alone z axis) and the vertical
the
axis denotes
transverse momentum (alone x axis). Dashed vertical lines indicate 2 U p , and 4 U p .
channels. First, direct (e, 3e) ionization channel, i.e. one electron gets ionized firstly, and then
it is driven back by the electric field to recollide with the parent nucleus, leading to the three
electrons ionized immediately. This TI process is defined as (0-3) channel. Second, a combined
S/NS ionization process where the first and the second electrons are released sequentially and
the third electron is ionized through a recollision with the second electron which is driven back
by the oscillating field. This TI process is defined as (0-1-3) channel. Third, a mixed TI process
is called (0-2-3) channel. In this channel, one electron is ionized by the laser field, and then it is
driven back by the electric field to recollide with the parent ion, leading to the second electron
emitted immediately and the third electron excited after recollision and released by the laser
field near the subsequent field maximum.
Three sample trajectories for (0-3) [the left column], (0-1-3) [the right column] and (0-2-3)
[the middle column] TI channels are plotted separately in Fig. 2, presented in longitudinal coordinate z [the upper rows], energy [the middle rows], and longitudinal momentum [the bottom
rows] versus the time for each electron, respectively. For the NSTI trajectory in the left column,
it is clearly seen that the three electrons are set free immediately after recollision [see Figs. 2(a)
and 2(b)] and accumulate almost the same high longitudinal drift momentum after the laser is
over [see Fig. 2(c)]. While for the trajectory in the middle column, only two electrons are set
free almost immediately after recollision and they acquire the similar high longitudinal drift
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9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.021433 | OPTICS EXPRESS 21438
(a)
z (a.u.)
200
(d)
200
0
0
0
−200
−200
−200
(e)
Energy (a. u.)
(b)
(h)
20
40
20
0
0
0
(f)
(c)
(i)
2
2
2
0
0
0
−2
−2
−2
z
P / (Up)1/2
(g)
200
0
2
4
6
8
10
0
Time (cycle)
2
4
6
8
10
0
Time (cycle)
2
4
6
8
10
Time (cycle)
Fig. 2. Three sample TI trajectories. The upper, middle, and bottom rows show the longitudinal coordinate z (parallel to the laser polarization), energy, and longitudinal momentum
versus the time for each electron, respectively. The arrows indicate the time when recollision occurs.
momentum from the laser field [see the gray solid and red dotted curves in Fig. 2(f)]. The third
electron is excited after recollision and released by the laser field [see the blue solid curve in
Fig. 2(e)]. After the laser is over, it acquires a very small drift momentum [see the blue solid
curve Fig. 2(f)]. For the NSTI trajectory in the right column, the first and the second electrons
are emitted sequentially [see the gray solid and red dotted curves in Fig. 2(h)] and the third
electron is released through a recollision with the second electron [see the blue solid and the
red dotted curves in Fig. 2(h)].
Table 1. The contributions of the different ionization channels to the total TI yield for the
three laser intensities.
0.5 PW /cm2
1.0 PW /cm2
2.0 PW /cm2
(0-3)
76%
41%
29%
(0-2-3)
24%
59%
(0-1-3)
71%
Similar to [46], we further statistically analyze the percentage contributions of different TI
channels to NSTI. As shown in table 1, the relative contribution of the (0-3), (0-2-3) and (01-3) channels changes with laser intensity. For I = 0.5PW /cm2 , the statistic result reveals that
about 76% of the TI occur through the (0-3) channel and it is the dominant channel for TI at low
intensity. At I = 2.0PW /cm2 , the contribution of the (0-1-3) channel to the total TI yield is over
70%, which indicates that the (0-1-3) channel is dominantly responsible ionization channel for
TI at high intensity. For I = 1.0PW /cm2 , the results show that both (0-3) and (0-2-3) channels
contribute significantly to NSTI and the contributions of the (0-3) and (0-2-3) channels to the
total TI yield are about 41% and 59%, respectively. Based on these results, we may draw the
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Received 17 May 2013; revised 11 Jul 2013; accepted 26 Aug 2013; published 5 Sep 2013
(C) 2013 OSA
9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.021433 | OPTICS EXPRESS 21439
conclusion that in the MIR regime, the responsible triple ionization channels for NSTI are
sensitively dependent on the laser intensity.
(a)
(0−3)
(0−2−3)
(b)
(0−3)
(0−2−3)
(c)
(0−3)
(0−1−3)
4
Counts (arb. u.)
3
2
3
2
2
1
1
1
0
−4
−2
ion
Pz
0
2
1/2
/ (Up)
4
0
−4
−2
Pion
z
0
2
1/2
/ (Up)
4
0
−4
−2
ion
0
2
4
1/2
Pz / (Up)
Fig. 3. (a) The longitudinal ion momentum distributions of (0-3) (red curve) and (0-23)(blue curve) trajectories at 0.5PW /cm2 . (b) The longitudinal ion momentum distributions of (0-3) (red curve) and (0-2-3) (blue curve) trajectories at 1.0PW /cm2 . (c) The longitudinal ion momentum distributions of (0-3) (red curve) and (0-1-3)
(dark green curve)
trajectories at 2.0PW /cm2 . The distributions are plotted in units of U p .
According to the different TI channels, we have segregated the trajectories shown in Figs.
1(b), 1(d) and 1(f), respectively, and the ion momentum distributions for the various classes of
trajectories are displayed separately in Figs. 3(a), 3(b) and 3(c). At I = 0.5PW
/cm2 , it is clearly
seen that for (0-3) trajectories the two peaks of the spectrum are around ±4 Up [see the red
curve in Fig. 3(a)]. For the(0-2-3) trajectories, both I = 0.5PW /cm2 and I = 1.0PW /cm2 , the
peaks also locate near ±2 Up [see the blue curves in Figs. 3(a) and 3(b)]. At I = 2.0PW /cm2 ,
Fig. 3(c) shows that for the (0-1-3) trajectories, the peaks locate at ±1.2 Up [see the dark
green curve in Fig. 3(c)]. The above results reveal that in the MIRregime, the (0-2-3) channel
is responsible for the double-hump spectrum with maxima at ±2 Up . Furthermore, if the (01-3) ionization channel is dominantly responsible for NSTI in
this regime, the locations of the
ion momentum peaks are much less than the values of ±2 Up . This is different from that
at NIR regime [30], where the authors
speculated that the (0-1-3) process is responsible for
the spectrum with maxima at ±2 Up . Additionally, Fig. 3 shows that the peaks of the ion
momentum spectra for the (0-3) and (0-2-3) [see Figs. 3(a) and 3(b)] or the (0-3) and (0-1-3)
[see Fig. 3(c)] trajectories are very close. Thus, the shape of the longitudinal ion momentum
spectra all show two wider peaks [see Figs. 1(b), 1(d) and 1(f), respectively] and the predicted
four-maximum structure in [33] is unobservable in the MIR regime.
To give an overall understanding of intensity-dependent evolution of the ion momentum
spectra for the various trajectories, we analyze the times of TI and recollision for different intensities. Back analysis of the TI trajectories also allows us easily to determine the recollision
and ionization times, which can provide insight into the sub-cycle dynamics of NSTI. We define
the recollision time tr to be the instant when one electron comes within the region r = 3 a.u.
after its departure from the core, and the TI time tT I to be the instant when all of the three electrons achieve positive energies, where the energy contains the kinetic energy, the ion-electron
interaction and half electron-electron interaction. Note that in the (0-3) and (0-2-3) channels,
three electrons are involved in the recollision encounter, while only two electrons are involved
for the (0-1-3) channel.
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Received 17 May 2013; revised 11 Jul 2013; accepted 26 Aug 2013; published 5 Sep 2013
(C) 2013 OSA
9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.021433 | OPTICS EXPRESS 21440
1
1
0.75
0.75
0.5
0.5
0.25
0.25
0.8
0.6
0.4
t
TI
(cycle)
1
(b)
(a)
0
0
0
0.25
0.5
0.75
1
0.2
0
0
0.5
0.75
1
1
1
1
(d)
(c)
0.75
0.75
0.5
0.5
0.25
0.25
0.8
0.6
0.4
t
TI
(cycle)
0.25
0
0
0
0.25
0.5
t (cycle)
r
0.75
1
0.2
0
0
0.25
0.5
0.75
1
t (cycle)
r
Fig. 4. The triple ionization phase tT I versus recollision phase tr (both in cycle) where
the intensities are (a) 0.5PW /cm2 , (b) 2.0PW /cm2 , (c) and (d) 1.0PW /cm2 , respectively. At 0.5PW /cm2 most of the TI trajectories are ionized through (0-3) channel and
at 2.0PW /cm2 they are ionized through (0-1-3) channel. For 1.0PW /cm2 we have separated the TI trajectories base on whether they get ionized through (0-3) (c) or (0-2-3) (d)
channels.
Figure 4(a) shows the triple ionization phase tT I versus recollision phase tr (both in cycle) for
the intensity 0.5PW /cm2 [47]. It is clearly seen that the most of recollisions occur in the range
0.35T-0.40T (or 0.85T-0.90T, where the T is the laser cycle), just before the zero crossing of the
laser field. It is consistent with the predication of the simple-man model [21]. As shown in the
Fig. 4(a), the dominant part of the population are along the diagonal tT I = tr , which indicates
that the TIs occur immediately after the three-electron recollision. As a consequence, for (03) trajectories, the three electrons from NSTI are more likely to set free with a small initial
momentum close to the zero crossing of the field and accumulate the same high longitudinal
drift momentum, which means that the three electrons are emitted predominantly to the same
direction with similar longitudinal momenta [see Fig. 2(c)].
For I = 1.0PW /cm2 , we have separated the TI trajectories according to whether they get
ionized through the (0-3) or (0-2-3) channel. Figures 4(c) and 4(d) display the phase tT I at time
of TI versus the phase tr at recollision for the (0-3) and (0-2-3) trajectories, respectively. For
the (0-3) trajectories, similar to the case at 0.5PW /cm2 , most of the population are along the
diagonal tT I = tr [see Fig. 4(c)]. But, for this intensity, the most of recollisions occur in the range
0.30T-0.35T (or 0.80T-0.85T) [see Figs. 4(c) and 4(d)] and it is less than that at 0.5PW /cm2 .
Particularly, Fig. 4(d) shows that for the (0-2-3) trajectories, most of the TIs occur around the
field maximum (0.25T and 0.75T), which is a reminder of impact excitation TI because there
is a sub-cycle time delay between TI and recollision. Thus, for the (0-2-3) trajectories, only
two electrons accumulate the same high longitudinal drift momentum and the third electron
acquires a very small drift momentum from the laser field [see Fig. 2(f)].
For the intensity 2.0PW /cm2 , Fig. 4(b) shows the most of recollisions occur in the range
0.28T-0.33T (or 0.78T-0.83T), just after the maximum of the laser field. As shown in the Fig.
4(b), the dominant part of the population are along the diagonal tT I = tr implies that TIs occur
immediately after the two-electron recollision. From what has been discussed above, we may
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Received 17 May 2013; revised 11 Jul 2013; accepted 26 Aug 2013; published 5 Sep 2013
(C) 2013 OSA
9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.021433 | OPTICS EXPRESS 21441
draw the conclusion that the contribution of the (0-3) channel to the total yield decreases gradually, and both the (0-2-3) and (0-1-3) channels (the partly sequential channel) make more and
more contributions to NSTI. That is to say, the contribution of the partly sequential channel increases gradually as the intensity increases. As a result, the width of the ion momentum spectra
becomes gradually narrow with the increase of the laser intensity.
Moreover, through careful examination of the Fig. 4 we find that the laser phase at recollision
varies with the laser intensity: for the intensities 0.5PW /cm2 , 1.0PW /cm2 and 2.0PW /cm2 ,
recollision times tr are around 0.375T(or 0.875T), 0.33T(or 0.83T) and 0.30T(or 0.80T), respectively. According to the classical consideration, if an electron is set to an oscillating laser
t0 (where the E0 (t) is a pulse
field of frequency ω and strength E(t) = E0 (t)sin(ω t) at a time envelope function), it acquires the drift momentum Pze (t0 ) = 2 Up cos(ω t0 ) after the laser
is over [28, 30, 33, 34]. For strong-field NSTI of atoms, the ion momentum vector is equal
to the negative sum of the three emitted electrons momentum vectors. Note that in the (03) channel, the three electrons are emitted by recollision and escape with similar high drift
momentum. As a consequence, for 0.5PW /cm2 , the
two-defined peaks of the ionmomentum
spectrum locate near Pzion = ±3 × Pze (tr ) = ±3 × 2 Up cos(ω × 0.375T ) = ±4.2 Up . While
for the (0-1-3) channel, an electron is ionized by the laser field and only acquires a very small
longitudinal drift momentum from the laser field. The other two electrons are set free immediately after recollision and accumulate
the similar high drift momentum. Thus, for 2.0PW /cm2 ,
ion
e
Pz = ±2 × Pz (tr ) = ±2 × 2 Up cos(ω × 0.30T ) = ±1.2 Up , respectively. At the intensity
2
1.0PW
/cm , the locations of the ion momentum peaks are slightly larger than the values of
±1.9 Up since the (0-2-3) channel has considerable contributions to TI at this intensity where
the third electron is ionized by the laser field near the field maximum. Therefore, the peaks shift
to the low momenta with the increase of the laser intensity.
In addition, a recent study by Lötstedt and Midorikawa has demonstrated that inclusion of
the laser magnetic field reduces significantly NSDI probability and this reduction is remarkably
different for different targets [48]. To explore if the laser magnetic field significantly influences
on the NSTI of neon atoms, we have performed a preliminary calculation with the magnetic
field for the case of I = 2.0PW /cm2 . Our calculation shows that when the magnetic field is taken
into account the triple ionization yield is about 0.044%, which is a little lower than the yield
of 0.047% without the magnetic field. For two-dimensional ion momentum distributions, the
numerical results show that, regardless of considering the magnetic field or not, the transverse
momenta
around zero and the longitudinal momenta distribute in the range
are concentrated
of −3 Up ∼ +3 Up . The main feature of the two-dimensional ion momentum distributions
do not change with or without the magnetic field, i.e., the magnetic field has little impact on
the momentum distribution. Furthermore, by back analysis of the classical trajectories, we find
that including the magnetic field, the contribution of the (0-1-3) channels to the total triple
ionization is about 73%, which is very close to 71% of the case without the magnetic field.
By comparing these results with and without the magnetic field above, it can be found that the
laser magnetic field has little impact on NSTI probability, the two-dimensional ion momentum
spectrum and the dominant ionization channel contributing to NSTI.
4.
Conclusion
In summary, the correlated three-electron dynamics in strong field NSTI of neon atoms by MIR
laser pulses has been systematically investigated with the full 3D classical ensemble model. The
various ionization channels at different laser intensities have been clearly identified by tracing
TI trajectories. At low laser intensity, the triply charged ions momentum spectrum exhibits a
pronounced double-hump structure and it is well consistent with the experimental result [45].
Back analysis reveals that the (0-3) ionization channel is dominantly responsible for NSTI pro-
#190761 - $15.00 USD
Received 17 May 2013; revised 11 Jul 2013; accepted 26 Aug 2013; published 5 Sep 2013
(C) 2013 OSA
9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.021433 | OPTICS EXPRESS 21442
cess at low intensity. While for moderate intensity, both (0-3) and (0-2-3) channels contribute
significantly to NSTI. At high intensity, the (0-1-3) channel play a dominant role in NSTI. As
a result, the shape of ion momentum spectra becomes narrow and the distinct maxima shift
towards the low momenta as the intensity increases. With the help of classical trajectory diagnosis, we achieve insight into the complex dynamics of the correlated three electrons in NSTI.
Acknowledgment
This work was supported by the National Science Fund for Distinguished Young Scholars
under Grant No. 60925021, National Natural Science Foundation of China under Grant No.
11004070, and the 973 Program of China under Grant No. 2011CB808103.
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Received 17 May 2013; revised 11 Jul 2013; accepted 26 Aug 2013; published 5 Sep 2013
(C) 2013 OSA
9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.021433 | OPTICS EXPRESS 21443