ETH Library
Generation of intense, carrier-
envelope phase-locked few-cycle
laser pulses through filamentation
Journal Article
Author(s):
Hauri, C.P.; Kornelis, W.; Helbing, F.W.; Heinrich, A.; Couairon, A.; Mysyrowicz, A.; Biegert, J.; Keller, U.
Publication date:
2004-10
Permanent link:
https://doi.org/10.3929/ethz-b-000038416
Rights / license:
In Copyright - Non-Commercial Use Permitted
Originally published in:
Applied Physics B 79(6), https://doi.org/10.1007/s00340-004-1650-z
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For more information, please consult the Terms of use.
DOI: 10.1007/s00340-004-1650-z
Appl. Phys. B 79, 673–677 (2004)
Rapid communication
Lasers and Optics
Applied Physics B
c.p. hauri
1
w. kornelis
1
f.w. helbing
1
a. heinrich
1
a. couairon
2
a. mysyrowicz
3
j. biegert
1,u
u. keller
1
Generation of intense, carrier-envelope
phase-locked few-cycle laser pulses
through filamentation
1
Swiss Federal Institute of Technology (ETH Zürich), Physics Department,
8093 Zürich, Switzerland
2
Centre de Physique Th
´
eorique,
´
Ecole Polytechnique, CNRS UMR 7644,
1128 Palaiseau Cedex, France
3
Laboratoire d’Optique Appliqu
´
ee,
´
Ecole Nationale Sup
´
erieure de Techniques Avanc
´
ees,
´
Ecole Polytechnique, 91761 Palaiseau Cedex, France
Received: 26 August 2004
Published online: 8 September 2004 • © Springer-Verlag 2004
ABSTRACT Intense, well-controlled light pulses with only a few optical cycles start to
play a crucial role in many fields of physics, such as attosecond science. We present an
extremely simple and robust technique to generate such carrier-envelope offset (CEO)
phase locked few-cycle pulses, relying on self-guiding of intense 43-fs, 0.84 mJ opti-
cal pulses during propagation in a transparent noble gas. We have demonstrated 5.7-fs,
0.38 mJ pulses with an excellent spatial beam profile and discuss the potential for
much shorter pulses. Numerical simulations confirm that filamentation is the mechan-
ism responsible for pulse shortening. The method is widely applicable and much less
sensitive to experimental conditions such as beam alignment, input pulse duration or
gas pressure as compared to gas-filled hollow fibers.
PACS 45.65.Ky; 42.65.Re
1 Introduction
Time resolved measurements
of electron dynamics in atoms and
molecules, which ultimately govern any
chemical reaction [1], wake-field par-
ticle acceleration, and the production
of energetic proton beams [2], benefit
tremendously from laser sources de-
livering intense, well-controlled light
pulses with pulse durations of only a few
optical cycles [3–5]. Such sources ful-
fill a central task in the generation of
attosecond extreme ultraviolet (XUV)
pulses [6]. Single attosecond pulse gen-
eration exploits infrared (IR) pulses of
only
2–3cycles that carry enough en-
ergy to be loosely focused to intensities
in excess of several
10
14
Wcm
−2
.The
availability of attosecond XUV pulses
in turn opens the way towards atto-
second-time domain spectroscopy [7].
As a first demonstration in this new
field, the inner-shell decay in a no-
ble gas atom could recently be directly
determined [8].
u Fax: +41-1-633-1059, E-mail: biegert@phys.ethz.ch
The main obstacle in these fields
is the difficulty in producing suitable
driving laser pulses [3]. This requires
not only intense, reproducible few-cycle
pulses, but also a control of the car-
rier phase with respect to the pulse
envelope [9–11]. Indeed, with intense
few-cycle laser pulses, the electric field
amplitude rather than the intensity en-
velope becomes the determining factor.
The electric field oscillations must then
be identical from pulse to pulse; i.e. they
must be carrier-envelope-offset (CEO)
phase-locked; and currently only a few
laser laboratories master the technology.
To become routinely available, simpli-
fication in the techniques of few-cycle
laser pulses production is necessary.
2 Generation of phase-locked
intense few-cycle
laser pulses
So far, the only successful
demonstration of CEO phase-locked
intense few-cycle laser pulses starts
with chirped-pulse amplification (CPA)
Ti:sapphire laser systems [12] typic-
ally providing 25- to
30-fs pulses (9
to 11 optical cycles at a center wave-
length of
800 nm) with energies of
a few millijoules per pulse [13]. In
order to generate few-cycle pulses, the
pulse spectrum is artificially broad-
ened through self-phase modulation via
propagation inside a gas-filled hollow
capillary [14], and then recompressed
spectrally. The capillary works in two
ways: Firstly, the light pulse is tightly
confined inside the capillary, which acts
like an extended spatial filter resulting in
a high spatial coherence, and secondly
its high intensity is maintained over
an extended distance, leading to large
spectral broadening through the non-
linear interaction with the gas medium.
The emerging pulse is then spectrally
recompressed typically with chirped
mirrors. Typically pulses in the range
of 6- to
8-fs can be routinely gener-
ated with pulse energies in the range
of
100–400 µJ. The shortest pulses ob-
tained with this technique yield pulses
as short as
3.8fswith an energy of 15 µJ
in the near-IR [15] and more recently,
2.8fs with 500 nJ [16]. However,both
energies are too low to be used directly
in the above mentioned fields. CEO
phase-stability requires the implemen-
tation of two phase-locked loops: a fast
one for the laser oscillator [9, 17] and
a slow one to correct for drifts in the
laser amplifier [18, 19].
While gas-filled hollow fibers con-
stitute the key ingredient to produce
few-cycle pulses, they have serious in-
herent limiting factors: Energy scalabil-
ity is limited (to about
0.4mJ); beam
pointing fluctuations of the incoming
beam directly translate into unwanted
674 Applied Physics B – Lasers and Optics
energy and pulse parameter fluctuations
of the outgoing pulses [20], a bane for
high field physics experiments; and the
performance critically depends on the
quality of the hollow fiber. Therefore
alternative approaches such as chirped
pulse optical parametric amplification
are being pursued [21]; the generation of
sub-3-cycle pulses, however, remains to
be demonstrated.
3 Self-generation of few-cycle
pulses through filamentation
We have found an experi-
mental approach, which considerably
simplifies the procedure. Instead of rely-
ing on the external guiding effect of the
capillary, we exploit the self-guiding ef-
fect that an intense optical pulse can ex-
perience when it propagates in a trans-
parent gas [22]. The self-guiding effect
removes the constraints of the capillary,
while it keeps and even expands on their
beneficiary aspects. These effects are
spatial filtering via self-guiding, spec-
tral broadening via self-phase modu-
lation, pulse self-shortening [23] and
CEO phase preservation [24]. As will
be shown, under suitable conditions,
that are easy to implement, one can ob-
tain intense, reproducible, CEO phase-
locked, few-cycle laser pulses with ex-
FIGURE 1 Mechanism for channel formation: For a typical beam intensity profile with a maximum
on axis, the intensity dependent refractive index (n = n
0
+ ∆n
Kerr
(I) = n
0
+ n
2
I) acts like a succes-
sion of increasingly converging lenses. In the absence of a limiting effect, this would lead to a beam
collapse on axis if the pulse power exceeds a critical value P
cr
= λ
2
/2πn
0
n
2
, which is several Gi-
gawatt in air at 800 nm. On-axis beam collapse is arrested by multi-photon ionization. This occurs
typically at intensities around 10
13
W/cm
2
in gases, giving rise to a weakly ionized plasma with an
electron density typically around 10
16
cm
−3
, and a corresponding reduction of the local refractive index
∆n =−N(I)/2N
cr
∼ 10
−4
. Here, N(I) denotes the intensity dependent free electron density and N
cr
,
the density above which the plasma becomes opaque. Thus, multi-photon ionization acts as a strong
regulating mechanism, limiting the beam intensity on axis and the dissipation of laser energy during
propagation
cellent beam quality by simply focus-
ing a laser beam in a gas cell and re-
compressing the output. Under optimal
conditions, our modeling predicts that
filamentation can even lead to pulses
very close to their fundamental limit of
a single cycle without the need of a final
recompression stage [25].
Filamentation, or self-guiding, oc-
curs when a sufficiently intense ultra-
short laser pulse propagates in a trans-
parent medium. Two physical effects
play a major role in the formation of
a filament: the self-focusing effect due
to intensity-dependence of the refractive
index of the medium, and defocusing
due to the formation of a plasma [26].
Both effects are schematically illus-
trated in Fig. 1.
It is important to stress that a fila-
ment is not a steady state. It has rich
temporal dynamics involving also other
effects such as group velocity disper-
sion, self-phase modulation, pulse self-
steepening and the Raman effect [27].
Despite the complex spatio-temporal
coupling that occurs from their com-
bined action, the pulse takes the form of
a narrow beam (
100 µm) surrounded by
a reservoir of laser energy. This reser-
voir feeds the filament core which be-
comes largely insensitive to initial con-
ditions. It maintains high peak intensity
around
10
13
W/cm [24] over a long dis-
tance, exceeding by orders of magnitude
the Rayleigh length even if the underly-
ing dynamics is complex and changing
rapidly.
In addition to the pulse spatial con-
traction, which is induced by the inten-
sity dependence of the refractive index,
broadening of the pulse spectrum arises
due to the time variation of the refractive
index (
n = n
0
+ ∆n
Kerr
(I ) = n
0
+ n
2
I ).
The corresponding phase variation adds
new frequency components to the spec-
trum: Red frequency components on its
ascending, and blue components on the
descending side. This results in a varia-
tion of the instantaneous frequency with
time (chirp). The addition of new fre-
quencies develops to the point of cre-
ating a quasi-continuum extending over
the entire visible spectrum and into the
infrared. This opens the possibility to
obtain shorter pulses, by a suitable re-
tardation of the red components with re-
spect to the blue ones.
One additional aspect of femtosec-
ond filamentation, which has no coun-
terpart in external guiding (hollow fiber),
is pulse self-compression [25, 28, 29].
The different nonlinear effects occur-
ring in filamentation lead to an im-
portant restructuring of the pulse time
profile. Some of these effects, such
as self-focusing, pulse self-steepening,
and self-phase modulation, act instanta-
neously. These effects tend to accumu-
late laser energy to the ascending part of
the pulse, whereas the time-delayed ef-
fects, such as photo-ionization and the
Raman effect, tend to cut off its trail-
ing part. Their combination eventually
leads to the formation of pulses that are
significantly shorter than the incident
pulse. One important facet, previously
overlooked, is the fact that pulse reshap-
ing by filamentation can be effective
down to the fundamental limit of nearly
one optical cycle.
4 Experimental results
We found that optimum pulse
shortening from
43 fs to 5.7fs could
be achieved by using two successive
gas cells at pressures of
840 mbar and
700 mbar of argon, as shown in Fig. 2.
The CEO-phase-locked input pulse
with an energy of
0.84 mJ was loosely
focused into the first cell where it gener-
ated a
10–15 cm long filament roughly
HAURI et al. Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation 675
FIGURE 2 Experimental setup: Two cells are filled with argon at 840 mbar and 700 mbar respectively.
CEO-phase-locked 43-fs IR pulses with 0.84 mJ energy form a 10–15-cm long filament in the middle
of the first cell and are compressed with chirped mirrors to 10.5 fs at 790 µJ. Sending those pulses into
the second cell results in a filament also 15–20 cm long that, after final recompression, leads to a 5.7-fs
pulse with 45% of the initial pulse energy in an excellent spatial profile
in the center of the cell, as estimated
from the length of the scattered broad-
band continuum. The emerging spec-
trum was recompressed with chirped
mirrors, resulting in a shortening by
a factor four while retaining
94% of
the input energy. Sending the
10.5-fs
pulse into the second gas cell, another
FIGURE 3 (a) Temporal intensity profile of compressed pulses as obtained with SPIDER for pressures of 840 mbar and 700 mbar of argon. The full
width at half maximum (FWHM) pulse duration of 5.7 fs corresponds to 2.1 optical cycles. The spatial profile, measured with a high resolution CCD
(WinCam, DataRay) is excellent, as can be seen in the inset. The associated spectrum and spectral phase are given in (b). (c) Time series from an f -2 f
spectral interferometry measurement. The CEO-phase lock is switched on after roughly 1.2 s with the emergence of fringes confirming the CEO phase lock.
(d) Transform-limited pulse duration supported by the normalized spectrum after the second gas-cell, shown in (e), before the chirped mirror compressor, as-
suming a flat spectral phase, perfect bandpass and phase characteristics of the chirped mirrors. (f) Normalized pulse spectrum after the first cell. The pressures
in the first and second cell were optimized for maximal spectral broadening and were measured to be 840 mbar and 1060 mbar respectively
15–20 cm long filament was formed,
leading after chirped-mirror recompres-
sion, to a
5.7-fs pulse with 45% of
the initial pulse energy,i.e.
0.38 mJ,in
an excellent spatial profile. Figure 3a
and b show a spectral phase interferom-
etry for direct electric-field reconstruc-
tion (SPIDER [30]) measurement of the
pulse temporal profile, spectral phase
and spectrum measured at a kHz sin-
gle shot rate [31]. The excellent spatial
quality of this pulse is revealed in the
inset of Fig. 3a. CEO phase stability is
confirmed through
f -2 f spectral inter-
ferometry [9, 19] with the persistence of
fringes confirming the phase-preserving
nature of the filaments. Figure 3c shows
a time series of such a measurement
where the CEO-lock, with one feed-
back for the oscillator only, has been
switched on after roughly
1.2s.The
measurement clearly confirms the for-
mation and steadiness of fringes, hence
confirming CEO-phase conservation.
Figure 3e shows the spectrum meas-
ured after the second gas-cell (before
the chirped mirror compressor), opti-
mized for maximal spectral width at
a pressure of
1060 mbar. It supports
a transform-limited pulse duration of
1.75 fs shown in Fig. 3d, assuming a flat
spectral phase. The spectrum after the
first cell, at a pressure of
840 mbar,is
shown in Fig. 3f.
We would expect that with bet-
ter dispersion compensation (i.e. better
chirped mirrors) we could obtain even
shorter pulses than the demonstrated
5.7fs.
We attribute the observed differ-
ences between results shown in Fig. 3a
676 Applied Physics B – Lasers and Optics
FIGURE 4 Modeled pulse propagation for second gas cell: (a) Intensity profile confirming the formation of a filament. (b), (c) Space-time profile of the pulse
at two locations inside the filament. (b) is calculated 92 cm from the focusing mirror for the second gas cell. Further propagation (25 cm) leads to a tightly
spatially and temporally confined light bullet
and d, respectively Fig. 3b and e to
a large extent as follows: First, the dif-
ference in the spectra is obviously due
to the chirped mirrors. The phase char-
acteristics of the chirped mirrors used in
the experiment are insufficient to pro-
duce a pulse much shorter than
6fs.This
limitation not only modifies the spec-
trum but, more importantly, limits the
compression. The dispersion introduced
by the mirrors being known, it will be
possible to design and fabricate appro-
priate chirped mirror [32, 33] structures
to obtain better compression. Secondly,
the dispersion in the exit window, con-
sisting of a
0.7mm thick fused silica
plate at Brewster angle, has a significant
effect on such ultra broadband pulses.
For instance, it increases the duration of
a transform-limited single-cycle pulse
seven-fold.
The robustness of the present ex-
perimental technique to obtain shorter
pulses with respect to variations in
input pulse and operating parameters
is essential. We have therefore care-
fully checked the influence of these
changes on the final pulse energy, dura-
tion and spatial profile and have found
that this method is surprisingly insen-
sitive to such changes. Therefore self-
compression through filamentation is
a very robust and reliable method to
generate intense few-cycle pulses, e.g.
a change in pressure of
100 mbar in-
fluenced the pulse duration by
0.2fs
only.
5 Numerical simulation
The measured results can be
well reproduced by a code calculating
the propagation of intense short laser
pulses in a transparent medium [34].
Our code solves the 3D nonlinear enve-
lope equation describing the evolution
of the field envelope. This approach has
been demonstrated to be valid down
to the single-cycle limit [35]. It accu-
rately reproduces experimental results
on filamentation in gaseous and solid
media. The model includes the physical
effects of diffraction, group velocity dis-
persion, self-focusing, self-steepening,
space-time focusing, Raman scatter-
ing, ionization, plasma defocusing as
well as photo-absorption and plasma
recombination.
We have calculated the propagation
inside the second gas cell, by using vari-
ous input conditions close to the meas-
ured input pulse parameters, such as
the pulse amplitude and phase (obtained
from a SPIDER measurement). Fig-
ure 4a gives the calculated spatial dis-
tribution of laser intensity, which con-
firms the formation of a filament. Fig-
ure 4b and c show the spatio-temporal
intensity distribution at two different
propagation distances. The temporal
evolution is illustrated by the transition
between Fig. 4b and c. We find spe-
cific locations where self-shortening of
the laser pulse takes place over sev-
eral centimeters with a minimum pulse
duration nearing 1.3 optical cycles. In-
terestingly, the calculated phase front of
an isolated self-compressed pulse such
as in Fig. 4c reveals a near flat surface
over several centimeters, evolving into
a parabolic shape (diverging beam). In
fact, the comparison between numeri-
cal and experimental results shows that
the pulse of Fig. 3a with a diverging
beam of excellent quality was collected
at a location close to optimal. It suggests
that the final external compression stage
is required by the presence of the exit
window.
6 Conclusions and outlook
We have demonstrated exper-
imentally, and confirmed theoretically,
that it is possible to obtain nearly sin-
gle cycle, CEO phase-locked pulses via
filamentation in a gas for the first time.
This technique presents a robust and
simple alternative to hollow fiber pulse
compression. The following aspects are
unique to this technique:
Flat phase front and intensity clamp-
ing: filamentary propagation has been
shown to yield an output pulse with a flat
phase front, a feature confirmed by our
