Generation of 2:5 μJ vacuum ultraviolet
pulses with sub-50 fs duration
by noncollinear four-wave mixing in argon
M. Ghotbi,* M. Beutler, and F. Noack
Max-Born-Institute for Nonlinear Optics and Ultrafast Spectroscopy, 2A Max-Born-Strasse, D-12489 Berlin, Germany
*Corresponding author: mghotbi@mbi‑berlin.de
Received July 21, 2010; accepted September 7, 2010;
posted September 27, 2010 (Doc. ID 131956); published October 13, 2010
Generation of sub-50 fs vacuum UV pulses with more than 2:5 μJ energy at a 1 kHz repetition rate is reported. The
pulses at 160 nm are produced using noncollinear difference-frequency four-wave mixing between the fundamental
andthird harmonicsof an amplifiedTi:sapphirelaser in argon.Whilethepulsedurationis maintainedby increasing
the phase-matching pressure, noncollinear interaction improves the conversion efficiency by 1 order of magnitude
in comparison with the previous results in collinear geometry.
© 2010 Optical Society of America
Ultrashort vacuum UV (VUV) pulses have many applica-
tions in time-resolved spectroscopy, because the electro-
nic transitions of many molecules and molecule clusters
are in the UV–VUV spectral range with subpicosecond
relaxation times [1,2]. Generation of sub-100 fs pulses
with >100 nJ energy in the VUV has been a challenge
for many years. The UV edge of the transparency range,
the phase matching (PM), and the large group velocity
mismatch of the nonlinear crystals strongly limit their ap-
plication in short pulse generation across this spectral
range [3,4]. The use of noble gases by applying their third-
or higher-order nonlinearities has been more successful
in generation of deep UV and VUV pulses. Two-photon
near-resonant four-wave difference-frequency mixing
(FWDFM) in argon resulted in generation of 300 fs pulses
at 155 nm . By generating higher harmonics, wave-
lengths down to 40 nm, but still with pulse durations
of several hundred femtoseconds , and 11 fs pulses
at the fifth harmonic (FiH) of a Ti:sapphire laser, but with
only a few nanojoules of energy , have been generated.
More recently, by applying hollow waveguides in a four-
wave mixing (FWM) process, 140 fs pulses in the 100 nJ
energy range by generation of the FiH of a 1 kHz
Ti:sapphire laser has been demonstrated . We have
also investigated collinear FWM in argon and demon-
strated generation of sub-50 fs pulses at 160 nm with
up to 240 nJ energy, also at a 1 kHz repetition rate .
Here we applied noncollinear configuration in a
FWDFM process for efficient generation of VUV pulses.
The noncollinear configuration has always been consid-
ered an importanttool for various purposes since the first
experiments in nonlinear optics [10–13]. In our experi-
ment, this configuration has been applied to improve
the conversion efficiency by increasing the nonlinearity
of the interaction medium with PM at higher pressures.
In the following we report the generation of high en-
ergy, sub-50 fs VUV pulses at 160 nm by a phase-matched
noncollinear FWDFM process between the fundamental
frequency (FF) and third harmonic (TH) of a 1 kHz
Ti:sapphire laser amplifier in argon. The VUV pulses,
as the FiH of the laser, have durations as short as
43 fs and maximum energies exceeding 2:5 μJ.
The pump laser provides up to 2:8 mJ pulses at 800 nm
with 42 fs duration. Using a 2:1 beam splitter, 67% of the
pulse energy is used to generate the TH pulses in a tri-
pling stage that provides up to 220 μJ pulses at 266 nm
with duration of ∼100 fs. The generated TH is combined
with the remaining fresh part of the fundamental pulse
(∼800 μJ) and focused into an argon-filled gas cell.
The FF is focused with an f ¼ 100 cm BK7 lens, while
the focusing of the TH is realized independently by an f ¼
50 cm MgF2lens. Each beam produces a few centimeters
long filament independently; after spatial and temporal
overlap, a brighter area in the interaction region is ob-
served. By increasing the noncollinear angle, the length
of the brighter area decreases, while this length in the
collinear configuration is more than 100 mm (longer than
both the FF and TH filaments). By increasing the angle to
15 mrad, it decreases to about 10 mm. FWM, using the
filaments in a collinear configuration for the generation
of visible pulses, has been realized in neon ; also re-
cently, the enhancement of TH generation efficiency by
noncollinear overlapping of two filaments has been ob-
served [15,16], but, in our experiment, there is no simple
way to test the effects of the presence of filaments. To
separate the generated VUV pulses from the FF and
the TH, we applied special dielectric high-reflecting
VUV mirrors (Layertec GmbH) that are also used for col-
limation and focusing of the beam into the experimental
chamber. By using a 100-μm-thick MgF2window, the
argon-filled FWM chamber is isolated from the second
experimental chamber, which is designed for pulse char-
acterization. See the schematic of the setup in our pre-
vious work .
In a collinear configuration, the optimum pressure for
VUV generation is low (∼28 mbar), and the conversion
process is governed mainly by the phase shift of the
Gaussian beams close to the focal region (Gouy phase
shift). This behavior has been investigated theoretically,
and analytical expressions for the phase shifts have been
derived . In the next steps, the interaction angle be-
tween the FF and TH beams was increased gradually and,
at each angle, the conversion efficiency for VUV genera-
tion was optimized by changing the pressure and correct-
ing the delay between the FF and TH pulses. According
3492OPTICS LETTERS / Vol. 35, No. 20 / October 15, 2010
0146-9592/10/203492-03$15.00/0© 2010 Optical Society of America
to the quadratic dependence of the efficiency on the
pressure , maintaining the PM condition at higher
pressures should result in a significant VUV power in-
crease. This condition can be satisfied in a noncollinear
FWM scheme, as is shown in Fig. 1. The calculated PM
curve for noncollinear FWDFM using the Sellmeier equa-
tion for argon from  and the measured experimental
data are shown in Fig. 2. By increasing the angle only to
about 25 mrad, PM pressure already reaches an amount
as high as 1:5 bar. Because of aperture size of the gas cell
entrance window, the maximum angle available in our
experimental setup was limited to about 18 mrad, corre-
sponding to a PM pressure of ∼600 mbar. It is important
to note that, besides the increase of the PM pressure, in-
creasing the angle φ results in decreasing the interaction
length between the FF and TH pulses. But still, if we ne-
glect all other nonlinear interactions and transversal spa-
tial effects, an estimation based on a one-dimensional
model [Eq. (1); effective interaction length is given by
interaction angle and beam diameter] shows a steady in-
crease of the conversion efficiency with higher pressure
under phase-matched interaction. However, we have not
observed this behavior experimentally. By increasing the
angle, at some point there is no more increase in the gen-
erated VUV and further increase of the interaction angle
results in lower energy of the VUV pulses. Because we
have observed depletion of the interacting beams during
the interaction and the increasing rate of the depletion
with an increase in pressure, we can attribute the exis-
tence of such optimum conditions to the depletion of
the interacting and also the generated VUV pulses via
multiphoton absorption and other nonlinear processes.
In our experimental setup, we found the maximum con-
version efficiencyat an angle of ∼15 mrad corresponding
to a PM pressure of ∼440 mbar. In these conditions and
considering the focusing spot sizes of the two beams
(d ¼ 150 μm), which also should be taken into account
, the calculated interaction length is ∼10 mm. This
amount is in good agreement with the measured length
of the bright column generated at the interaction region
inside the gas cell.
The FiH pulse energy was measured using a special
VUV energy probe (QF-16C, Star Tech Instruments).
By increasing the pressure while maintaining the PM con-
dition, the VUV pulse energy was improved by 1 order of
magnitude. While in collinear geometry at a pressure of
28 mbar, the VUV pulse energy is about 240 nJ, in a non-
collinear configuration, by increasing the angle φ to
15 mrad at a PM pressure of 440 mbar, the pulse energy
exceeds 2:5 μJ. We investigated the behavior of the gen-
erated VUV pulse energies at this pressure in more detail.
In the low-pulse-energy regime of the interacting beams,
the generated VUV shows the expected [see Eq. (1)] lin-
ear and quadratic dependences on FF and TH pulse en-
ergies, respectively. In this regime, even with 50 μJ of FF
and 80 μJ of TH, the generated VUV pulse still has a con-
siderable amount of 100 nJ. With increasing pulse ener-
gies, the VUV generation rate becomes slower and its
behavior changes to linear dependence on the TH and
even weaker dependence on FF pulse energies that can
be a result of absorption. The generated VUV pulses from
the noncollinear configuration are more stable compared
with the linear interaction. In the short term, the VUV
energy fluctuation is very small (<5%) and, in a longer
interval of few hours, the average VUV energy remains
To investigate the pressure dependence of the VUV
generation conversion efficiency, we measured VUV
pulse energy at different pressures but at a fixed interac-
tion angle. The results of this measurement at φ ¼
15 mrad, together with the theoretical curve, are shown
in Fig. 2. The data show an asymmetric behavior with the
pressure. Considering only the phase mismatch, Δk, the
theoretical curve shows a symmetric behavior. A similar
asymmetric behavior in the collinear configuration was
observed, which could be explained by the theory based
on the Gouy phase shift  but, in a noncollinear con-
figuration, we have associated this asymmetry to the
quadratic dependence of the conversion efficiency on
p according to the relation 
where N (which is proportional to p) gives the number
density of the argon atoms, χ3is the third-order nonlinear
coefficient, I is the intensity, L is the interaction length,
and n is the refractive index. In a fixed pressure, I5ωis
maximized when Δk ¼ 2k3ω− kω− k5ω¼ 0. Also, to si-
mulate the smooth drop at higher pressure, we have in-
troduced an absorption term of expð−γpÞ, with γ as the
between the FF and TH beams in the FWDFM process.
(Color online) Wave-vector diagram: noncollinear PM
collinear angle, φ, between the FF and TH beams in the
phase-matched FWDFM process for FiH generation in argon.
Theoretical calculation for the PM curve (solid curve) and ex-
perimental data (stars) are shown. Inset, theoretical calculation
(solid curve) and experimental data (stars) showing the depen-
dence of the generated VUV pulse energy on pressure at a fixed
noncollinear angle of φ ∼ 15 mrad. Both the calculated curve
and the experimental data are normalized.
(Color online) Pressure dependence of the non-
October 15, 2010 / Vol. 35, No. 20 / OPTICS LETTERS3493
optimization factor. The good agreement between the ex- Download full-text
perimental data and the analytical curve can be seen in
the inset of Fig. 2. Both the experimental data and the
calculated curve are normalized.
The characterization of the VUV pulses was performed
by spectral and temporal measurements. A typical spec-
trum of the VUV pulses at 440 mbar is shown in the inset
poral measurement of the generated VUV pulses was per-
formed inside the second chamber, which was filled with
tion using a time-of-flight (TOF) mass spectrometer. A
small part of the FF, as the probe beam, was focused col-
linearly with the VUV pulse into the interaction region of
trace is shown in Fig. 3. An FWHM of 50 fs for the Gaus-
sian fit corresponds to a pulse duration of 43 fs, consider-
ing the linear dependence of the signal on the VUV
intensity and its cubic dependence on the FF intensity
using the relation τ2vuv¼ τ2corr− τ2FF=3. The time–
bandwidth product of Δτ:Δν ∼ 0:65 for the generated
when a Gaussian shape is assumed.
In conclusion, we have demonstrated the generation of
sub-50 fs VUV pulses with energies as high as 2:5 μJ at
1 kHz repetition rate using a simple experimental setup
by noncollinear PM in a FWDFM interaction in argon.
Practical VUV pulse energy, together with shorter dura-
tion compared with the previous experimental results,
makes this source attractive for application in spectro-
scopy of small molecules and clusters.
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damental and VUV pulses in a xenon-filled TOF mass spectro-
meter. The cross-correlation signal is the measured ion rate.
The FWHM of 50 fs for the Gaussian fit corresponds to a pulse
duration of 43 fs. Inset, typical spectrum of the generated VUV
pulses at 160 nm and 440 mbar with an FWHM of 1:3 nm.
(Color online) Cross-correlation trace between the fun-
3494OPTICS LETTERS / Vol. 35, No. 20 / October 15, 2010