Three-dimensional spatiotemporal pulse
characterization with an acousto-optic
pulse shaper and a Hartmann–Shack wavefront sensor
Seth L. Cousin,1Juan M. Bueno,2Nicolas Forget,3Dane R. Austin,1,* and J. Biegert1,4
1ICFO—Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels, Barcelona, Spain
2Laboratorio de Óptica, Universidad de Murcia, Campus de Espinardo (Ed. 34), 30100 Murcia, Spain
3FASTLITE, Centre Scientifique d’Orsay—Bât. 503—BP 45, 91401 Orsay, France
4ICREA—Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain
*Corresponding author: email@example.com
Received June 1, 2012; revised June 1, 2012; accepted June 28, 2012;
posted July 2, 2012 (Doc. ID 165763); published July 31, 2012
We demonstrate a simplified arrangement for spatiotemporal ultrashort pulse characterization called Hartmann–
Shack assisted, multidimensional, shaper-based technique for electric-field reconstruction. It employs an acousto-
optic pulse shaper in combination with a second-order nonlinear crystal and a Hartmann–Shack wavefront sensor.
The shaper is used as a tunable bandpass filter, and the wavefronts and intensities of quasimonochromatic spectral
slices of the pulse are obtained using the Hartmann–Shack wavefront sensor. The wavefronts and intensities of the
spectral slices are related to one another using shaper-assisted frequency-resolved optical gating measurements,
performed at particular points in the beam. This enables a three-dimensional reconstruction of the amplitude
and phase of the pulse. We present some example pulse measurements and discuss the operating parameters of
the device. © 2012 Optical Society of America
OCIS codes: 320.7100, 320.5540, 140.3295, 320.7080.
The characterization of femtosecond optical pulses is a
central component of ultrafast technology and is routi-
nely accomplished using techniques based in spectrogra-
phy  or interferometry . In their most basic forms,
these methods ignore or average over any spatial varia-
tion in the temporal profile. However, spatiotemporal
coupling occurs commonly in ultrafast optics, for exam-
ple through misaligned dispersive elements or nonlinear
pulse propagation . The opportunities as well as the
problems that arise from such coupling have motivated
the extension of temporal characterization methods to
the spatiotemporal domain. One common approach is to
combine a temporal characterization of a point in the
beam with a set of spectrally resolved wavefront mea-
surements, obtained using lateral shearing interfero-
metry , test-plus-reference interferometry , or a
Hartmann–Shack wavefront sensor . Since these ex-
tensions add complexity and alignment, it is worthwhile
searching for more simple and robust implementations,
particularly ones in which the optical elements play dual
roles in both the temporal and spatial characterization.
In this Letter, we present such an implementation:
Hartmann–Shack assisted, multidimensional, shaper-based
technique for electric-field reconstruction (HAMSTER),
persive filter (AOPDF) . In combination with a second-
order nonlinear crystal and a spectrometer, the AOPDF
ods; here we use baseband interferometric frequency-
resolved optical gating (bFROG) . The AOPDF can also
be operated as a tunable bandpass filter, whose output is
directed onto a Hartmann–Shack wavefront sensor [9,10].
quasimonochromatic spectral slices of the pulse is ob-
larly dispersed pulses from a Ti:sapphire amplifier.
Figure 1 shows a schematic of the device. The mea-
surement plane M is relayed to the AOPDF by the tele-
scope formed by f ? 500 mm lenses L1 and L2. It is then
relayed by the telescope formed by f ? 200 mm lenses
L3 and L4, via a flip-mounted mirror FM, to either the
lenslet plane of the Hartmann–Shack wavefront sensor
(Thorlabs WFS-150) or to iris I2. The point in the beam
selected by I2 is used for temporal characterization and
can be chosen by lateral translation of retroreflector R. A
third 4-f telescope, consisting of f ? 500 mm lens L5 and
f ? 50 mm lens L6, forms a 10× reduced image of the ir-
ised measurement plane on a 50 μm beta-barium borate
crystal cut for type-I conversion. The f ? 50 mm lens L7
images the generated sum-frequency beam onto the en-
trance slit of the spectrometer (Avantes AvaSpec-2048-
USB2). Filter F (Schott BG39) removes the fundamental.
The dispersion of lenses L1–L6 and the AOPDF are cali-
brated using a separate device or interferometry and
compensated by the AOPDF during measurements. Note
that the telescope L1–L2 is only necessary in order to
tiotemporal measurement device; the acronyms are described
in the text. Planes conjugate to the measurement plane M are
indicated by dashed lines.
(Color online) Schematic setup of the HAMSTER spa-
August 1, 2012 / Vol. 37, No. 15 / OPTICS LETTERS3291
0146-9592/12/153291-03$15.00/0 © 2012 Optical Society of America
measure the pulse at external plane M rather than at
A measurement is performed by programming the
AOPDF to act as a tunable bandpass filter, directing
its output to the wavefront sensor, and sequentially
acquiring the wavefronts of sufficiently narrow spectral
slices across the bandwidth of the pulse. The spatial
phase and intensity profiles (the latter inferred from
the intensity of the focal spots formed by the lenslet
array) are combined to form the three-dimensional spa-
tiospectral electric field E?x;y;ω?A?ω?exp iB?ω?, up to
unknown frequency-dependent scaling A?ω? and phase
B?ω? factors. (While A?ω? could be inferred from the
spectral response of the wavefront sensor and the
AOPDF, it is more convenient to use the spectrum re-
trieved by the bFROG.) The AOPDF output is then direc-
ted to the temporal characterization arrangement. The
point ?x0;y0? selected by I2 for temporal characterization
is located in the Hartmann–Shack images by sending an
irised beaminto the system such that it passes through I2.
After inserting FM, this beam marks the selected point on
the sensor. This calibration is independent of the incident
beam direction and need only be performed once. The
AOPDF is programmed to produce time-delayed and
phase-shifted replicas for the bFROG measurement. In-
version of the bFROG trace [up to the second harmonic
generation frequency-resolved optical gating (FROG)
ambiguities of absolute phase and arrival time] yields
E?x0;y0;ω?, from which one obtains A?ω? and B?ω?
and hence the full three-dimensional complex amplitude
of the pulse. The direction of time ambiguity is resolved
by applying a known phase using the AOPDF and repeat-
ing the measurement. Further Fourier transforms yield
the profile in any combination of the spectral/temporal
and spatial/transverse-wavenumber domains.
The pulse parameter restrictions introduced by the
AOPDF and the wavefront sensor are quite acceptable
in our implementation. At 800 nm, the AOPDF is capable
of characterizing pulses with transform limits above 20 fs
and durations below 500 fs , while the smallest
obtainable spectral slice is 0.3 nm. The spatial aperture
is 2 mm. The spatial resolution is limited by the pitch of
the lenslet array of the wavefront sensor, in our case
146 μm. Two artifacts of the AOPDF can, in principle,
worsen this. First, the device applies a group-delay-
dependent displacement of the beam in the diffraction
plane [12,13], which we take as the yz plane here. In
our setup, this coupling is v ? 0.1 μm∕fs. This causes
lateral movement of the replicas during the bFROG scan.
The induced loss of spatial resolution is equal to the pro-
duct of v and the bFROG delay range and is insignificant
for the parameters considered here. Second, the wave-
length tuning of the AOPDF depends on the input beam
angle in the diffraction plane, necessitating a compro-
mise between spectral resolution and angular accep-
tance in the diffraction plane. We measured this
coupling to be 0.26 nm∕mrad. Finally, inhomogeneity
in the acoustic wave in the AOPDF can produce a spatial
intensity modulation (approximately 10%) along the dif-
fraction direction. This may be easily diagnosed by
small translations of the AOPDF but cannot be easily
As an example, we characterized pulses which had
passed, with incident angle 58.1° ? 0.2°, through an
N-SF11 equilateral prism located at the measurement
plane. In accordance with the coupling between AOPDF
incidence angle and wavelength described above, the
dispersion was in the xz plane. The pulses were from
a Ti:sapphire chirped-pulse amplification system, with
35 fs FWHM, center wavelength 795 nm, and 1∕e2beam
radius 1.25 mm. Using a pulse shaper inside the amplifier,
we applied a spectral phase of −1000 fs2to compensate
for the dispersion of the center of the beam in the prism.
The pulse energy incident upon the AOPDF was 9 μJ. The
wavefronts were sampled at 2 nm increments, and a
0.4 mm diameter portion of the center of the beam
was characterized by the bFROG. The reconstructed
spatiotemporal profile, represented as a surface of half-
maximum intensity, is shown in Fig. 2(a). The measured
pulse front tilt is 6.63° ? 0.05°, consistent with the theo-
retical value  of 6.64° ? 0.06° inferred using the inci-
dent angle. Another comparison with theory is the
transverse chirp variation in the direction of angular
dispersion, caused by propagation through different
lengths of prism glass. The extracted quadratic spectral
phase is plotted against x in Fig. 2(b), along with a lin-
ear fit (to the central part of the beam) of slope
510 ? 20 fs2∕mm. This compares well with the theo-
retical value of 507 ? 6 fs2∕mm. Otherwise, the pulse
is nearly identical to that measured without the prism.
To observe the dispersive effect of propagation on the
angularly dispersed beam, we moved the prism 70 mm
forward of the object plane. The measured pulse is simi-
lar, but with an additional quadratic spectral phase of
1350 ? 80 fs2∕mm, implying a dispersion per unit length
of 19.3 ? 1 fs2∕mm. This is consistent with the value of
19.1 ? 0.4 fs2∕mm expected from theory .
A general restriction of combining spectrally resolved
wavefronts with a single temporal characterization is that
the latter must contain all frequencies in the entire beam
. Our device offers a convenient way of alleviating this.
By translating the retroreflector R in the transverse
plane, we can select different points in the beam ?xn;yn?
to be temporally characterized. An unambiguous recon-
struction is possible if the entire ?x;y;λ? volume of the
pulse is connected a combination of “moves,” which
may either use the spectrally resolved wavefronts and
are constrained to a plane of fixed λ or use the temporal
prism-dispersed pulse, represented as a surface of 50% peak in-
tensity, with projections along the coordinate axes. (b) Mea-
sured quadratic spectral phase versus position along the axis
of angular dispersion x (red, left axis) with linear fit (red
dashed). Normalized intensity projected onto the x axis (blue,
(Color online) (a) Spatiotemporal intensity of the
3292OPTICS LETTERS / Vol. 37, No. 15 / August 1, 2012
characterizations and are constrained along one of the
measurement points ?xn;yn?. To demonstrate this, we
placed the prism 371 mm before the object plane of
the HAMSTER. At this propagation distance, angular dis-
persion leads to a spatial chirp, and not all frequencies
have sufficient intensity at the central point of the beam.
Figure 3(a) shows the slice y ? 0 through the spatiospec-
tral intensity volume. We obtained bFROG measure-
ments at the points indicated by the horizontal blue
lines (all were at y ? 0). As will generally be the case,
there was some redundancy in the data since the spectra
at these points have some overlap. The system is there-
fore overdetermined, and we use separate least-squares
minimizations for the intensity and phase. The ambigu-
ities present in each measurement—the aforementioned
A?ω? and B?ω? for the wavefronts and their intensities,
and the absolute phases, arrival times, and arbitrary scale
factor for the bFROG reconstructions—are treated as
free parameters. The phase equations are weighted by
the local intensity. Both the intensity and phase equa-
tions may be robustly solved using a least-squares mini-
mization. In Figs. 3(b)–3(d), the spectral intensity and
phase reconstructed at each temporal characterization
point is compared with that obtained directly from the
bFROG measurements. The intensities agree except
for a few isolated points caused by the reconstruction
being close to the maximum temporal window of the
bFROG, required for the dispersed, narrowband pulses.
The phases agree except in places where the spectral
intensity is low.
In summary, we have demonstrated three-dimensional
spatiotemporal characterization of ultrashort pulses by
combining a shaper-assisted FROG with a Hartmann–
Shack wavefront sensor. Our setup exploits the growing
availability of compact monolithic implementations of
these devices to perform a task that normally requires
a more complex and alignment-intensive setup.
The authors acknowledge support from the Spanish
Ministerio De Ciencia E Innovacion (MICINN) through
its Consolider Program (SAUUL—CSD 2007-00013) and
“Participation in ELI” (CAC-2007-37) as well as through
“Plan Nacional” (FIS2008-06368-C02-01) and the Catalan
Agència de Gestió d’Ajuts Universitaris i de Recerca
(AGAUR) with SGR 2009-2013. Funding from LASERLAB-
supported by a Marie Curie Intra-European Fellowship
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pulse measured 371 mm after the prism. The horizontal blue
lines indicate the points temporally characterized by the
bFROG. (b)–(d) Spectral intensity (blue, left axis) and phase
(red, right axis) at the three temporally characterized points.
Faint, thick lines show the final reconstructed profiles, while
thin, dark lines show what is directly retrieved by the bFROG
(Color online) (a) Spatiospectral intensity profile of
August 1, 2012 / Vol. 37, No. 15 / OPTICS LETTERS 3293