Metrology of few-cycle
NIR femtosecond pulses using SEA-SPIDER.
Fig. 1: SEA-SPIDER concept
Ultrashort optical pulses can be used in time-resolved experiments
to capture extremely fast events, analogous to flash photography.
However, detailed knowledge of the pulse is required for accurate
measurements. Unfortunately, a direct measurement of the temporal
structure of the pulse is currently not possible because the pulse
duration (<<10-13s) is at least an order of magnitude
shorter than current detector response times (>10-12s).
Such a problem can be overcome by measuring the pulse in the spectral
domain (the amplitude of each frequency and their relative phase,
i.e. the 'arrival time' of each frequency component). Current detectors
are 'slow', measuring the average power of the field, thus it is
not possible to measure the phase directly.
The most widely used characterisation methods include frequency resolved
optical gating (FROG
) and spectral phase interferometry for direct
electric-field reconstruction (SPIDER
). Although these techniques have been proven
characterisation methods in the sub-10-fs range, their application
can become very challenging or even impossible under certain conditions.
These include the cases when: (1) the spectrum is ultra-broadband
(e.g. over an octave), (2) the spectrum is highly modulated, (3) the
pulse exhibits space-time coupling (STC), (4) real-time measurement
is required for use in a phase compensation feedback system and (5)
it is desirable to have single shot acquisition. At Oxford, we have
developed a variant of SPIDER which uses a spatially encoded arrangement
(SEA-SPIDER [3,4]) which has
been optimised for sub-10-fs pulses in the near infrared (NIR) and
can overcome the aforementioned issues.
Fig. 2: SEA-SPIDER interferograms.
(a) FTL pulse, (b) Positive dispersion, (c) Negative dispersion. Dashed
line represents fringe contour = phase gradient.
The difficulties in measuring sub-10-fs pulses lie in the method
of encoding the pulse-shape information in conventional FROG and SPIDER.
FROG requires a 2D data set that encodes a 1D field. It can operate
near the spectral sampling limit (given by the Whittaker-Shannon theorem)
and uses an iterative deconvolution algorithm to reconstruct the field.
However, a FROG apparatus is usually configured to spectrally and
temporally oversample the pulse so that it can measure complex pulse
shapes with little adjustment. The size of data and reconstruction
time increases nonlinear with the pulse complexity and is not suited
for real-time measurement. For an octave spanning spectrum, a non
collinear geometry is required, which causes temporal smearing of
the FROG trace due to the thickness of the pulse beams. Single shot
acquisition can only be accomplished in the absence of STC because
the spatial dimension of the beam is used to encode temporal information,
the resulting trace can become ambiguous in the presence of STC. Conventional
SPIDER records a 1D data set and uses a direct, linear reconstruction
algorithm which makes it ideally suited for real-time, single shot
acquisition and phase compensation feedback. However, the phase is
encoded in the spacing of spectral fringes and thus SPIDER oversamples
the spectrum significantly. If the spectral amplitude has regions
of low spectral intensity or high structure, then a very high spectral
resolution is required in order to resolve the fringes if phase errors
are to be avoided. However it is possible to measure STC and perform
single shot acquisition simultaneously with rapid reconstruction.
Fig. 1 shows the basic idea for SEA-SPIDER. The pulse to be measured
(test pulse) upconverts with two spatially titled, temporally delayed
and highly chirped pulses in a type II nonlinear crystal. During the
interaction time, this test pulse will see a different quasi-monochromatic
frequency from each of the chirped pulses. Thus after the upconversion,
two signal pulses are produced which are spectrally shifted replicas
of the test-pulse. These two signal pulses are then imaged onto the
entrance slit of a 2D imaging spectrometer such that interference
between them causes fringes in the spatial domain. The interference
pattern can be represented by equation 1. Provided the pulse has no
spectral phase, the distance between each fringe would be Kx, where
K is the difference in the mean wavevector of each pulse and x is
the spatial position. However, if there is any phase on the test-pulse,
then the shear Ω between the two signal pulses modulates the
fringe pattern and thus allows the test-pulse phase to be recovered.
The fringes are induced in the spatial domain, thus the spectrum can
be sampled at the Whittaker-Shannon limit, thus a low resolution spectrometer
can be used to record ultrabroadband pulses.
Fig. 3: Accuracy of SEA-SPIDER. The
test pulse was measured before and after traversing 1cm fused silica.
The difference in the phase was compared to the theoretical phase
of fused silica.
Figure 2 to the right shows three experimental SEA-SPIDER interferograms
of a sub-10-fs pulse. From equation 1, it is evident that SEA-SPIDER
traces can show some intuitive behaviour which allows manual phase
compensation / optimisation without the need to reconstruct. This
intuitive nature arises from the fact that the contour of the fringes
directly map the gradient of the spectral phase, which itself is equal
to the dispersion. For example, figure a is the result for a Fourier
transform limited (FTL) pulse (i.e. zero phase) - the fringes appear
completely horizontal. Figures b and c correspond to positive and
negative group velocity dispersion (GVD) respectively. This is shown
by the positive or negative slope in the fringe pattern (as shown
by the dashed lines.
Figure 3 compares the phase of a glass block as measured by the SEA-SPIDER
with the theoretical phase calculated using the Sellmeier coefficients
for that glass. The agreement is excellent over the whole spectrum
of the pulse, even in regions of low spectral intensity. The phase
is recovered over the whole extend of the spectrum, even in the presence
of noise on the interferogram. Due to the large spectrum required
to support few-cycle pulses, any slight phase can result in significantly
stretching the pulse, thus it is critical that the phase is measured
over the whole spectral bandwidth with very high accuracy.
As SEA-SPIDER measures the spectrum and phase at every position in
a slice through the beam, it is possible to measure STC directly (although
a complete space-time measurement requires a further measurement).
The next step is to use the device on the output of the hollow-core
fibre system to measure frequency dependant mode size (FDMS) and spatial
chirp. Due to the sensitivity of the device, it should be possible
to measure the pulse phase while performing experiments (e.g. high
harmonic generation) simultaneously and possibly with single shot
acqusition as well.
 Using phase retrieval to measure the intensity
and phase of ultrashort pulses: frequency-resolved optical gating
Rick Trebino and Daniel J. Kane, J. Opt. Soc. Am. A - Optics Image
Science and Vision, 10 (5), 1101, (1993)
 Spectral phase interferometry for direct
electric-field reconstruction of ultrashort optical pulsesC. Iaconis
and A. Walmsley, Opt. Lett., 23 (10), 792-794, (1998)
 Interferometric technique for measuring
broadband ultrashort pulses at the sampling limit Ellen M. Kosik,
Aleksander S. Radunsky, Ian A. Walmsley, and Christophe Dorrer, Opt.
Lett., 30 (3), 326-328, (2005)
 Sub-10-fs pulse characterization using spatially
encoded arrangement for spectral phase interferometry for direct electric-field
reconstruction Adam S. Wyatt, Ian A. Walmsley, Gero Stibenz and
Günter Steinmeyer, submitted Opt. Lett. January 2006