2.1 Ultrafast solid-state lasers - ETH - the Keller Group

Ref. p. 134] 2.1 Ultrafast solid-state lasers 125
to the spectral shear as with the concatenation method. The phase information of the resulting
interferogram allows the direct reconstruction of the spectral phase of the input pulse. Combined
with the measured spectrum of the pulse the actual pulse can be calculated without any prior
assumptions.
Three design parameters determine the range of pulse durations that can be measured by a
certain SPIDER apparatus: the delay τ, the spectral shear δω and the group-delay dispersion
GDD up used to generate the strongly linearly chirped upconverter pulse. These three parameters
are related as:
δω =
τ
GDD up
. (2.1.95)
The delay τ, which determines the positions of the two side peaks of the Fourier transform of
the interferogram, is chosen in such a way as to assure that the side peaks are well-separated
from the center peak. On the other hand, the fringe spacing of the interferogram is proportional
to 2π/τ and thus τ must be sufficiently small such that the spectrometer is able to fully resolve
the fringes. The stretching factor GDD up is then chosen such that the spectral shear δω, which
determines the sampling interval of the reconstructed spectral phase, is small enough to assure
correct reconstruction of the electric field in the time domain according to the Whittaker–Shannon
sampling theorem [00Dor]. The constrained relationship for τ and δω expressed by (2.1.95) means
that with a particular SPIDER setup, only pulses with a limited range of pulse durations can be
measured. A set-up for the sub-10-femtosecond regime in described in [99Gal].
2.1.7.3.3 Comparison between FROG and SPIDER techniques
The highest acquisition rates for single-shot pulse characterization reported so far were 1 kHz using
SPIDER [03Kor] and 30 Hz using FROG [03Gar]. FROG is not well suited for high acquisition
rates for two reasons: FROG requires the measurement of a 2D trace which makes the acquisition
itself inherently slow and moreover the FROG algorithm uses an iterative process which requires a
minimum number of steps for convergence depending on the complexity of the measured pulse. SPI-
DER however only requires the acquisition of two 1D spectra: the so-called SPIDER interferogram
and the optical spectrum of the pulse. Furthermore, the SPIDER algorithm is deterministic since
it is based on two Fourier transforms with intermittent spectral filtering to reconstruct the spectral
phase of the pulse. An additional Fourier transform is then required to calculate the electric field in
the time domain and therefore the pulse reconstruction is fast. SPIDER is thus well suited for high
acquisition rates and real-time operation. SPIDER has been shown to achieve high accuracy, i.e.
the reconstructed electric field matches well with the physical field of the pulse [02Dor1], and high
precision [02Dor2], implying a small spread between several reconstructions of the field obtained
from the same data. In particular the SPIDER technique is reliable in the presence of limited
experimental noise [00And, 04Jen]. SPIDER offers more bandwidth than any other technique and
we even can measure pulses in the single-cycle regime [03Sch]. In addition, SPIDER still gives valid
results even if the beam profile is not spatially coherent anymore because we can spatially resolve
these measurements [01Gal]. A direct comparison between FROG and SPIDER techniques in the
sub-10-femtosecond regime is given in [00Gal2].
Only fully characterized pulses in phase and amplitude will provide reliable information about
pulse shape and pulse duration – this becomes even more important for pulses with very broad and
complex spectra. In such a situation any other technique, such as fitting attempts to IAC traces,
is very erroneous and generally underestimates the pulse duration.
Landolt-Börnstein
New Series VIII/1B1