Two-dimensional spectral shearing interferometry resolved in time for ultrashort optical pulse characterization

Lelek et al. Vol. 25, No. 6/June 2008/ J. Opt. Soc. Am. B A17 Two-dimensional spectral shearing interferometry resolved in time for ultrashort optical pulse characterization Mickaël Lelek, 1, * Frédéric Louradour, 1 Alain Barthélémy, 1 Claude Froehly, 1 Tigran Mansourian, 2 Levon Mouradian, 2 Jean-Paul Chambaret, 3 Gilles Chériaux, 3 and Brigitte Mercier 3 1 Laboratoire XLIM, Faculté des Sciences et Techniques de Limoges, Unité Mixte de Recherche (UMR) CNRS 6172, 123 Avenue Albert Thomas, 87060 Limoges Cedex, France 2 Department of Quantum Electronics, Yerevan State University, Yeravan 375049, Armenia 3 Laboratoire d Optique Appliquée, École Nationale Supérieure des Techniques Avancées (ENSTA), Ecole Polytechnique, Unité Mixte de Recherche (UMR) CNRS 7639, Chemin de la Hunière, 91761 Palaiseau Cedex, France *Corresponding author: mickael.lelek@cea.fr Received November 5, 2007; revised February 4, 2008; accepted February 6, 2008; posted February 11, 2008 (Doc. ID 89316); published April 7, 2008 We present a new scheme for coherent measurement of ultrashort optical pulses that relies on spectral shearing interferometry combined with all-optical time gating. The spectral phase is encoded along a temporal coordinate resulting in a two-dimensional (2D) self-referenced and self-calibrating set of data. The method works without time delay between the two interfering signals. The pulse amplitude and phase are reconstructed with a high signal-to-noise ratio using a direct algorithm that applies a Fourier transform (FT) to the 2D recorded interference pattern. Characterization of low-energy, high-repetition-rate femtosecond pulses of various shapes and validation of a single-shot operation are reported. 2008 Optical Society of America OCIS codes: 320.7100, 320.7160, 190.4360, 120.5050, 300.6420. 1. INTRODUCTION Nowadays complete amplitude and phase characterization of ultrashort optical pulses has become an essential tool for many fundamental physics experiments such as extreme ultraviolet (XUV) attosecond pulse generation or proton acceleration [1 3], and for fundamental chemistry experiments as well [4,5]. In the last decade several methods for the coherent characterization of optical pulses have been reported. Among them one can find the wellestablished spectral phase interferometry for direct electric field reconstruction (SPIDER) technique [6,7] that is based on shearing interferometry applied to the spectral domain. Recently two new schemes for spectral shearing interferometry have been proposed to improve a standard SPI- DER taking advantage of the two-dimensional (2D) nature of their related interferograms. In spatially encoded arrangement SPIDER (SEA-SPIDER) [8] the spectral phase information is encoded along an additional spatial dimension, while in the case of two-dimensional spectral shearing interferometry (2DSI) [9] it is encoded as a function of a variable phase delay. It results in several significant benefits over standard SPIDER. SEA-SPIDER and 2DSI work with zero delay between the two interfering signals. This feature eliminates the need for a precise calibration of the delay that is particularly advantageous in the case of broadband pulse characterization [9]. The signal-to-noise ratio is higher in comparison with conventional SPIDER, thanks to the redundancy in the 2D interference pattern that additionally displays an intuitive and direct representation (i.e., before digital processing) of the studied spectral phase. In this paper we report a novel scheme for selfreferenced spectral shearing interferometry, referred to as two-dimensional spectral shearing interferometry resolved in time (2D-SPIRIT). 2D-SPIRIT is an evolution over conventional spectral shearing interferometry resolved in time (SPIRIT) [10,11]. Its basic principle is very close to the principle of superposition of optical radiation and beating to extract the time signal (SORBETS) [12] that also relies on time-resolved spectral interferometry. In SORBETS the temporal resolution is performed using a sensitive but expensive streak camera. In SPIRIT, the streak camera is replaced by a passive nonlinear timegating device. In conventional SPIRIT the fixed optical gating provides a single time sample, resulting in a onedimensional (1D) spectral shearing interferogram similar to the one delivered by conventional SPIDER. In 2D- SPIRIT the gating time is varied, resulting in a 2D set of data lying in the time-frequency domain. It will be demonstrated that 2D-SPIRIT offers the same above-mentioned improvements as SEA-SPIDER and 2DSI (e.g., delay cancellation, high signal-to-noise ratio, and intuitive and direct representation). 2D-SPIRIT is compatible with a single-shot operation, which is not the case with 2DSI. More importantly, it will be demonstrated that 2D-SPIRIT is fully self-calibrating, which is not the case with SEA-SPIDER or 2DSI. Indeed it will be shown 0740-3224/08/060A17-8/$15.00 2008 Optical Society of America

A18 J. Opt. Soc. Am. B/ Vol. 25, No. 6/ June 2008 Lelek et al. that the spectral shear involved in 2D-SPIRIT can be independently extracted from the recorded data to the spectral phase to be measured. 2. TWO-DIMENSIONAL SPIRIT BASIC PRINCIPLE The 2D-SPIRIT procedure is as follows. Two replicas of the tested pulse are launched into a standard grating lens spectrograph with a small angular shear. In conventional SPIRIT (in conventional SPIDER as well) a delay is required between the two twin pulses for subsequent Fourier transform (FT) processing. In 2D-SPIRIT the two replicas are synchronously sent to the spectrometer. There is no additional delay between the two interfering replicas. As a consequence there is no additional spectral modulation, contrary to conventional SPIDER and conventional SPIRIT. At the spectrograph output, two identical spectra are superimposed with a slight shift in space. At a given point where two sheared frequencies interfere, the temporal signal takes the form of periodical time beatings. The resulting 2D intensity function is given by I,t!E! 2 1 + cos t +, where E is the spectral amplitude of the unknown signal, and t and represent time and frequency, respectively. is the frequency shear while stands for the first derivative of the spectral phase under study. The key feature of the method is that the spectral phase distribution is encoded in the phases of the beat notes, =. The periodicity of the beats allows for subsequent Fourier analysis leading to the precise measurement of their phases. Moreover, the value of the actual frequency shear is encoded in the time period T of the beat notes, T=2 /. This is the main improvement over SEA-SPIDER and 2DSI in which interferograms do not contain any information for shear calibration. The next step consists of detecting this nonstationary spectral interference pattern with a temporal resolution better than T (which typically lies in the picosecond domain). For this purpose, a fraction of the initial femtosecond pulse is derived beforehand in order to play the role of a temporal gate. It is mixed with the beatings in a thin crystal that is located at the output of the spectrograph and is cut for sum-frequency generation. The gate pulse is spatially shaped to uniformly cover the whole spectrum pattern. A standard variable delay line permits one to vary the sampling time or, in the case of a single-shot operation, to use a space-time shaping setup. In the latter case, time is encoded along a second spatial dimension that is orthogonal to the spectral line. In these two configurations, which will be presented in more detail herein, a 2D time-frequency interferogram is recorded using a CCD linear array or a CCD matrix, respectively. In the last step, 2D-SPIRIT involves a direct phaseretrieval algorithm that is very similar to that of 2DSI [9]. First, starting from the 2D set of data recorded in the time-frequency domain, a 1D fast Fourier transform (FFT) along the time axis (i.e., for a given value of ) is computed. Then the phase of one of the two sideband peaks of the FFT is recorded as a function of giving the measurement of =. Then the unknown spectral phase is deduced from numerical integration and division by. The actual value of is directly encoded into the position of the selected sideband peak. For this reason the device is self-calibrating, which is the main advantage of 2D-SPIRIT over SEA-SPIDER and 2DSI. Note that the temporal beat period T=2 / does not depend on position (i.e., on ). It means that can be precisely deduced by averaging over the full spectral bandwidth, which reduces sensitivity to noise. The spectral amplitude is determined by the integration of the 2D set of data with respect to time. Then the time profile of the pulse is calculated after a last FT. This reconstruction algorithm is not the only method. It is also possible to computea2dft[8] and thus to eliminate more noise upon filtering (although, of course, a 1D FFT is still required to get the shear). In addition, the extracted phase can be concatenated rather than integrated. However, Dorrer and Walmsley [13,14] have shown that both approaches lead to equivalent performances (integration being easier to implement). 3. LOW-ENERGY, HIGH-REPETITION-RATE FEMTOSECOND PULSE CHARACTERIZATION A. Experimental Setup The setup that was used for the validation of 2D-SPIRIT in the case of high-repetition-rate femtosecond pulse train characterization is depicted in Fig. 1. CCD linear array SFG crystal =415 nm Filter L1 x Diffraction grating 1 Cylindrical lens S Time gate pulse Pulse 2 Variable delay line Step motor = 830 nm Tested pulse z y Angular shear Pulse 1 Ti:Sa oscillator Fig. 1. 2D-SPIRIT experimental setup in the case of a high-repetition-rate pulse train characterization. SFG, sum-frequency generation. L2

Lelek et al. Vol. 25, No. 6/June 2008/J. Opt. Soc. Am. B A19 We worked with a Ti:sapphire oscillator that delivered short pulses at a 75 MHz repetition rate with a duration and spectral width that were equal to 100 fs and 10 nm (full width at half-maximum in intensity), respectively. In this experiment the carrier wavelength was equal to 0 =830 nm. Only 15 mw of average power were required at the input of the 2D-SPIRIT device. The pulse under test was first split into two orthogonally polarized beams. One path was divided into two replicas (pulse 1 and pulse 2 in Fig. 1) using an arrangement that took the form of a balanced Mach Zehnder interferometer. A slight angular shear of a few milliradians was introduced between the two replicas by playing with the Mach Zehnder s recombination plate adjustment. Then the two synchronized but angularly separated pulses were dispersed by a diffraction grating (600 grooves/mm), and their spectra were displayed at the focal plane of lens L1 (see Fig. 1) with a slight shift in space. At one point of the spectral line two frequencies, and + ( being a fraction of the spectrum width [11]), were superimposed, resulting in a beat note. The key point is that the phases of the beat notes depend on the spectral phase being measured. The perfect cancellation of the delay between the two interfering beams was performed by adjusting two additional standard delay lines (not shown in Fig. 1) that were located in the two arms of the Mach Zehnder. Synchronization was checked, working with zero spectral shear by standard spectral interferometry (see Subsection 5.B). At the input, a fraction of the incident signal was extracted by a polarizing beam splitter to serve as the time gate. The gate pulse crossed a variable delay line that was driven by a step motor at constant speed 266.6 m/s. Then it was mixed with the space time beats inside a sum-frequency generation -barium borate (BBO) type II crystal that was located in the focal plane of L1. Before mixing, the gate beam was spatially enlarged in order to uniformly overlap the sheared spectra, thanks to cylindrical lens L2. The nonlinear crystal was used in a noncollinear configuration that allowed an improved filtering of the second harmonic radiation. For a given position of the slowly scanning delay line (i.e., at t=t i ), a single blue spectrum [i.e., a linear pattern proportional to I t=t i, ] was recorded by a standard CCD linear array that was running at video rate. The whole data acquisition lasted 10 s, leading to the recording of 250 spectra corresponding to 250 different values for the time gate delay (t i+1 =t i + t with t=71 fs). Two examples of a 2D-SPIRIT interferogram that were obtained after numerical integration of the 250 1D spectra are shown in Fig. 2(a). B. Measurement of the Dispersion Added by a Piece of Glass In this subsection, we present the quantitative validation of 2D-SPIRIT during the experimental determination of the spectral phase added by an F4 glass parallel plate. Two measurements were successively done with and without the dispersive plate that was introduced before the 2D-SPIRIT apparatus. The dispersion introduced by the glass plate induced a fringe linear tilt that is clearly seen in Fig. 2(a). As can be seen in Fig. 2(b), the measured Fig. 2. Measurement of the spectral phase added by 12 cm of an F4 piece of glass. (a) 2D-SPIRIT interferograms, left, without glass; right, with glass. The time beat period that has been deduced from these recordings was equal to T=1.25 ps. The corresponding infrared spectral shear was equal to = 2 0 / c T =1.84 nm (i.e., =5.03 rad/ps). 0 =830 nm. c denotes the light velocity in vaccum. (b) Gray solid curve, phase deduced from the Sellmeier relation; dotted curve, measured spectral phase; dashed dotted curve, spectral amplitude. data perfectly match the theoretical curve that was deduced from the Sellmeier law. The same measurement has been made with a onedimensional spectral shearing interferometry resolved in time (1D-SPIRIT) [11]. If we compare the results obtained with 1D-SPIRIT and 2D-SPIRIT, we can see that the measurement is more precise with 2D-SPIRIT because of a better signal-to-noise ratio. C. High-Order Spectral Phase Measurements In this subsection, we show that 2D-SPIRIT is able to reconstruct more complex pulses. For this purpose we added a pulse-shaping device to the experimental setup [15]. Various passive phase masks were introduced in the spectral plane of a zero dispersion line that was located before the 2D-SPIRIT device. Figure 3 shows experimental results in the cases of cubic spectral phase and a higher-order phase structure. A 2D-SPIRIT pattern directly displays an intuitive representation of the actual spectral phase distribution that might be very useful dur-

A20 J. Opt. Soc. Am. B/ Vol. 25, No. 6/ June 2008 Lelek et al. Fig. 3. (a) (c) Pulse with a cubic spectral phase. (d) (f) Pulse with a higher-order spectral phase. (a), (d) 2D-SPIRIT interferogram. (b), (e) Phases of the time beatings (solid black curve), reconstructed spectral phase (solid gray curve), and pulse spectral amplitude (dashed dotted curve). (c), (f) Second-order autocorrelations deduced from 2D-SPIRIT (dashed curve) and a conventional second-order autocorrelator (MINI from APE) (solid curve), respectively. ing real-time optimization of a laser system, for example. Second-order autocorrelation of the reconstructed pulse was calculated and then compared to the one directly measured with a standard autocorrelator. Figures 3(c) and 3(f) also show good agreement between these two measurements. 4. SINGLE-SHOT TWO-DIMENSIONAL SPIRIT As previously seen, the key feature of 2D-SPIRIT relies on encoding the phase to be retrieved along a time coordinate. In the case of a high-repetition-rate train of identical pulses, this time coordinate is related to the slow variation of a mechanically conventional (motor) driven delay line. In the case of a single-shot operation, the availability of a time gate with a variable delay is more complex. For this purpose we added a space time shaping setup in the gate path (see Fig. 4). It was made of an additional diffraction grating (diffraction grating 2 in Fig. 5) whose grooves were parallel to the setup plane (xz horizontal plane in Fig. 5). Close to grating 2, which was in a Littrow configuration, the energy front of the pulse was tilted with respect to the vertical y axis with an angle approximately equal to twice the grating tilt angle: =arctan 2 tan. To avoid spatial dispersion of the gate beam, grating 2 was imaged by cylindrical lens L3 without magnification onto the plane of the BBO crystal (plane P). In that plane the gate beam was large (L1 and L2 formed a confocal system). The gate s instantaneous intensity was constant along the x axis while the gate delay varied linearly along the y axis. This configuration is very similar to the one that can be found in a single-shot autocorrelator [16]. The two sheared spectra were displayed in the image focal plane of lens L1 that coincided with plane P. In that plane the frequency of the sheared beams varied along the x axis (spectral axis). L1 was of a cylindrical type that performed imaging only in the xz plane. In the yz plane the size of the sheared beams remained unchanged (i.e., large). In this situation the beat note that took place in plane P did not vary along the y axis. In so doing, the three-dimensional (3D) frequency space time x-y-z interference pattern that encoded the phase information was sampled by the gate at time intervals that depended upon the position along the y axis. The

Lelek et al. Vol. 25, No. 6/June 2008/J. Opt. Soc. Am. B A21 Fig. 4. Basic principle of the single-shot 2D-SPIRIT. is the angular tilt that separates the two replicas of the pulse being measured. z is the propagation axis. x is the spectral axis. stands for the frequency shear. T=2 / is the time period of the time-frequency beatings that take place at the spectrometer output. The time-frequency beatings are uniform along the vertical axis y. calibration of the time axis was deduced from the optogeometrical properties of grating 2 that fixed the space time gate slope t/ y (see Subsection 5.A). The second harmonic 2D pattern that resulted from the sum-frequency generation between the signal and the gate was filtered and then recorded by a conventional integrating CCD camera (768 576 pixels) located in the xy plane. Examples of single-shot 2D-SPIRIT interferograms are shown in Fig. 5(b). During this experiment we worked with a chirped pulse amplified (CPA) system operating at a 1 khz repetition rate with a central wavelength of 795 nm. At the in- Fig. 5. (a) Single-shot 2D-SPIRIT experimental setup. Diffraction grating 2 (1440 grooves/mm) was in a Littrow configuration with its grooves parallel to the setup plane. It was tilted by 35 with respect to the vertical axis y. L2 and L1 were cylindrical lenses working in the setup plane. L3 was a cylindrical lens working in the plane that was orthogonal to the setup plane. (b) Examples of 2D-SPIRIT interferograms. (1) Case of a FT limited pulse and (2) case of a chirped pulse that was produced after variation of the compressor of the CPA system.

A22 J. Opt. Soc. Am. B/ Vol. 25, No. 6/ June 2008 Lelek et al. put of the 2D-SPIRIT setup, the pulse energy was equal to 30 mj. First, we characterized the pulse that was directly exiting the laser system. A typical interferogram shown in Fig. 5(b)(1) was processed leading to a reconstructed pulse that is displayed in Fig. 6(c). The deduced pulse duration 72 fs was very close to the one 70 fs that was simultaneously measured using a conventional SPI- DER device. Figure 5(b)(2) shows the recorded data for a chirped pulse that was produced by a variation of the CPA compressor s settings. The resulting fringe tilt is clearly seen even before digital processing. These observations confirm that 2D-SPIRIT provides a direct representation of the spectral phase of the pulse that might be useful for real-time optimization of a laser chain. Furthermore, in the left part of Fig. 6(a), one can directly observe a large phase jump. This modulation was related to a coating defect that was located at the surface of one of the two gratings that composed the compressor of our CPA system. Again 2D-SPIRIT provides a direct and intuitive representation of the spectral phase of the pulse being measured. In a last step, we quantitatively studied the pulse modifications that occurred owing to changes in the compressor s adjustments. Figure 7 shows the second-order dispersion that was deduced from 2D-SPIRIT measurements for a different distance between the two gratings of the compressor. Comparison between experimental results and theoretical behavior of the compressor (solid line in Fig. 7) reveals a good quantitative agreement. There exists a strong analogy between 2D-SPIRIT and SEA-SPIDER/2DSI. In fact, the two implementations of 2D-SPIRIT are completely analogous to the two implementations of 2D-SPIDER. For SPIDER, 2DSI generates the carrier fringes by scanning the absolute phase between the two pulses. In SEA-SPIDER, this is done by mapping a delay to space between the two signals. In 2D- SPIRIT, these methods are done in an exact analogy. However, the key point is that in 2D-SPIRIT the shear and the carrier fringes are related, allowing a calibration of the spectral shear. 5. CALIBRATION AND SETTINGS A. Time Axis Calibration and Shear Measurement Accuracy The main advantage of 2D-SPIRIT is that the spectral shear is contained within the collected data. Indeed, the value of the spectral shear is directly linked to the beat period T=2 /. The measurement of T requires a preliminary calibration of the time axis of the 2D-SPIRIT interferogram. This calibration can be done once for all during a preliminary procedure. Afterward, it will not depend on the pulse being measured. Fig. 6. (a) Single-shot 2D-SPIRIT interferogram that was recorded at the output of the CPA system. (b) Measured time beat phases (gray curve) together with the spectral amplitude (black curve). A phase jump on the left part of the spectrum is clearly seen. This particularity coincides with a strong modulation of the spectral amplitude. (c) Deduced temporal intensity profile. The beat period T is close to 2 ps. It is much larger than the pulse duration 0.072 ps that serves as a time window. As a consequence, the contrast of the 2D interferogram is high.

Lelek et al. Vol. 25, No. 6/June 2008/ J. Opt. Soc. Am. B A23 Fig. 7. Second-order dispersion amount imposed on the pulse as a function of the relative distance between the two diffraction gratings that composed the compressor of the CPA system. These data were deduced from single-shot 2D-SPIRIT measurements. The solid diagonal line represents the theoretical data that were deduced from the optogeometrical properties of the compressor. In the case of a multishot operation, time-axis calibration is directly linked to the following parameters: (i) the translation speed of the step motor that is located on the gate path and (ii) the acquisition rate of the spectra. In our experiment, these parameters were equal to 133 m/s and 25 spectra/s, respectively. Because 133 m/s refers to the step motor and 25 spectra/s refers to the acquisition rate, this resulted in a time-axis sample equal to dt=35 fs. The measured beat period was close to T=1 ps, the number of recorded beat periods was at least equal to n=4, and the corresponding shear measurement accuracy was equal to d / =dt/n T 1%. In the case of a single-shot operation, the time-axis calibration is related to the slope of the energy front of the gate beam at the place where it is mixed with the sheared beams {i.e., in the focal plane of lens L1 [see Fig. 5(a)]}. At that place the situation is the same as the one at the direct exit of grating 2. Indeed the cylindrical lens L3 images the grating 2 onto the image focal plane of cylindrical lens L1 without magnification. In our experiment, diffraction grating 2 had 1440 grooves/mm. It was used under Littrow configuration at the first order 0 =795 nm. The energy front tilt angle with respect to the y axis that was calculated from the grating law was equal to =54.5. The corresponding time space slope of the gate was equal to t/ y=4.727 fs/ m. The image focal plane of lens L1 was imaged without magnification onto the CCD whose pixel pitch was equal to 11 m. It resulted in a time-axis sampling resolution equal to dt =52 fs. The measured beat periods were typically equal to T =2 ps with more than n =8 measurable beat periods [for an example, see Fig. 6(a)]. So the corresponding shear measurement accuracy was equal to d / =dt /n T 0.3%. B. Cancellation of the Delay between the Sheared Signals 2D-SPIRIT, SEA-SPIDER, and 2DSI operate with zero delay between the two sheared signals. In SEA-SPIDER and 2DSI, this condition is satisfied thanks to the geometry of the setup. In the configuration of 2D-SPIRIT, the situation is not so direct. The delay cancellation must be checked during a preliminary step that is carried out once and for all. First, the angular tilt at the output of the interferometer is set to zero so that there is no shear. Spectral interferometry is used to set zero delay with the required accuracy. Then, a change in the tilt between the two arms is introduced in order to impose the relevant spectral shear. This last operation might result in an undesirable additional delay that might cause an error in the reconstructed spectral phase. This additional delay has been estimated in our particular experiment, taking into account the following parameters: distance between the fulcrum of the tilt and lens L1 200 mm, L1 focal lens 100 mm, value of the tilt 6 mrad, and precision of the centering of lens L1 1mm ; then the maximum path difference between the two sheared beams was estimated at 2 m. It corresponded to a residual delay of 7 fs. So we concluded that this effect can be neglected in the case of 100 fs pulses. Concerning the measurement of broadband ultrashort pulses of smaller duration (i.e., t =10 fs, for example), a configuration that can ensure zero delay is essential. The goal is to perfectly cancel the delay between the fulcrum of the angular shear [point S in Figs. 1 and 5(a)] and the sum-frequency mixing crystal. This can be performed by introducing an additional relay optic between S and the diffraction grating 1. S must be imaged onto grating 1, which must be located in the rear focal plane of lens L1. In that way the two sheared pulses that are synchronized in S are still synchronized in the image focal plane of L1, where the interferometric mixing takes place. C. Spectrometer Resolution Let us remember that T denotes the time period of the beats being involved in 2D-SPIRIT. t denotes the duration of the pulse to be measured that also serves for sampling the beats. Proper time gating requires that t be significantly smaller than T. We already demonstrated in [11] that this condition is fulfilled for a sufficiently small shear, D /10 N, where N denotes the time bandwidth product of the pulse under test Dt D =N. For a correct phase retrieval, the number n of recorded fringes (i.e., the number of sampled beat periods) must be large, at least 2. It means that the duration of the impulse response of the spectrometer in use in the 2D-

A24 J. Opt. Soc. Am. B/ Vol. 25, No. 6/ June 2008 Lelek et al. SPIRIT setup is long enough to include a large number of time beats. In the spectral domain it corresponds to = /n with n 2, where denotes the resolution limit of the spectrometer. Therefore we can conclude that the resolution of the spectrometer must fulfill =D /10 N n. 6. CONCLUSION In conclusion 2D-SPIRIT is a novel self-referenced spectral shearing interferometry scheme for the complete characterization of ultrashort pulses. The tested amplitude and phase are recorded in a 2D interferogram that makes use of a time coordinate. The method is fully selfreferenced and self-calibrating, which results in true single-shot capabilities. We have demonstrated that the method is applicable to a low-energy, unamplified, highrepetition-rate pulse train. 2D-SPIRIT is also extremely well-suited for the measurement of low-repetition-rate, high-energy, amplified ultrashort pulses. In spite of some complexity from the point of view of its basic principle, the single-shot 2D-SPIRIT configuration has proved to be very simple to adjust in practice. Further work is under way to show that the method permits a large variety of implementations such as the use of the walk-off of a birefringent plate for spectral shearing [12], the characterization of an extremely wide spectral bandwidth signal with a high signal-to-noise ratio, together with the determination of some kind of space time couplings [17]. ACKNOWLEDGMENT This work was supported by the North Atlantic Treaty Organization (NATO) within the framework of the Science for Peace (SfP) program (project 978027). REFERENCES 1. J. Faure, Y. Glinec, J. Santos, V. Malka, S. Kiselev, A. Pukhov, and T. Hosokai, Observation of laser pulse selfcompression in nonlinear plasma waves, Phys. Plasmas 13, 013103 (1998). 2. J. Faure, C. Rechatin, A. Norlin, A. Lifschitz, Y. Glinec, and V. Malka, Controlled injection and acceleration of electrons in plasma wakefields by colliding laser pulses, Nature 444, 737 739 (2006). 3. E. Lefebvre, E. d Humières, S. Fritzler, and V. Malka, Numerical simulation of PET isotope production with laser-accelerated ions, J. Appl. Phys. 100, 113308 (2006). 4. A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses, Science 282, 919 922 (1998). 5. L. Banares, T. Baumert, M. Bergt, B. Kiefer, and G. Gerber, The ultrafast photodissociation of Fe CO 5 in the gas phase, J. Chem. Phys. 108, 5799 5811 (1998). 6. C. Iaconis and I. A. Walmsley, Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses, Opt. Lett. 23, 792 794 (1998). 7. L. Lepetit, G. Cheriaux, and M. Joffre, Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy, J. Opt. Soc. Am. B 12, 2467 2474 (1995). 8. E. M. Kosik, A. S. Radunsky, I. A. Walmsley, and C. Dorrer, Interferometric technique for measuring broadband ultrashort pulses at the sampling limit, Opt. Lett. 30, 326 328 (2005). 9. J. R. Birge, R. Ell, and F. X. Kärtner, Two-dimensional spectral shearing interferometry for few-cycle pulse characterization, Opt. Lett. 31, 2063 2065 (2006). 10. V. Messager, F. Louradour, C. Froehly, and A. Barthelemy, Coherent measurement of short laser pulses based on spectral interferometry resolved in time, Opt. Lett. 28, 743 745 (2003). 11. M. Lelek, F. Louradour, A. Barthelemy, and C. Froehly, Time resolved spectral interferometry for single shot femtosecond characterization, Opt. Commun. 261, 124 129 (2006). 12. P. Kockaert, M. Haelterman, P. Emplit, and C. Froehly, Complete characterization of (ultra)short optical pulses using fast linear detectors, IEEE J. Quantum Electron. 10, 206 212 (2004). 13. C. Dorrer and I. A. Walmsley, Accuracy criterion for ultrashort pulse characterization techniques: application to spectral phase interferometry for direct electric field reconstruction, J. Opt. Soc. Am. B 19, 1019 1029 (2002). 14. C. Dorrer and I. A. Walmsley, Precision and consistency criteria in spectral phase interferometry for direct electricfield reconstruction, J. Opt. Soc. Am. B 19, 1030 1038 (2002). 15. C. Froehly, B. Colombeau, and M. Vampouille, Shaping and analysis of picosecond light pulses, in Progress in Optics, E. Wolf, ed. (North-Holland, 1983), Vol. 20, pp. 65 153. 16. K. Oba, P.-C. Sun, Y. T. Mazurenko, and Y. Fainman, Femtosecond single-shot correlation system: a timedomain approach, Appl. Opt. 38, 3810 3817 (1999). 17. C. Dorrer, E. M. Kosik, and I. A. Walmsley, Spatiotemporal characterization of the electric field of ultrashort optical pulses using two-dimensional shearing interferometry, Appl. Phys. B 74, S209 S217 (2002).