Temporal characterization of ultrashort laser pulses is performed using a number of methods, such as frequency-resolved optical gating (FROG) [1], spectral-phase interferometry for direct electric-field reconstruction (SPIDER) [2], multiphoton intrapulse interference phase scan (MIIPS) [3], and DazScope/chirp scan [4], dispersion scan [5], and modifications of these. These methods are generally not spatially resolved, and it usually must be assumed that the pulse is transversely homogeneous. This is often not the case for few-cycle laser pulses. Even simple optical elements like lenses can introduce pulse front distortions [6]. More complicated spatiotemporal couplings may arise when using elements that induce a strong spatial dispersion (i.e., prisms and gratings) [7].

A straightforward approach to adding spatial resolution to a pulse-measurement technique is to spatially multiplex the technique across the laser beam [8]. The FROG and SPIDER techniques can be extended to include one spatial dimension, yielding information either on spatiotemporal couplings [7,9] or allowing the temporal characterization of a spatial slice of the pulse [10,11]. Other approaches rely on spatially resolved nonlinear cross-correlation with a reference pulse [12–14]. Alternatively, pulses can be spatially sampled and compared to a well-known reference pulse, either using spectral interferometry [15,16] or holographic techniques [17]. The reference pulse is often a small, homogeneous portion of the pulse itself, characterized using one of the techniques mentioned above. A convenient feature of spectral interferometric methods is the ease of alignment: an optical fiber is used for sampling the beam transversely, and the spectral phase is measured with respect to the reference pulse. Alternatively, in holographic methods, the reference beam is spatially and spectrally filtered, and a complete reconstruction can be obtained by scanning the reference wavelength with a high spatial resolution.

The method presented in this Letter is based on spatially resolved Fourier transform spectrometry, and it is related to both spectral and holographic approaches. The principle is illustrated in Fig. 1. A well-known, homogeneous reference pulse with a variable delay is spatially interfered with the pulse to be measured on the chip of a CCD camera. The delay between the two pulses is scanned using a Mach–Zehnder interferometer, essentially corresponding to a spatially resolved linear cross-correlation. This is well known to provide the same information as spectral interferometry (a property extensively used in time-domain Fourier spectroscopy [18,19]). Each pixel of the CCD chip thus acts as a spectrometer, and the local spectral phase difference between the pulse to be measured and the reference pulse can be retrieved for each pixel. Similar techniques have been used extensively to characterize surfaces with white-light interferometers [20] and to measure distortions produced by optical elements [21].

 

Fig. 1. Principle of the method. The pulse is split into two by a beamsplitter (BS1). The most intense part is focused with an off-axis parabola, and a pinhole is used to filter the beam and create a homogeneous spherical wave. Another beam-splitter (BS2) recombines the beams, and they spatially interfere on a CCD camera chip.

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Consider an ultrashort pulse in the spectral domain $\tilde{U}(\omega )=|\tilde{U}(\omega )|\exp i\varphi (\omega )$ and the corresponding time domain complex field $U(t)=|U(t)|\exp i\psi (t)$. The linear cross-correlation between two pulses is given by

By applying the Fourier transform, Eq. (2) can be separated in 3 terms: a DC component and two terms around ${\omega }_0$ and $-{\omega }_0$, where ${\omega }_0$ is the carrier frequency:

In general, the three terms are easily separable in the frequency domain. The second term of Eq. (3) can be rewritten as

If the reference’s spectral amplitude and phase are known, then the unknown pulse can be characterized, provided the reference contains enough spectral content to cover the unknown pulse’s spectrum.

For a full spatial characterization, a reference pulse that is homogeneous across the whole interaction region (in this case, a CCD camera) is needed. Then the spectral amplitude and phase of the unknown pulse can be obtained at any point in space, characterizing it completely. Even if the reference is not characterized, inhomogeneities within the unknown pulse profile can still be measured.

The most important part of the process is to create a reference beam that is homogeneous across the whole detector. This can be achieved by selecting a small portion of the original pulse by simply expanding a replica of the unknown pulse. The level of homogeneity can be arbitrarily high, at the expense of energy available in the reference beam to interfere with the original beam. Spatially filtering the beam further increases its homogeneity.

The source is a titanium-sapphire ultrafast oscillator (Venteon GmBH, pulse:one OPCPA seed laser) with a large spectral bandwidth (around 620–1020 nm) supporting a pulse duration of 6.2 fs FWHM.

To characterize the spectral phase of the reference pulse, the d-scan [5] technique was used (Fig. 2). A pair of BK7 wedges was used both for dispersion control and for the d-scan. The d-scan relies on recording SHG spectra as a function of glass insertion. The spectral phase is then retrieved iteratively from the measured fundamental spectrum and the SHG spectra.

 

Fig. 2. Temporal characterization of the reference pulse. (a) Measured (left) and retrieved (right) d-scan traces. (b) Measured spectral intensity and retrieved phase. The inset shows the intensity time profile for the reference glass insertion, yielding a pulse duration of 6.6 fs FWHM.

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A small central portion of the beam of around 200 μm diameter was temporally characterized. This was large enough to provide good SHG signal, and assumed to be small enough as to be considered homogeneous and used as a reference. Both the fundamental spectrum and the SHG spectra were measured using a broadband grating-based CCD-line spectrometer (Avantes AvaSpec). A pulse duration of 6.6 fs FWHM was obtained for the reference glass insertion (0 mm on the d-scan plots).

The main setup for complete spatiotemporal pulse characterization is based on a Mach–Zehnder interferometer (Fig. 1). The pulse is split in two by a $90/10$ cube beamsplitter, and the most intense part is used to create the reference. For this, the beam is spatially filtered by focusing it with an off-axis parabola with 50 mm focal length through a 20 μm pinhole, creating a very uniform spherical wave. The beams are then collinearly combined using a 2% reflection beamsplitter and sent to the CCD camera. At the CCD camera, the reference beam is much larger than the CCD chip, so only a small portion of the reference beam is used. Even though the reference beam is made using most of the available energy, at the CCD camera its intensity is only around 3% of the beam to be characterized. This is still enough to obtain a good contrast.

A piezo stage with closed-loop feedback (piezosystem jena) is used to scan the delay between the arms, and the acquisition was done with a CCD camera (IDS uEye). The scanning range for this particular case was 500 fs, with 2048 steps. To keep the memory usage low and increase the signal-to-noise ratio, the resolution was decreased by a factor of 10 in each direction, by taking every 10th pixel in each direction and averaging it with its 8 nearest neighbors. The end array size was 128 by 102 pixels. The scans presented here took around 30 min to acquire.

Since the interferogram depends only on the phase difference between the pulses, the beamsplitters can be thick, but it is convenient that the pulses’ paths in glass are as similar as possible. If the interferometer is unbalanced, the difference in optical paths introduces a phase difference between the two arms, which would either have to be compensated by a glass plate, or numerically subtracted. Since the reference wave is spherical, its curvature is later removed numerically.

The $A_1(\omega )$ term is obtained from each pixel’s interferogram. Assuming the reference is homogeneous enough to allow us to neglect spatial variations, the spectral amplitude and phase of the pulse can be spatially resolved:

We start with a pulse with as little distortion as possible. Figure 3 shows the retrieved integrated spectral power obtained by Fourier transforming all the interferograms (an example of a single pixel interferogram is shown in the inset) and adding them all together and then comparing it to the spectrum measured directly with the spectrometer. The actual scanning delay range is 500 fs. The offset between the sharp spectral features around 620 nm measured in the two different ways is probably due to a slight inaccuracy in the spectrometer wavelength calibration.

 

Fig. 3. Comparison between the spectrum directly measured using a linear CCD array spectrometer (black line) and the spectrum of the full beam obtained from Fourier transforming each pixel’s interferogram (interferogram example shown in inset) and adding them all together (gray line).

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In our case the combined spectral response of the CCD camera and the beam splitters resulted in a rather flat spectral response of the whole system. If this was not the case, the spectral response of the system could have easily been corrected using the independent spectral measurement.

Figure 4 shows the three-dimensional reconstruction of the intensity profile of the pulse. No spatiotemporal distortions were detected in this case, and therefore the pulse duration and shape are approximately constant across the whole spatial profile.

 

Fig. 4. Reconstruction in the space–time domain of the laser beam as it hits the CCD camera. Isosurfaces shown are set at 0.8, 0.5, and 0.2 of the maximum intensity.

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To test the setup in a more challenging case, we used it to characterize a pulse with pulse front tilt. To introduce pulse-front tilt, we used a single-pass prism compressor, as in [17]. The three-dimensional (two spatial dimensions and time) intensity reconstruction is shown in Fig. 5. In this case, the spectral reference phase was not added, so the reconstruction corresponds to the case where the reference beam would be Fourier-limited. This situation mimics the case where a pulse is compressed in time as best as possible, but spatiotemporal distortions are present.

 

Fig. 5. Reconstruction in the space-time domain of the laser beam as it hits the CCD camera. The isosurface shown is set at 0.5 of the maximum intensity.

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It is not clear what kinds of distortions are present from the intensity reconstruction alone. The pulse-front tilt is revealed by comparing the intensity profile with the propagation direction of the pulse, which is determined by its wavefront. This can be evidenced by plotting the real part of the retrieved complex field. Figure 6 shows vertical (top) and horizontal (bottom) cuts of the pulse at its center. The intensity profile is plotted in the left column, while the real part of the reconstructed complex field, showing the wavefront tilt along one of the dimensions, is shown in the right column. Different spectral contents are also observed across the beam (not shown), as expected.

 

Fig. 6. (a), (b) Intensity and (c), (d) real part of the complex field plotted for vertical (a), (c) and horizontal (b), (d) cuts across the center of the beam.

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The pulse temporal width at a central pixel is of about 7 fs, while the duration of the pulse as a whole is of about 35 fs.

In conclusion, we have presented a technique that allows for the complete spatiotemporal characterization of ultrashort laser pulses. Since it works by scanning in the time domain, it is especially well suited for high-repetition rate sources and few-cycle pulses, as the scanning range depends on the duration of the Fourier-transform limit of the pulse. The technique provides an intuitive idea of spatiotemporal distortions, even when the reference is not characterized in time.