A novel apparatus for the single-shot measurement of the temporal pulse contrast of modern ultra-short pulse lasers is presented, based on a simple yet conceptual refinement of the self-referenced spectral interferometry (SRSI) approach. The introduction of the spatial equivalent of a temporal delay by tilted beams analyzed with a high quality imaging spectrometer, enables unprecedented performance in dynamic, temporal range and resolution simultaneously. Demonstrated consistently in simulation and experiment at the front-end of the PW laser Draco, the full range of the ps temporal contrast defining the quality of relativistic laser-solid interaction could be measured with almost 80 dB dynamic range, 18ps temporal window, and 18fs temporal resolution. Additionally, spatio-temporal coupling as in the case of a pulse front tilt can be quantitatively explored.
© 2017 Optical Society of America
In relativistic laser-matter interaction at peak laser intensities well beyond 1018 W/cm2 full knowledge of spatial and temporal focal spot characteristics is crucial. Prominent applications as the generation of intense high harmonic radiation and, in particular, advanced laser plasma ion acceleration  require the temporal pulse-contrast, i.e. the temporal evolution of the laser intensity relative to the peak intensity, of 100 TW to PW class lasers to be carefully controlled. With the processes relying on the clean interaction of ultra-short pulses of typically 30 fs duration with solid target surfaces, the temporal pulse profile has to be described with a dynamic range of at least 108 and few 10 fs resolution in order to assess target ionization, heating, and subsequent expansion during the rise of the laser pulse intensity in the few 10 ps range . Subtle differences have been observed to strongly influence, e.g. proton acceleration performance  and, as a last resort, single-shot plasma mirrors are employed to boost contrast for the exploration of the performance limits [4,5].
Highest dynamic (~1011) and wide temporal range (~1 ns) combined with a temporal resolution on the scale of the pulse duration are routinely provided with delay-scanning third order auto-correlation techniques (for reference, cf. Sequoia, Table 1). Time-consuming measurements (requiring up to 105 pulses) validate ASE (amplified spontaneous emission) contrast and pre-pulses on the few 10 ps to ns-scale to be on a negligible level below 10−10 for state-of-the-art chirped pulse amplification (CPA) 100 TW class laser systems [e.g 3.]. Yet, even at a pulse repetition rate of 10 Hz the method proves inappropriate for the investigation of contrast sensitive problems in real time. Self-referenced spectral interferometry (SRSI) techniques [9–11] on the other hand (for reference, cf. Wizzler, Table 1) robustly provide highest resolution single-pulse information on the intensity contrast as well as on the spectral phase of the laser pulse. Though insufficient in temporal (1 ps) and dynamic (105) range for the complete analysis of the rising pulse, the method allows for feedback based improvement of the sub ps-contrast with already significant impact on proton acceleration .
Closing this gap in temporal and dynamic range represents one of the most challenging single shot metrology tasks in the field of high power lasers and related secondary radiation sources. Current approaches rely on single-shot cross-correlation (SSCC) between the pulse and a cleaned reference [7,8]. Although single-shot dynamics of 1010 have recently been demonstrated , the temporal encoding concepts significantly limit the number of sampling points as summarized in the Table 1.
Furthermore, none of these techniques provides information on spatio-temporal coupling, i.e. the spatial variation of temporal properties of the light and vice-versa [12,13]. This coupling requires attention in large aperture CPA laser systems as it significantly influences the final focus quality  and interaction dynamic . To our knowledge, only one single shot compatible and completely self-referenced measurement has been performed in a new implementation of the SPIDER (spectral phase interferometry for direct electric field reconstruction) technique .
In the present work we demonstrate that a conceptually refined approach based on SRSI and implemented with cross-polarized wave (XPW) [16,17] reference beam preparation can be applied to characterize the laser pulse in single shot mode with an unprecedented combination of an extended time excursion (ETE) or wide range of up to 18ps and an ultra-fast resolution of 20fs. Together with the achieved increase in dynamic range to 108 this novel SRSI-ETE instrument allows for the full and high resolution characterization of the ps-contrast of typical 100 TW to PW class lasers. The paper details the concept of the apparatus illustrating high dynamic range and high resolution diagnostic capabilities both theoretically and experimentally. Measurements of the ps pulse contrast of the first CPA stage of the dual CPA Draco PW laser at HZDR as well as of a contrast improved XPW test beam confirm the performance of the apparatus and are quantitatively cross-checked against scanning third order CC devices. Finally, a similar set of simulations and experimental results demonstrates the additional single shot spatio-temporal pulse characterization capacity of the method.
2. Extended Self-Referenced Spectral Interferometry concept
SRSI [9–11] is an interferometric technique where, as sketched in Fig. 1(a), an input pulse replica experiences a variable delay τ and is recombined with a self-generated reference pulse. For ultrafast pulses reference pulse generation relies on non-linear temporal filtering by cross-polarized wave generation (XPW) [16,17] providing a broadened spectrum and flattened spectral phase. This is in analogy to well-known pulse cleaning in the spatial domain by a Fourier-plane filter like a pin-hole in the focal plane of a lens. Fourier Transform Spectral Interferometry (FTSI) processing  then enables the retrieval of the spectral amplitude and phase of both input and reference pulses from the spectral interferogram illustrated in Fig. 1(b).
In the following, we introduce two conceptual modifications of the original SRSI idea: first, taking advantage of the additional information provided by an imaging spectrometer in the spatial dimension, and second, introducing a well-controlled spatio-temporal coupling by adding an angular offset between the two beams entering the imaging spectrometer. These refinements of the concept simultaneously result in unprecedented contrast dynamic, temporal range and spatio-temporal capabilities, and are referred to as Self-Referenced Spectral Interferometry with Extended Time Excursion (SRSI-ETE).
Employing an imaging spectrometer increases the dynamic range of the pulse contrast measurement. We perform simulations assuming a transform limited pulse (50nm FWHM width, centered at a wavelength of 800 nm) with a super Gaussian spatial beam profile. This sample pulse exhibits a pre-pulse at an intensity ratio of 10−3 at a delay of τpp = −4 ps. The SRSI delay in the simulation is set to τ = 6ps. In the standard collinear SRSI configuration  the imaging spectrometer records identical spectral interferograms for all transverse coordinates of the pulse [Fig. 2(a)] representing the beam profile. Following inverse FT analysis in the spectral domain only, the non-interference or DC term centered around 0 in time domain and the two interference or AC terms, symmetrically shifted by + -τ in time domain, can be identified and filtered in the temporal domain. So the DC term is the one filtered by the red box, and the AC term the one filtered by the black box [Fig. 2(b)]. The green curve in Fig. 2(d) depicts the square of the AC term which under the assumption of an ideal reference pulse represents a good approximation of the temporal intensity contrast of interest of the pulse replica. Averaged over 100 spatial spectrometer lines the green curve shows a contrast dynamic limited to about 106 mainly by detector shot noise (Signal-to-Noise Ratio SNRω considered in the simulation amounts to 1500:1, corresponding to spectrometer specifications, see below). Applying FT analysis in both spectral and spatial dimensions [Fig. 2(c)] further enhances the dynamic range of the measurement by roughly one order of magnitude (factor of 100 compared to √100 for the averaging of the 100 lines) . The black curve in Fig. 2(d), representing the square of only the central line in Fig. 2(c) evidences this substantial enhancement of the dynamic range.
Figure 2(d) also directly reveals ambiguities in the signal reconstruction, and in particular in the straightforward interpretation of the square of the AC term. Though well reflecting the input pulse intensity including the pre-pulse at τpp = −4 ps (dark grey shaded areas), the particular choice of the τ = 6ps SRSI delay results in an artifact at τppa = −2 ps, where AC and DC origins cannot be distinguished by the applied filtering method. Such temporal aliasing issues limit the temporal range of the device to only one third of the 18ps complete range.
A simple change in the beam geometry, however, can be applied to completely resolve this fundamental aliasing issue. As spectral and spatial dimensions play a symmetric role in the Fourier domain, the filtering can either be applied in the temporal or the spatial frequency domain. We therefore extend the simulation by introducing an additional small angle between the pulse replica and the reference pulse in the axis of the spectrometer entrance slit. This acts as the spatial equivalent of the temporal delay. Together with the standard SRSI delay, the spectral interferogram now appears tilted on the detector [Fig. 3(a)]. FT in spectral and spatial domains [Fig. 3(b)] results in separated DC and AC terms not only in time but also in spatial frequency. Efficient filtering can now be performed in the spatial frequency domain, completely eliminating the previous aliasing issues. As a consequence the viable temporal range is extended by a factor of three up to the full 18ps range as illustrated in Figs. 3(c) and 3(d) and to be compared to Fig. 2(d). As evidenced by Fig. 3(b) the temporal window is asymmetrical relative to the AC term. Tuning the optical delay allows to tailor the contrast observation region either before or after the pulse.
The full SRSI iterative algorithm [9,11] is also used to reconstruct the temporal intensity of the replica (red curve on Fig. 3(d)). Yet, direct comparison with the square of the AC term (black curve) shows that this process leads to a slightly higher noise level, possibly due to noise amplification in the data processing. As further illustrated by the inset of Fig. 3(d) the temporal intensity of the original pulse (grey filled curve) is nearly perfectly well recovered through the AC term squared for super Gaussian spectral amplitude shape. Furthermore, as for any cross-correlation device, all the different pulses are correlated with the same reference pulse so that their ratios compared to the main pulse are conserved and the square of the AC term represents a valid approximation for the contrast analysis of the pulse. . This property remains valid as long as the XPW filtered pulse has a clean contrast which extends the temporal contrast measurement capability beyond the usual SRSI limit. Also to optimize the contrast dynamic, the AC term should be maximized meaning that the modulation should be as high as possible.
3. Experimental setup
The SRSI-ETE setup relies on a conventional dispersion balanced Mach-Zehnder interferometer as sketched in Fig. 4. While the first arm generates the optical SRSI delay, the second is used for reference generation. This arm includes a telescope built from parabolic mirrors with a 1mm thick BaF2 crystal in its center for efficient XPW generation between crossed polarizers. Optimal signal-to-noise ratio in single-shot operation requires pulse energies of about 100 nJ in the reference beam obtainable with about 100 µJ at the interferometer input. The two beams are directly recombined onto the spectrometer slit with a small relative angle along the slit axis. This set-up is versatile, and depending on the choice of the final focusing mirror, the complete beam, or only parts, can be analyzed. Care has been taken for the selection of optical components in order to avoid parasitic light or pulse distortions and spatial filtering is applied at the entrance of the spectrometer.
The spectrum is recorded by an imaging spectrometer (Princeton Iso-Plane 320) read-out by a cooled PIXIS 16 bits CCD camera with 256x1024 pixels. The horizontal dimension of the output image represents the spectral domain (from 350THz≈856nm to 400THz≈750nm) while the vertical represents the selected spatial dimension (6.6mm over 256 pixels).
To experimentally investigate the dynamic range of the SRSI-ETE and to demonstrate its qualification for single shot wide range high resolution contrast measurement, the instrument was tested on the first CPA stage of the double CPA Petawatt laser system DRACO at Helmholtz-Zentrum Dresden-Rossendorf as sketched in Fig. 5. For this test, stretched pulses with 10 mJ energy are picked off from the amplification chain and compressed with a Treacy compressor in air to about 25 fs pulse duration (FWHM). These pulses are either used directly, or contrast-improved with an additional XPW filter. Reference measurements are performed with a scanning third order cross-correlator (Sequoia, cf. Tab. 1).
4. Temporal characterization properties
As already introduced with the simulation results in section 2, the SRSI concept intrinsically provides a higher dynamic range on the temporal signal than expected from the dynamic range of the spectrometer [10,18]. Assuming uniform spreading of white noise over the recorded image of the interferogram the same holds true for its Fourier equivalent in temporal and spatial frequency domains, while the signal is concentrated on few pixels. Following , the dynamic range of the contrast measurement can be estimated by the product of the filling factor of the detector array F, the number of pixels Npixels, and the signal-to-noise ratio SNRωtoFigs. 2 and 3, the filling factor can be maximized up to the 256 lines of the spatial dimension, leading to a temporal contrast ofFig. 6(a). Experimentally, the full beam profile was sampled and thus less than a third of the image could be used for the analysis (cf. insets of Figs. 6(b) and 6(c)), limiting the dynamic range to few times 108. In Fig. 6 the measurement of the temporal intensity profile is represented by the AC term squared (black curves) and compared with third-order cross-correlation diagnostics (orange curves). The overall agreement between the two measurement techniques is excellent. Few differences on pre- or post-pulses result from different non-optimal beam guiding optics. As an example, the pre-pulse observed at 8.6 ps on the SRSI-ETE signal is due to a front side reflection of the first beam splitter of the setup (BS1 in Fig. 4). The delay matches exactly the optical path difference of front and back reflections for 1.1mm UV-fused silica beamsplitter at 45°. In Fig. 6(b), the beam is analyzed directly at the output of the compressor. Around the main pulse a picosecond pedestal at a contrast level of 10−4 lasting for about 2ps is preceded and followed by few smaller pulses. The noise level reached with the SRSI-ETE lies between −70 and −80dB, while the third-order CC lowest level on the same temporal window is −90dB. To further check that only the pre-pulse at −8.6 ps is due to the instrument, the pedestal and the pre- or post-pulses are removed by an additional XPW cleaning stage. The reduced energy level of the XPW filtered pulse results in a smaller dynamic range of the third-order CC measurement (80dB despite longer accumulation for each point) while the SRSI-ETE dynamic range remains unchanged.
The temporal resolution of the device is defined by the inverse of the bandwidth in the frequency domain to yielding 18fs. Correspondingly, the temporal range of the instrument is defined by the inverse of the spectrometer resolution to as confirmed by the measurements presented in Figs. 6(b) and 6(c). The SRSI delay used was about 1 ps resulting in a 10ps time window ahead of the pulse. The inset on the right of Figs. 6(b) and 6(c) highlights the achieved temporal resolution, 18fs for SRSI-ETE compared to more than 100fs for the scanning third-order CC .
Some post- and pre-pulses on Fig. 6(b) are symmetric with respect to the main pulse. This symmetry can hint on their origin. If it is before amplification we expect non-linear temporal diffraction as demonstrated by Liu et al.  and illustrated in . Post- or pre-pulses before amplification give rise to symmetric pre- or post-pulses even at low B integral values (non linear diffraction efficiency is proportional to B2 ). To ensure that this observation is not an artifact, the measurementwas repeated with an additional marker post-pulse generated by a thin glass plate after the compressor and in Fig. 7(a) (and b zoomed) the grey dotted curve shows the result mirrored in time with respect to the main peak. Peaks marked A, B and C correspond to post-pulses that have symmetrical pre-pulses. The intentional post-pulse marked D shows no significant corresponding pre-pulse. Non-linear diffraction efficiency for the cases A, B and C can be estimated to be about 10% indicating an origin before the main B integral contributor, the amplifier.
As the measurement gives access to amplitude and phase of the AC term, spectrogram information can be processed. The resulting spectrogram shown in Fig. 7(c) distinguishes the spectral amplitude of pre- or post-pulses and pedestals. As an illustration of these additional capabilities, an analysis for the areas 1 (main pulse), 2, and 3, averaging over ten data columns in time on the spectrogram, is shown in Fig. 7(d). The blue shift observed for the pedestal part before the pulse could be due to non-linear origin , but no significant red shift is observed on the pedestal part after the pulse.
5. Spatio-temporal characterization properties
The measurement uses temporal and spatial shifts simultaneously. The symmetric roles between spectral and spatial dimensions imply that “spatiogram” like spectrogram information can easily be processed from the data. Indeed, the AC terms of the Fourier domain image corresponds to the focal spot intensity both in time domain and along the spatial dimension defined by the slit. It thus represents a direct spatio-temporal characterization of the pulse.
We now present simulations of a pulse with a spatio-temporal shift, a pulse-front tilt of 18fs/mm . The calculated interferogram looks similar to a pulse without pulse front tilt [Fig. 8(a)] but the 2D Fourier domain [Fig. 8(b)] clearly indicates a time spreading of the temporal intensity in the focal plane. The shift is easier to evaluate if the AC term is filtered out and Fourier transformed back into the spatial domain only [Fig. 8(c)]. In this way the slope of the pulse front tilt is perfectly well recovered. When the temporal intensity is compared between a single spatial point and the complete beam, the effective pulse duration rises from 31fs to 44fs [Fig. 8(d)].
To experimentally confirm the accuracy of this unique spatio-temporal measurement, a 0.5° wedge was inserted into the input beam just in front of the SRSI-ETE device so that it introduced a pulse front tilt of about 18fs/mm [Fig. 9(c)]. The pulse front tilt could be perfectly well measured if the initial pulse front tilt (without the wedge) and beam distortion is taken into consideration. The measurement confirm the pulse duration stretching from 31fs to 44fs from a single spatial point to the complete beam [Fig. 9(f)]. To check that this pulse front tilt was not introduced by the instrument, the XPW filtered pulse was also measured and compared to its seeding pulse [Figs. 9(b) and 9(c)]. As expected from the cubic spatial, temporal and spatio-temporal effects at the focal spot, the XPW generation filters out the temporal, spatial and spatio-temporal defaults. The remaining pulse front tilt is extremely low and probably due to residual wedge effects on the optics of the instrument. At this low pulse front tilt value, the effect on pulse duration is negligible [Figs. 9(d)-9(e)].
In conclusion, we have simulated and demonstrated experimentally that self-referenced spectral interferometry in an extended time excursion configuration enables an unprecedented combination of temporal resolution and dynamic range for a single-shot measurement with intrinsic spatio-temporal capability. Temporal intensity contrast could be analyzed with almost 80 dB dynamic range and an 18 ps excursion time, only limited by the currently used camera. These values perfectly well match the rising slope of state-of-the-art 100 TW to PW class lasers. Detailed knowledge and understanding of the temporal behavior of the pulse in this range is fundamental for the control of laser absorption mechanisms in laser-solid interactions and thus essential for the development of, e.g., application oriented laser driven particle accelerators. We thus expect the novel instrument presented here to not only provide new insight into relativistic laser matter interaction but to serve as an online reference tool for the shot-to-shot analysis of modern high power lasers. A single data set provides access to spectrograms, spatio-temporal characterization of the main pulse or pre- and post-pulses, as well as spatial and temporal focus intensity of the pulse.
Higher performance than presently achieved can be expected with the next generation of imaging spectrometer read-out cameras. The dynamic is limited by pixel quantum efficiency, well depth and active pixels number. It can be maximized exceeding 109 in single shot with 2048 x 512 pixels having a well depth of 6x105 electrons and a quantum efficiency higher than 70% over the laser pulse bandwidth. The temporal range also benefits from a higher number of active pixels along the spectral dimension, and up to 36ps can be expected.
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