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Abstract
The single-shot cross-correlation of the short optical pulses generated by two laser facilities is acquired using random quasi-phase-matching of the counter-propagating beams in a disordered ferroelectric crystal. Transverse sum–frequency generation of the two counter-propagating pulses at different central wavelengths yields their time-dependent background-free cross-correlation after spectral filtering. Their relative delay is directly determined on every shot from the measured cross-correlation, making it a simple diagnostic for jitter studies and temporal characterization.
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1. Introduction
Temporal metrology is an enabler for ultrafast optics. Because characterizing ultrashort optical pulses requires a bandwidth much higher than what can be obtained with photodetection and electronics-based digitization, temporal diagnostics relying on nonlinear optics have been developed [1]. The electric field, in the time or frequency domain, fully describes an isolated optical pulse. Most diagnostics are self-referencing and typically provide no information on arrival time relative to an external reference, e.g., single-shot timing and jitter statistics over a collection of pulses. This information can, however, be extracted from the cross-correlation obtained by nonlinear wave mixing of the pulse under test with an ancillary pulse in a nonlinear crystal. This process has mostly been used with cross-correlations averaged over a large number of pulses generated at a high repetition rate, in which case the relative delay is not known for every pulse and the jitter statistics can only be indirectly determined [2–4]. Cross-correlations are also useful for pulse characterization when a relatively short ancillary pulse is available because the link between the measured data and shape of the pulse under test is more straightforward than with autocorrelations. To this effect, single-shot cross-correlators have been developed to characterize the contrast of low-repetition-rate laser systems over a large temporal range [5–7]. In these devices, the relative delay between interacting pulses is mapped onto a transverse spatial variable. Large delays generally require relatively large beams and large crossing angles in the nonlinear crystal, which increase the energy requirement, complicate the experimental implementation, and set additional requirements on the phase-matching conditions.
Random quasi-phase-matching in a disordered material allows for nonlinear interactions that cannot be phase matched in standard spatially uniform crystals [8,9]. In particular, crystals with domains of random size and orientation of their nonlinear polarizability allow for broadband nonlinear interactions over long propagation distances [10] and nonlinear interactions in geometries where wave mixing is performed at arbitrarily large angles. The most striking demonstration of these geometries is the observation of transverse second-harmonic generation (SHG) of a single beam and two counter-propagating beams [11,12]. The latter geometry is particularly interesting because it simply maps out the relative delay between counter-propagating pulses onto their common propagation axis. Transverse SHG has been used with high-repetition-rate trains of short pulses to acquire intensity autocorrelations [13,14], chirp-sensitive experimental traces [15], d-scan traces using the inherent dispersion of the nonlinear crystal to induce the required range of dispersion [16], and the cross-correlation of two pulse trains originating from the same laser after temporal distortions have been introduced on one of them [17]. There are no reports of single-shot operation with a source at a low repetition rate. The properties of conical sum–frequency generation (SFG) have been studied [18], but no SFG-based temporal diagnostic has been reported. Another phenomenon that generates an intensity-dependent nonlinear signal independent of the angle between the two spatially overlapped beams is two-photon fluorescence. It has been used for single-shot autocorrelation based on counter-propagating beams and orthogonally propagating beams [19–21]. The absence of phase-matching requirements allows, in principle, for cross-correlation measurements of pulses at different wavelengths, but a material with suitable two-photon cross-section spectrum must be identified. By contrast, random quasi-phase-matching in a disordered ferroelectric crystal allows for broadband and flexible operation at different wavelengths, provided that the fundamental and generated wavelengths are within the transmission window of the crystal.
We demonstrate a single-shot cross-correlator based on SFG of counter-propagating beams in SBN61 (SrxBa1−xNb2O6 with x = 0.61). This diagnostic measures the cross-correlation between two laser facilities operating at different central wavelengths. It allows one to determine the relative delay between the pulses generated by each facility on every shot, thereby supporting precise co-timing and the study of their relative jitter. Counter-propagation in the 10-mm crystal yields an ∼150-ps temporal range. The experimental configuration is detailed in Sec. 2. The performance of the cross-correlator, measured cross-correlations, and jitter properties are described in Sec. 3.
2. Experimental configuration
2.1 Laser sources
We measure the cross-correlation of optical pulses with instantaneous power profile PA(t) and PB(t) generated by two laser facilities at central wavelengths λA = 1053 nm and λB = 1170 nm, respectively [Fig. 1(a)]. The two beams are focused in a counter-propagating configuration in a target chamber designed for Raman-amplification studies [22]. Each system is seeded by a mode-locked laser (GLX200, Time-Bandwidth Products) synchronized to a laboratory-wide reference signal around 76 MHz. That signal is obtained by passive doubling and amplification of a stable commercial oscillator operating at 37.998938 MHz (SC Sprinter Crystal Oscillator, Wenzel Associates). The repetition rate of the amplified pulses getting to the target chamber is 5 Hz. For timing studies, the SBN61 crystal is located at the common focus of the two beams. The 1053-nm and 1170-nm beams are focused by singlet lenses with focal lengths equal to 1215 mm and 800 mm, respectively.
Fig. 1. (a) Experimental configuration. (b) Example of signals acquired by the camera: transverse SHG of the 1053-nm pulse, transverse SHG of the 1170-nm pulse, and transverse SFG of the two pulses after spectral filtering (from top to bottom).
The 1053-nm pulse originates from the Multi-Terawatt (MTW) laser, a chirped-pulse-amplification system that can generate subpicosecond pulses at energies of tens of joules using optical parametric amplifiers (OPA’s) and Nd:glass amplifiers [22]. Because energies of the order of 1 μJ are sufficient for the cross-correlation setup, only the first amplifier before the main stretcher is used. In that amplifier, a slightly chirped seed pulse from the mode-locked laser is amplified in a BBO (beta-barium borate) crystal by a short pump pulse [23,24]. After that, the pulse propagates in the main Offner triplet stretcher, the inactive amplifiers, and the compressor. The output pulse’s duration ΔτA at 1053 nm is adjusted via translation of the Offner triplet imaging system relative to the static diffraction grating in the stretcher.
The 1170-nm pulse is the idler of an optical parametric chirped-pulse–amplification system operating with a signal at 920 nm and a pump at 526.5 nm [25]. The idler pulse generated in the last BBO OPA is recompressed from 1.5 ns to ∼120 fs by a grism-based compressor, whose slant distance adjusts the output pulse’s duration ΔτB. This source can generate several millijoules of energy, and attenuation was implemented using optical densities. Additionally, an iris located in the near field was used to decrease the beam size, thereby allowing for a further reduction in energy and mitigation of the shot-to-shot variations in pointing and far-field shape.
2.2 Nonlinear crystal and imaging
A 5 × 5 × 10-mm3 SBN61 crystal (Laserand) is located at the center of the target chamber. This crystal, with randomly oriented domains having an average size of the order of 3 μm, allows for phase matching of counter-propagating beams [12]. For this application, both laser beams are extraordinarily polarized, i.e., their linear polarization state is parallel to the crystal axis. The resulting time-independent transverse SHG signal from each beam, proportional to ${\textrm{C}_\textrm{A}} = \int {P_\textrm{A}^2} (t )\textrm{d}t$ and ${\textrm{C}_\textrm{B}} = \int {P_\textrm{B}^2} (t )\textrm{d}t,$ and time-dependent SFG signal, proportional to ${\textrm{C}_{\textrm{AB}}}(\tau )= \int {{P_\textrm{A}}(t )} {P_\textrm{B}}({t - \tau } )\textrm{d}t,$ are also extraordinarily polarized. The full length of the 10-mm crystal is re-imaged onto a triggered camera (Manta 146B, Allied Vision). The SHG signal measured for each pulse is shown in Fig. 1(b). For the 1053-nm source, the SHG signal is spatially varying because of the longitudinal variation in intensity around the focus. The smaller near-field beam size at 1170 nm yields a larger far field and longer Rayleigh range after focusing, resulting in an SHG signal that is approximately constant along the longitudinal direction. Considering the central wavelength of the interacting pulses (1053 nm and 1170 nm), the SFG spectrum is centered at 554 nm. A bandpass filter (central wavelength: 550 nm; bandwidth: 40 nm) removes the delay-independent SHG signal resulting from each beam at 526.5 nm and 585 nm, allowing for background-free acquisition of the SFG signal [Fig. 1(b)]. Incomplete filtering of the SHG signal generated by the 1170-nm pulse at shorter wavelengths yields a background of the order of a few percent of the peak SFG signal. All the waves are well above the transparency cutoff of SBN61 (∼ 400 nm).
The relative delay τ between the two counter-propagating pulses is mapped onto the longitudinal coordinate z following the relation τ = z [1/v(λA) + 1/v(λB)], where v(λ) is the group velocity in SBN61 at wavelength λ. Using the Sellmeier coefficients for the extraordinary axis of SBN61 [26], one can determine 1/v(λA) = 7.68 ps/mm and 1/v(λB) = 7.63 ps/mm, i.e., the 10-mm-long crystal corresponds to a 153-ps temporal window. The time-to-space calibration and camera pixel size set the sample spacing to 250 fs in the time domain, which is sufficient for the pulse durations and jitters of interest (note that the jitter can be determined with accuracy much better than the sample spacing). The use of an imaging system with higher magnification would support higher-resolution measurements.
The group-velocity dispersion of the SBN61 crystal can modify the temporal waveforms of the two counter-propagating pulses, essentially modifying the cross-correlations measured at different relative delays τ. The group-velocity dispersion is equal to 273.9 fs2/mm and 215.8 fs2/mm at 1053 nm and 1170 nm, respectively. The impact of these dispersions over the 10-mm crystal length is small, resulting, for example, in stretching from 120 fs to 130 fs at 1170 nm over the 10-mm crystal length. This has no practical impact on jitter measurement and pulse-shape characterization in the current demonstration, but the impact of dispersion should be considered when measuring the cross-correlation of shorter pulses. Conversely, large chromatic dispersions leading to significant pulse broadening can be used to generate experimental traces that depend on the phase of the input pulses [15,16].
For the high-repetition-rate sources used in the previously reported demonstrations of autocorrelation acquisitions, the camera’s exposure time can be set to increase the measured nonlinear signal. This cannot be done for single-shot acquisition. Based on an initial set of experiments performed with the same crystal using a 7-ps, 76-MHz source at 1053 nm (Lynx, Time-Bandwidth Products), subpicosecond pulses with energy of the order of 1 μJ and a focal-spot size of the order of 50 μm were predicted to generate a measurable SFG signal. The calculated fluence in these conditions, 0.03 J/cm2, is approximately 10× smaller than the reported multipulse ablation threshold in a similar crystal (Nd3+:SBN) with a 1-kHz train of 110-fs, 795-nm pulses [27]. The typical energies used for the experiments reported in this article are 0.2 μJ at 1053 nm and 2 μJ at 1170 nm. These energies resulted in acquired cross-correlation signals of the order of 1000 counts, to be compared to the noise standard deviation, which was of the order of 10 counts. No bulk or surface damage of the SBN crystal has been observed after tens of hours of operation at 5 Hz under these conditions.
Transverse SHG yields a spatial distribution that represents the cross-correlation of the pulses at 1053 nm and 1170 nm, but imaging of this distribution onto the camera results in a convolution with the corresponding point-spread function (PSF). The PSF has been modeled as a Gaussian function with a full width at half maximum (FWHM) equal to 700 fs. This value has been determined by comparing the measured time-independent, one-beam SHG signal at one end of the cross-correlator time base to the convolution of a sharp-edge rectangular function with a Gaussian function of various width.
2.3 Cross-correlation processing
The timing of a measured cross-correlation relative to the cross-correlator temporal axis is determined using a linear fit of the phase of its Fourier transform over a suitable range of frequencies [28]. The collection of timings determined over a set of measured cross-correlations represents the statistics of the jitter between the two laser sources. The cross-correlations measured in identical experimental conditions can be retimed by their respective delay relative to the cross-correlator timebase to determine the average pulse shape. Figure 2 shows examples of single-shot cross-correlations before and after retiming, demonstrating the excellent on-shot reproducibility. Random quasi-phase-matching leads to high-frequency spatial modulations of the measured SFG signal because the magnitude of the signal originating from a particular spatial point z, i.e., relative delay τ, depends on the particular (random) arrangement and size of the ferroelectric domains. This effect is partially mitigated by the spatial averaging arising from diffraction within the sample and the PSF of the imaging system between the sample and camera.
3. Experimental results
3.1 Time-range characterization
The delay between the two laser facilities has been scanned to determine the range and accuracy of the cross-correlator using an electronic delay line (EDL) based on mechanical trombones. This programmable device (PDL-30A, Colby Instruments) controls the output phase of the 76-MHz reference signal for the mode-locked seed source of the 1053-nm laser system. The delay between the two pulses has been determined for 15 different delays induced by the EDL with steps of 10 ps [Fig. 3(a)]. At each induced delay, 100 cross-correlations have been acquired and processed. The averaged delay depends linearly on the induced delay over the 140-ps tested range, with a linear-regression coefficient equal to 0.997, showing excellent accuracy of the time calibration calculated using the group velocity of SBN61 [Fig. 3(b)]. The delay error (difference between the measured delay and the delay nominally induced by the EDL) is smaller than 0.5 ps over the entire range [Fig. 3(c)]. Transverse SFG signals were observed over ∼150 ps, consistent with the calculated temporal range, but the reconstructed delays have error of the order of 1 ps for extreme delays because of clipping of the relatively long cross-correlation signals.
Fig. 3. (a) Measured relative timing at 15 different delays induced by the EDL every 10 ps (100 acquisitions at each delay); (b) average measured timing as a function of the timing shift induced by the EDL; (c) timing error.
A similar experiment was performed with delay steps equal to 1 ps (Fig. 4). The observed error between measured and induced delay is again ∼0.5 ps, with a linear-regression coefficient equal to 1.014. The standard error for the determined average measured delay at a given induced delay is ${\sigma / {\sqrt N ,}}$ where σ is the standard deviation of the measurement due to jitter (typically 0.65 ps, as shown in Sec. 3.2) and N = 100 is the number of measurements at each delay. The determined average delay therefore has a confidence interval at 95% with half width equal to 0.13 ps. The observed discrepancy between the average measured timing and induced timing shift, which is several times larger than that, is therefore most likely due to the mechanical delay line, which has a nominal 1-ps resolution, or synchronization drift/jump of the modelocked lasers occurring during the measurements.
Fig. 4. (a) Measured relative timing at 21 different delays induced by the EDL every 1 ps (100 acquisitions at each delay); (b) average measured timing as a function of the timing shift induced by the EDL; (c) timing error.
3.2 Jitter characterization
The jitter between the two laser facilities has been determined in different experimental conditions. In a first set of experiments, the duration of either the 1053-nm or 1170-nm source has been modified. Data were collected as follows:
- • with both sources at best compression (ΔτA = ΔτA,0, ΔτB = ΔτB,0). These data sets are composed of 1000 cross-correlations.
- • with the 1053-nm source at best compression (ΔτA = ΔτA,0) and the 1170-nm source operating with a detuned compressor (ΔτB > ΔτB,0). These data sets are composed of 1000 cross-correlations at each setting.
- • with the 1170-nm source at best compression (ΔτB = ΔτB,0) and the 1053-nm source operating with a detuned stretcher (ΔτA > ΔτA,0). These data sets are composed of 100 cross-correlations at each setting.
The collection of delays measured at 5 Hz in one specific configuration is the full characterization of the on-shot jitter between the two sources without assumption on its statistical distribution. Although the measured collections are consistent with normal distributions, a few outliers have been observed and identified as resets of the synchronization system of either modelocked laser during data acquisition. The shot-to-shot jitter between the two laser sources is expected to be independent of the pulse shapes. The observed variation in statistical properties is either due to drift of the two mode-locked lasers relative to their respective synchronization signal, drift of the optical path between the two laser facilities or nonideal behavior of the cross-correlator. For example, operation with a detuned stretcher at 1053 nm leads to a decrease in the cross-correlation signal because the energy reaching the SBN crystal is constant. Operation with a detuned compressor at 1170 nm was compensated by an increase in energy to approximately maintain the signal-to-noise ratio. Figure 5(a) presents the measured rms jitter as a function of the FWHM duration of the measured, averaged cross-correlation. The jitter measured for the two sources at best compression for three different sets of data measured on the same day is between 0.6 and 0.7 ps (blue diamonds). As discussed later, this value is consistent with the jitter calculated from the jitter reported by the synchronization unit of each mode-locked oscillator. The determined jitter does not change significantly with the cross-correlation duration, but longer pulses at 1053 nm generally result in larger jitter because of the lower signal-to-noise ratio (black circles). Maintaining the signal-to-noise ratio when performing measurements with the longer pulses at 1170 nm yields values similar to those observed at best compression (red squares). The histograms corresponding to acquisition with both sources at best compression and with different durations of the 1170-nm source are shown in Fig. 6. They are consistent with a normally distributed relative jitter between the two sources.
Fig. 5. (a) The rms jitter as a function of the cross-correlation FWHM, measured with the two sources at best compression (blue diamonds), with the 1170-nm source at best compression and varying duration ΔτA of the 1053-nm source (black circles), and with the 1053-nm source at best compression and varying duration ΔτB of the 1170-nm source (red squares). (b) rms jitter as a function of the attenuation on the photodiode synchronization signal, determined from the acquired cross-correlations (red squares) and from the rms jitter σA and σB of the two oscillators (black circles). The grayed area represents the range of rms jitters calculated from σB and the range of σA observed during a 1-min interval at each attenuation.
Fig. 6. Probability histogram of the delay between the two laser sources measured (a) with the two sources at best compression (ΔτA = ΔτA,0, ΔτB = ΔτB,0), (b) with ΔτA = ΔτA,0 and ΔτB ≈ 1 ps, and (c) with ΔτA = ΔτA,0 and ΔτB ≈ 3 ps. The bin size is 0.1 ps in all cases. A normal distribution with identical standard deviation has been added to (a), (b), and (c) (red lines).
In a second set of experiments, the jitter between the two laser facilities has been measured when the jitter of the mode-locked laser seeding the source at 1053 nm is purposely increased. To do so, radio-frequency attenuators, with attenuation ranging from 1 to 13 dB, are added between the photodiode measuring the oscillator’s pulse train and the laser synchronization unit. For each attenuation, a set of 1000 cross-correlations has been acquired and processed to quantify the jitter between the two facilities. The synchronization unit of each laser reports its rms jitter relative to the reference signal at 76 MHz, which is determined by a true-rms-to-dc converter operating on the laser-integrated phase detector after low-pass filtering. The jitter on the seed for the 1170-nm source is σB = 0.35 ps. The jitter on the seed for the 1053-nm source, σA, ranges from 0.52 to 2.70 ps for attenuations between 0 and 13 dB. For high attenuations, the reported jitter fluctuates in time; the lowest and highest values observed during a 1-min interval are used to set error bars on σA. The reference signal is comparatively very stable (its jitter determined from its phase-noise properties is smaller than 15 fs,). Therefore, σA and σB are dominated by noise from the oscillators, and the jitter on the two output-pulse trains is uncorrelated. The relative jitter between the two oscillators, ignoring other potential sources of jitter arising from amplification and propagation in the laser system, can be calculated as $\sqrt {\sigma _\textrm{A}^2 + \sigma _\textrm{B}^2} .$
Figure 5(b) shows the relative jitter determined from the cross-correlations acquired with the SBN crystal and the calculated jitter, as defined above. The data clearly show the degradation in relative jitter between the two laser facilities when one of the mode-locked lasers operates in nonoptimal conditions. There is generally an excellent agreement between the relative jitter measured at the output of the two laser facilities and the jitter calculated from the respective jitter of each oscillator. This shows that there are no additional sources of significant jitter on these two systems in the current operating conditions. Figure 7 displays the histograms measured for attenuations equal to 0 dB, 9 dB, and 12 dB, which lead to measured rms jitter equal to 0.63 ps, 1.58 ps, and 2.23 ps, respectively.
Fig. 7. Probability histograms of the delay between the two laser sources measured (a) with a nominal synchronization-photodiode signal, (b) with a 9-dB attenuation, and (c) with a 12-dB attenuation. The bin size is 0.1 ps in all cases. A normal distribution with identical standard deviation has been added to (a), (b), and (c) (red lines).
3.3 Pulse-shape characterization
The operation of the cross-correlator for pulse-shape measurements, in the presence of jitter, has been demonstrated in various experimental configurations. Removal of the shot-to-shot jitter allows for averaging over multiple shots to increase the signal-to-noise ratio (SNR). As shown in Fig. 2(a), the shot-to-shot jitter is not negligible compared to the width of the cross-correlation. Averaging without delay removal leads to a significant broadening of the cross-correlation [Fig. 8(a)], and in particular, the averaged cross-correlation has a Gaussian shape for large values of the rms jitter induced by large attenuations on the photodiode reference signal. Higher values of the rms jitter have no significant impact on the cross-correlations averaged after removal of the determined on-shot jitter [Fig. 8(b)].
Fig. 8. Averaged cross-correlation (a) without and (b) with removal of the on-shot jitter, with nominal synchronization-photodiode signal (blue line), with a 9-dB attenuation (red line), and with a 12-dB attenuation (yellow line).
With the current experimental configuration and signal acquisition, a single on-shot cross-correlation measurement has a SNR of the order of 20 dB [Figs. 9(a) and 9(c)]. Averaging over multiple acquisitions after removal of the random on-shot delay leads to a significant improvement of the SNR, approximately equal to the square root of the number of acquisitions [Figs. 9(b) and 9(d)]. In particular, the SNR is close to 40 dB when averaging over 1000 acquisitions, allowing one to identify low-level features on the cross-correlation.
Fig. 9. Measured single-shot and averaged cross-correlations on a linear (first row) and logarithmic (second row) scale after on-shot delay removal. (a) and (c) correspond to ten successive acquisitions. (b) and (d) correspond to averages over 10, 100, and 1000 successive acquisitions.
The cross-correlation between the two laser facilities has been measured for different pulse durations ΔτA at 1053 nm, keeping the 1170-nm pulse at best compression (ΔτB = ΔτB,0). The measured cross-correlations averaged over 100 acquisitions have been compared with the cross-correlations calculated using the temporal properties of the optical pulses. At 1053 nm, the output spectrum (with FWHM equal to 5 nm) and a spectral phase with a small residual third-order dispersion (0.04 ps3) are used to calculate the pulse shape at best compression. This residual spectral phase is inferred from the measured cross-correlation data in the absence of a temporal diagnostic reconstructing the phase. The second-order dispersion calculated from the parameters of the stretcher is added to the spectral phase when the stretcher slant distance is detuned from best compression. At 1170 nm, the pulse shape at best compression is obtained using a commercial SPIDER device (APE GmbH). The measured and calculated cross-correlations, shown for 1053-nm operation at best compression and two different durations corresponding to second-order dispersions of –0.26 and –0.46 ps2, are in good agreement [Fig. 10(a)]. The measured and calculated FWHM’s of the cross-correlation are in good agreement for a large range of slant distances, demonstrating the usefulness of this diagnostic to precisely set the laser parameters [Fig. 10(b)].
Fig. 10. (a) Measured (round markers) and calculated (continuous lines) cross-correlations for residual second-order dispersions of the 1053-nm pulse equal to 0 ps2 (dark blue), –0.26 ps2 (light blue), and –0.46 ps2 (red). (b) Measured (round markers) versus calculated (dashed line) FWHM for different dispersions at 1053 nm.
4. Conclusion
We have demonstrated the first single-shot cross-correlator based on random quasi-phase-matching in a disordered nonlinear crystal and its operation on laser sources at a relatively low repetition rate. The cross-correlation of two pulses from different laser facilities is generated via transverse sum–frequency generation in an SBN61 crystal. The relative delay extracted from the cross-correlation on every shot allows for the determination of the jitter statistics between the two laser sources. The large temporal range arising from the counter-propagating geometry, 153 ps in a 10-mm crystal, and subpicosecond resolution make the diagnostic suitable for co-timing and optimization of the two laser systems used in this demonstration. The single-shot operation of the diagnostic is attractive for providing on-shot temporal information to interpret laser–matter experiments, and averaging over multiple acquisitions enhance the SNR after removal of the shot-to-shot jitter. In this demonstration, the SHG signals from each pulse are filtered out before photodetection, therefore leading to background-free acquisition of the time-dependent cross-correlation generated by SFG. The technique is applicable to any two sources provided that the fundamental waves and the SFG wave are within the transparency range of the crystal, although the background caused by SHG of either source, if it cannot be filtered out, might reduce the signal-to-noise ratio.
This simple approach supports the determination of the relative timing between two laser sources on a single shot, which is particularly important for low-repetition-rate sources. It also offers a direct approach to single-shot determination of the time-varying instantaneous power of an optical pulse by cross-correlation with a shorter ancillary pulse. Such determination is important for the development and optimization of chirped-pulse–amplification systems delivering pulses close to their Fourier transform–limited duration, but also for systems delivering pulses with a coherence time much shorter than their duration. The latter pulses look promising for mitigating laser–plasma instabilities in high-energy laser–matter interaction via advanced pulse-shaping [29–31] and spectral incoherence [32,33]. Accurate single-shot temporal characterization with high resolution and long record length is paramount for safe operation and optimal interaction with the targets. SBN crystals as long as 20 mm are commercially available, leading to a 300-ps temporal window. Longer acquisition windows can be obtained by combining multiple crystals or implementing multiple passes in a single crystal with different relative delays between the two sources. Cross-correlations in disordered nonlinear crystals can also support the optimization of spatial overlap and timing in complex experiments involving multiple laser beams, such as the counter-propagating geometry used for Raman amplification [34] and the crossing of beams at large angles used for Compton scattering [35].
Funding
National Nuclear Security Administration (DE-NA0003856); Office of Science (DE-SC0016253); University of Rochester; New York State Energy Research and Development Authority.
Acknowledgment
The authors thank I. A. Begishev, S. Bucht, R. Roides, M. V. Ambat, and K. McMillen for experimental assistance during this campaign. This report was prepared as an account of work sponsored by an agency of the U.S. Government. Neither the U.S. Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the U.S. Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the U.S. Government or any agency thereof.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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