Demonstration of Single‐Shot Measurements of 1013 Ultrahigh‐Contrast Pulses by Manipulating Cross‐Correlation

In strong‐field physics experiments with high‐intensity lasers, single‐shot characterization of the temporal contrast between the laser pulse peak and its temporal pedestal is important; this allows fast optimization of the pulse contrast and meaningful comparison with theory for each pulse shot. To date, high contrast ratios of 1010 have been demonstrated in single‐shot measurements for petawatt (PW) lasers. However, ultrahigh contrast ratios of ≈1013, as required for the planned 200 PW lasers, pose challenges to high‐intensity laser technologies and have thus far remained open for investigation. This article reports a pilot demonstration of ultrahigh‐contrast measurements by adapting a single‐shot cross‐correlator (SSCC). An evaluation method for the SSCC detection limit is introduced. The strategy mimics the test beam with known spatial contrast, whose cross‐correlation is equivalent to that of a test pulse with ultrahigh temporal contrast. The ultimate contrast measurement limit of 1013 is achieved, which corresponds to the highest pulse intensity by optical damage and the lowest temporal pedestal by single‐photon detection. The photon noise of the detector is observed and becomes dominant as the temporal pedestal of the optical pulse decreases. The demonstrated detection ability is applied to a high‐contrast laser system, suggesting the accessibility of ultrahigh‐contrast measurements.

DOI: 10.1002/adpr.202100105 In strong-field physics experiments with high-intensity lasers, single-shot characterization of the temporal contrast between the laser pulse peak and its temporal pedestal is important; this allows fast optimization of the pulse contrast and meaningful comparison with theory for each pulse shot. To date, high contrast ratios of 10 10 have been demonstrated in single-shot measurements for petawatt (PW) lasers. However, ultrahigh contrast ratios of %10 13 , as required for the planned 200 PW lasers, pose challenges to high-intensity laser technologies and have thus far remained open for investigation. This article reports a pilot demonstration of ultrahigh-contrast measurements by adapting a single-shot cross-correlator (SSCC). An evaluation method for the SSCC detection limit is introduced. The strategy mimics the test beam with known spatial contrast, whose cross-correlation is equivalent to that of a test pulse with ultrahigh temporal contrast. The ultimate contrast measurement limit of 10 13 is achieved, which corresponds to the highest pulse intensity by optical damage and the lowest temporal pedestal by single-photon detection. The photon noise of the detector is observed and becomes dominant as the temporal pedestal of the optical pulse decreases. The demonstrated detection ability is applied to a highcontrast laser system, suggesting the accessibility of ultrahigh-contrast measurements.
ultimate measurement limit set by the photon noise of the detector. While the dynamic range of the DSCC measurements can easily be tested by adjusting the optical attenuation during the corresponding long scanning times, it is assumed that the dynamic-range test of the SSCC measurements must rely on ultrashort pulses with known contrasts better than 10 13 . In addition, the test pulse must have a sufficiently high power, e.g., %100 GW, to achieve high intensities within a correlation area of %10 Â 10 mm 2 . Such a high-power ultrahigh-contrast pulse has not yet been available; therefore, all SSCC designs have not been tested in practice. In the current work, we mimicked a test pulse in the spatial domain based on time-to-space mapping and evaluated the efficacy of the SSCC device to measure contrast of the order of 10 13 .

SSCC Test Strategy
The principle of SSCC measurements can be explained simply as follows: a femtosecond test pulse with a picosecond noise pedestal is recorded using an oscilloscope with an adaptor. Here, the adaptor plays a key role in temporal magnification and converts the test pulse into a series of nanosecond-spaced temporal slices. As shown in Figure 1a, the adaptor relies on a correlation unit of noncollinear third-harmonic generation (THG) and a detection unit of a fiber-array-mediated photomultiplier tube (PMT) (see details in Section 3.2). If the test pulse has a uniform beam profile in the noncollinear plane (xÀz), then the noncollinear THG allows time-to-space mapping to enable a test pulse I(t) represented by the correlation function A (2) where the delay τ has a linear dependence on the transverse variable x as τ ¼ γx and the coefficient γ of the time-to-space mapping can be determined by the noncollinear angle α. [17,19] With the parallel detection of a 100-pixel fiber array along x, the transversely distributed A(x) is further mapped to a series of temporal slices spanning 500 ns. [8,19] Such a temporally magnified signal series can be resolved using the PMT and oscilloscope; this is the typical procedure for single-shot contrast measurement.
If the test laser beam I(ξ) is spatially nonuniform and has an ultrahigh spatial contrast between the beam center and surrounding areas, the THG correlation function becomes A (2) (x) ¼ I(ξ) I 2 (ξ À x). [17,20] Therefore, a spatially shaped beam I(ξ) can also produce the same correlation function as the test pulse I(t) does (Figure 1b). This suggests an alternative scheme to test the device dynamic range. As shown in Figure 1c, a test beam I(x) is synthesized by spatially packaging a high-intensity narrow beam at the center of a continuous-wave (CW) wide beam. Given the measurement frame of time-to-space mapping, the high-intensity femtosecond beamlet mimics a peak pulse under test, and the weak CW beamlet mimics a temporal noise pedestal. In other words, the synthesized beam acts as a test pulse with a known contrast set by the intensity ratio of the two beamlets.
In the temporal cross-correlation (Figure 1a), the noncollinear angle α determines the coefficient γ of time-to-space mapping, so an increase in α can enlarge the temporal window of the singleshot measurements. [17,19] In the spatial cross-correlation (Figure 1b), a noncollinear angle α must be chosen for group velocity matching between the interacting waves, as typically performed in a noncollinear optical parametric amplifier (OPA). [21] In the case of unmatched group velocities, the femtosecond pulse peak and the CW pedestal in the synthesized beam will have different temporal overlaps with the sampling pulses in the correlation crystal, which degrades the THG correlation and renders the contrast measurements unfaithful. For convenience, the temporal cross-correlation in Figure 1a also adopts the noncollinear angle α for group velocity matching.  www.advancedsciencenews.com www.adpr-journal.com

Light Sources
As shown in Figure 2, two types of 1054 nm test lasers obtained by second-harmonic generation (SHG) of 2108 nm lasers were alternately applied as inputs to the SSCC in the experiments.
One was a high-contrast spatial test beam comprising a highintensity femtosecond narrow beam and low-intensity CW wide beam, and the other comprised a high-contrast temporal test pulse from the SHG of a single-shot optical parametric chirped-pulse amplification (OPCPA) laser. Each test laser is independently coupled to the SSCC using the translation stage TS-1. A 1 kHz femtosecond OPA (OPerA SOLO, Coherent) pumped by a Ti:sapphire regenerative amplifier (Astrella, Coherent) delivered 330 μJ, 50 fs pulses at 2108 nm that were further converted to 120 μJ femtosecond pulses at 1054 nm by SHG with a 1 mm-thick LiNbO 3 crystal. This 1 kHz, 1054 nm femtosecond laser and a single-frequency CW fiber laser (Rock single-frequency laser, NP Photonics) were synthesized into a high-contrast spatial test beam. The second test laser source relies on the SHG of a 2108 nm OPCPA system. The OPCPA pump laser comprises the aforementioned CW fiber laser with a 2 ns waveguide modulator, a 10 Hz Nd:YLF regenerative amplifier, and a single-shot three-stage Nd:glass amplification system that delivers a 1 J, 2 ns pulse at 1054 nm. The 2108 nm femtosecond OPA pulse was stretched to 1.5 ns using a pulse stretcher, then amplified to 80 mJ by an OPCPA with a 22 mm-thick LiNbO 3 crystal and 1 GW cm À2 pump intensity, and finally compressed into a 30 mJ, 300 fs pulse using a pulse compressor. This 2108 nm femtosecond OPCPA beam was further converted to a 10 mJ femtosecond pulse at 1054 nm by SHG with a 4 mm-thick β-BBO crystal, which served as the high-contrast temporal test pulse.

SSCC Device
One of the key components of the SSCC is an adaptor that temporally magnifies the test pulses and allows accommodation with the PMT and oscilloscope. Such an adaptor consists of a correlation unit of noncollinear THG, a detection unit of fiber array, and a PMT. In the THG correlation unit using in this work (Figure 2), the 1054 nm test pulse was doubled in frequency using a 4 mmthick β-BBO crystal (θ ¼ 22.8 ) to produce a 527 nm sampling pulse. Owing to the nonlinear process of SHG, this sampling pulse will be cleaner than a test pulse. [22] The remaining test pulse at 1054 nm, after passing through a half-wave plate, serves as another incident pulse to the THG correlation. The angle of intersection between the test and sampling beams was 33.6 , and the THG correlation adopted a type-I β-BBO crystal (θ ¼ 61 ) of size of 38 (x) Â 10 (y) Â 2 (thickness) mm 3 . The laser beams of both the test and sampling pulses were nearly uniform in the x domain and covered the entire crystal. The noncollinear THG performed time-to-space mapping and induced a temporal window of 120 ps. The generated 351 nm correlation signal A (2) (x) with a beam width of W x ¼ 38 mm was imaged onto a 12.5 mm-wide fiber array by a cylindrical lens ( f ¼ 100 mm).
In the SSCC detection unit, the fiber array consisted of 100 UV fibers (OPTRAN UVNS, CeramOptec) with incremental lengths of 1 m, in which the 1st and the 100th fibers were 2.6 and 101.6 m long, respectively. The UV fiber with a core diameter of 105 μm had a high transmission (%10 dB km À1 ) at 351 nm. The correlation signal A (2) (x) was coupled to the fiber array by a cylindrical lens with f ¼ 30 mm, and collected by a fiber bundle, which outputs a series of 5 ns-delayed temporal slices spanning 500 ns. Consequently, serial detection can be used instead of parallel detection. In this study, a PMT (H10721-113, Hamamatsu) was used as the detector. To accommodate a high dynamic range and ensure a linear response of the PMT, a series of variable fiber www.advancedsciencenews.com www.adpr-journal.com attenuators were applied to reduce the signal intensities in the different fiber channels. In addition, a bandpass filter with high transmission for a 351 nm correlation signal was added between the fiber bundle and PMT to suppress the noise interference from the scattering of both the 1054 nm test and 527 nm sampling lasers. These two types of laser pulse peak scattering typically have intensities of approximate 10 À6 relative to the 1054 and 527 nm lasers, [23] which are larger than the 351 nm correlation signal for the temporal pedestal of the test pulse and will therefore severely degrade the pulse contrast measurements. The SSCC device was slightly modified to evaluate the contrast measurement limit (Figure 3). In the first modification, the spatially uniform test beam was replaced with a synthesized highcontrast beam. A 1054 nm mirror with 40% reflectivity and 60% transmission was used to combine the femtosecond narrow beam and CW wide beam. The transmitted femtosecond narrow beam had 25 μJ pulse energy, 150 fs duration, and 0.38 mm (x) Â 1.8 mm (y) beam spot, providing an intensity of 30 GW cm À2 The reflected wide CW beam had 30 mW full power and 38 mm (x) Â 2.5 mm (y) beam spot, rendering a full intensity of 40 mW cm À2 . In the second modification, the 50 μJ femtosecond sampling laser at 527 nm was focused onto the correlation crystal to produce a beam spot similar to that of the femtosecond narrow beam at 1054 nm and a high intensity of 60 GW cm À2 . To achieve the THG correlation function A (2) (x), the sampling laser was scanned in the x direction using the translation stages TS-2 and TS-3. The other parameters of the synthesized test beam and sampling beam are as previously noted. The third modification reduced the noncollinear THG angle from 33.6 to 13.8 and the β-BBO crystal orientation (θ) from 61 to 36.5 to match the velocities of the two incident waves. By scanning the sampling laser beam along the x direction, we obtained a maximum THG signal peak of %9 μJ. This position, corresponding to the THG signal peak, is defined as x ¼ 0. The THG efficiency relative to the narrow-beam femtosecond pulse at 1054 nm was 36% for the pulse energy and 12% for the photon number. The THG signal peak produced was imaged into the 50th channel of the fiber array. The total transmission from the correlation crystal to the PMT was measured to be 25%.

Evaluation of Dynamic Range with a Spatially High-Contrast Test Beam
In the test experiment for the 1054 nm SSCC, the correlation unit adopted a β-BBO crystal of size of 38 (x) Â 10 (y) Â 2 (thickness) mm 3 and noncollinear angle α ¼ 13.8 . A temporal window of %50 ps, the maximum attainable delay between the test and sampling pulses deduced from the noncollinear angle of 13.8 and clear aperture of 3.75 cm in the x direction, was obtained. [19] Consequently, the delay per unit crystal size is 13.3 ps cm À1 , which defines the coefficient of time-to-space mapping. In addition, the fiber-pixel time was 500 fs because the entire fiber array with 100 pixels is matched to the temporal window of 50 ps. A 1 kHz repetition rate of the femtosecond beamlet with a width of W x ¼ 0.38 mm was obtained by SHG of the 2108 nm OPA system and was maintained at a fixed intensity of 30 GW cm À2 at the crystal surface, while the CW beamlet with a width of W x ¼ 38 mm was varied in intensity. Because the high-intensity (%60 GW cm À2 ) sampling beam at 527 nm in the SSCC also had a narrow width of W x ¼ 0.38 mm, the test experiments were performed by beam scanning along the x direction. As shown in Figure 3a, the contrast measured by our device agrees well with the intensity ratio of the two beamlets. The detectable CW beamlet intensity can be as low as 3.5 mW cm À2 , indicating an ultrahigh dynamic range of %10 13 .
The input/output relationship of the PMT is briefly introduced herein. The PMT (H10721-113, Hamamatsu) used in the SSCC has an anode radiant sensitivity of 2.2 Â 10 5 A W À1 . A photon at  . Dynamic-range tests with synthesized high-contrast beams. a) Measured THG correlation function A (2) (x) at two CW intensities. Each dataset was averaged over 16 shots with the oscilloscope. b,c) Recorded 5000-shot PMT photovoltages at the 51th fiber channel (corresponding to the THG signal at x ¼ 0.38 mm) and two CW intensities of 3.5 mW cm À2 and 40 mW cm À2 . d,e) Histograms of the photon numbers detected per shot corresponding to (b) and (c), respectively. In (d), the first bin has a large number of shots (3878), which has been purposely divided by 20 to obtain a clear plot.
www.advancedsciencenews.com www.adpr-journal.com 351 nm has an energy of 5.66 Â 10 À19 J, corresponding to 2.8 Â 10 À10 W in the PMT characteristic time of 2 ns. According to these specifications, a single photon of the THG correlation signal triggers an anode current of 6.16 Â 10 À5 A, and is further converted to a voltage of 3 mV with a coupling resistance of 50 Ω. Therefore, the recorded average photovoltage of 3.1 mV at the CW intensity of 3.5 mW cm À2 corresponds to only one THG photon from a fiber pixel (Figure 3b,d). In this situation, the shot-to-shot fluctuations are of the order of 250%, which is typical for single-photon detection with the characteristics of white noise. [24] At higher THG photon numbers (>10), the fluctuations are greatly reduced (Figure 3c), and the distribution of the detected photon numbers differs slightly from that of a Poisson distribution having the same average flux (Figure 3e). Consequently, the observed severe fluctuations due to photon noise eventually limit the SSCC measurement for ultrahigh-contrast pulses. At this point, it is also clear that the DSCC measurements may not be reliable owing to the fluctuations of photon and laser noises. The ultimate measurement limit of 10 13 contrast achieved here nearly corresponds to the highest pulse intensity setting for the SSCC damage threshold and the lowest noise pedestal setting for single-photon detection.
Notably, the measurement ability demonstrated here can be linearly scaled up with the transverse size (W y ) of the test laser beam and/or correlation crystal. Because nonlinear crystals, such as LBO and YCOB, can be made as large as W y % 100 mm, [25] we anticipate an attainable extreme dynamic range of %10 14 . Figure 4 shows two SSCC measurements for a real 1054 nm ultrashort pulse with %40 GW peak power. The temporal window of the SSCC was increased to 120 ps using a larger noncollinear angle of α ¼ 33.6 . As noted in Section 3.1, the 1054 nm temporally high-contrast test pulse was generated through SHG of the 2108 nm OPCPA output, which is expected to have an ultrahigh contrast beyond 10 12 . [22] However, the full-window (120 ps) single-shot measurement by the SSCC showed a ratio of only %3 Â 10 10 around À105 ps (black curve in Figure 4). This measurement-limited intensity ratio of %3 Â 10 10 can be attributed to the low intensity of the test pulse. The intensity of the total test pulse was only 10 GW cm À2 because the test beam with a limited energy of %10 mJ and limited power of %40 GW was transformed to a large beam size that spanned the entire correlation crystal in the x direction in the full-window measurement. To enhance the dynamic range of the single-shot full-window measurement to up to 10 13 , a 1054 nm test pulse with a high power of 200 GW was necessary but unavailable in our experiments. Therefore, we reduced the beam size in the x direction by a factor of five to obtain a high intensity of 50 GW cm À2 . However, this compromised approach reduces the single-shot temporal window to only 24 ps, which is linearly proportional to the beam width in the x direction. [19] In this case, six-shot measurements with a small window (24 ps) were applied to form a full-window (120 ps) plot. Each pair of successive measurements was equally delayed by 20 ps by adjusting the translation stage TS-2, which resulted in a 4 ps temporal overlap between two successive measurements for data normalization. A real contrast as high as %0.5 Â 10 13 was achieved by the six equally delayed single-shot measurements (red curve in Figure 4). The improved contrast measurements over two orders of magnitude are consistent with the theoretical expectation that the THG correlation signal has a cubic dependence on the total intensity of the test pulse.

Conclusion
We demonstrated the ability of a single-shot resolution of 10 13 ultrahigh-contrast pulses by manipulating the cross-correlation. Based on the equivalence of the cross-correlation function, the detection limit of the SSCC was studied using a spatially high-contrast test beam synthesized by spatially packaging a high-intensity narrow beam at the center of a CW wide beam. By setting the high intensity of the narrow beam close to the SSCC damage threshold and the low intensity of the CW beam down to the order of a few photons, we observed detectioninduced photon noise and demonstrated the photon-noiselimited SSCC measurements for an ultrahigh contrast of %10 13 . Although the temporally high-contrast test pulse was limited in power, multishot measurements of such real test pulses also verified the ability of the SSCC. A true single-shot measurement for an ultrahigh contrast of %10 13 can thus be anticipated with a test pulse having a high power of %200 GW, which should be feasible with SHG from a terawatt-class laser. The demonstrated ability is ready for a broad diagnosis from current PW lasers to the expected 200 PW lasers in the future and beyond. To further enhance the measurement ability of the SSCC beyond 10 13 , one may apply the plasma-mirror technique to separate the weak temporal pedestal from the intense pulse peak as well as consider two SSCC devices to separately measure the temporal pedestal and peak pulse. [26] This route is promising for relaxing the limitation of the SSCC damage threshold because the intense pulse peak  Figure 4. Two SSCC measurements for a real ultrashort pulses. The black curve represents a full-window (120 ps) single-shot measurement at a low intensity (10 GW cm À2 ), whereas the red curve consists of six equally delayed small-window (24 ps) measurements at a high intensity (50 GW cm À2 ).
www.advancedsciencenews.com www.adpr-journal.com can be attenuated drastically without impeding the temporal pedestal.