1.

Introduction

Many petawatt (PW) laser systems with the benefit of chirped pulse amplification (CPA)¹ and optical parametric CPA² techniques have been demonstrated in the past decade.³ State-of-the-art high-power laser systems can produce intense pulses with peak powers of 10 PW.⁴ In the future, laser systems may reach the 100-PW level⁵ with focal intensities of ${10}^{21}$ to ${10}^{24}\mathrm{W}/{\mathrm{cm}}^2$.⁶ Ultrahigh intense laser pulses have been applied in the field of laser–matter interaction,⁷ such as proton or electron acceleration in thin solid targets^8–10 and electron generation in fast-ignition inertial confinement fusion.^11,12 For these applications, the temporal contrast (TC) of the ultraintense laser pulse is one of the most important parameters. Because the ionization threshold intensity of most solid targets is in the range of ${10}^{11}\mathrm{W}/{\mathrm{cm}}^2$, the TC of ultraintense laser pulses should be higher than ${10}^{10}\text{–}{10}^{13}$ to avoid damage to the target by the high-intensity background or prepulses. Recently, compressed ultrahigh intense laser pulses with ${10}^{12}$ TC have been developed.¹³ Because most PW laser systems run at low repetition rates or even single shot, single-shot characterization of the TC of an ultraintense laser pulse is crucial.

Although many techniques have been developed to improve the TC of ultraintense laser pulses,^14–16 only a few methods have been proposed for single-shot characterization of the TC. The first and most frequently used method for the measurement of the TC of single-shot pulses¹⁷ is third-order autocorrelator (TOAC). A time window of $\sim 200\mathrm{ps}$ and a dynamic range of ${10}^6$ were obtained using a pulse replicator in the TOAC.¹⁸ Using the optical parametric amplification process to generate the sampling pulse, a dynamic range as high as ${10}^{10}$ and a 50-ps time window with a 700-fs time resolution were achieved by Qian’s group based on a fiber-array-based detection system.¹⁹ With typical TOAC and third-order cross correlator (TOCC) processes, it is hard to achieve single-shot pulses with simultaneous high dynamic range, precise time resolution, high-pulse contrast fidelity, and wide time window, which are the most important parameters for TC characterization. Recently, the SRSI-ETE method was demonstrated, which has a time resolution as high as 20 fs.^20–22 However, the dynamic range is limited by the signal-to-noise ratio of the detector and, at present, the highest achievable value is ${10}^8$. Together with the TC reduction method, ${10}^9$ dynamic range has recently been obtained using SRSI-ETE.²³

In this paper, we propose a single-shot measurement method named “fourth-order autocorrelation” for the single-shot TC characterization of ultraintense laser pulses. In this method, frequency-degenerate third-order nonlinear processes, such as cross polarization wave generation (XPW),^16,24 self-diffraction (SD),^25,26 and transient grating (TG),²⁷ have the potential to generate cleaner signal pulses, which can then be used as the cleaning reference (or sampling) pulses for the next sum-frequency mixing (SFM) process together with the test pulse. In the proof-of-principle experiment, the SD process is used to generate the cleaning sampling pulse in the single-shot fourth-order autocorrelator (FOAC). A single-shot measurement with ${10}^{11}$ dynamic range, 65-ps time window, and 160-fs time resolution has been achieved.

Compared with previous single-shot TOAC or TOCC methods, the single-shot FOAC has the following advantages. First, cleaner sampling pulses are generated by the third-order nonlinear processes and, as a result, higher fidelity measurement is achieved. Second, the closeness of the sampling pulse and test pulse central wavelengths results in a high time resolution for the single-shot measurement, owing to the neglecting influence of the group velocity mismatch (GVM) during the SFM process. Third, hundreds of microjoule sampling pulses are generated by a simple SD process, and a ${10}^{11}$ dynamic range is achieved. Furthermore, two improvements are made in the proof-of-principle experiment to reduce the noise and extend the time window. First, the beta-barium borate (BBO) crystal for SFM is cut with a large angle to reduce the noise from the second-harmonic generation (SHG) signals of both the sampling pulse and test pulse. Second, the aperture of the BBO crystal for SFM is extended to a width of 21 mm, which can support a 65-ps time window in single-shot measurement.

2.

Principle of Fourth-Order Autocorrelation

To further explain the principle of fourth-order autocorrelation, we will compare it with second- and third-order correlations, which are used in the characterization of pulse duration and TC, respectively. In the second-order autocorrelation, the ultrashort pulse to be measured, which is shown in Fig. 1(a), is used as its own sampling pulse by splitting the pulse into two replicas $I(t)$ and $I(t-\tau )$. As a result, the corresponding autocorrelation signal is given by

Fig. 1

(a) The testing pulse with a postpulse, (b) the second-order autocorrelation signal, (c) the third-order autocorrelation signal, and (d) the fourth-order autocorrelation signal.

To measure an asymmetric pulse shape and the TC of an ultraintense laser pulse, third-order autocorrelation was proposed in 1993.¹⁷ First, the sampling pulse is obtained using the typical SHG of the test pulse. Then it is followed by a frequency nondegenerate SFM process, which is also a second-order nonlinear process. The corresponding signal can be expressed as

To solve these two problems, fourth-order autocorrelation is proposed here. In the fourth-order autocorrelation, the sampling pulse is generated by frequency-degenerate four-wave mixing processes, such as SD, XPW, and TG, which are third-order nonlinear processes. Then the fourth-order autocorrelation signal is obtained by the following SFM process. As a result, a third-order nonlinear process and a second-order nonlinear process make up the fourth-order autocorrelation, which can be expressed as

3.

Single-Shot FOAC

As single-shot characterization of the TC is necessary for most PW laser systems, which are run at low repetition rates or even single shot. Single-shot FOAC will be demonstrated here. Different from delay-scanning setup, both single-shot second-order autocorrelator and single-shot TOAC encode time into space using a special beam-crossing geometrical arrangement in the final SFM process.^19,29 In single-shot TOAC or TOCC, the two crossing beams have different central wavelengths, which can suppress the SHG scattering noise of the two incident pulses using dichroic shortpass filters. However, the large difference in wavelength will lead to a relatively large GVM in SFM process, which will seriously affect the time resolution of single-shot autocorrelator. The time resolution can be expressed as $l\times (\frac{1}{v_s\cos \theta }-\frac{1}{v_p\cos \alpha })$, where $l$ is the thickness of the nonlinear crystal, $v_s$ and $v_p$ are the group velocities of the sampling pulse and the test pulse, respectively, and $\theta$ and $\alpha$ are the crossing angles of the test pulse and sampling pulse, respectively. As a result, the thickness of the nonlinear crystal for SFM should be chosen to balance the high time-resolution and intense autocorrelation signal, which will affect the intensity improvement of the autocorrelation signal.

Different from single-shot TOAC or TOCC in the proposed single-shot FOAC, the sampling pulse has the same wavelength as the test pulse. Therefore, the influence of GVM on the time resolution is removed as shown in Fig. 2. Then a thicker nonlinear crystal can be used to obtain relatively high-correlation signal, which will result in a measurement with high dynamic range. Previous works have shown that the frequency-degenerate four-wave mixing processes XPW,^16,24 SD,^25,26 and TG²⁷ satisfy this requirement very well. These three processes achieve a cleaning pulse with the same wavelength. Among them, the XPW³⁰ and SD³¹ processes have been used to obtain seed pulses with high TC in ultrahigh intense laser systems. SD has the ability to improve the TC by seven orders of magnitude in single glass plates.²⁵ This is the highest TC enhancement achieved with a single-stage process. Furthermore, more than $500\mu \mathrm{J}$ first-order SD signal can be obtained in a glass plate.²⁵ As a result, only the SD process is explored in the following proof-of-principle experiments.

Fig. 2

The GVM in TOAC and FOAC.

4.

Optical Setup and Experiment

The optical setup of FOAC using the SD process is shown in Fig. 3. The input beam is split by a beam splitter with a 30:70 reflection/transmission ($R:T$) ratio. The transmitted beam is used for the clean sampling pulse generation based on the SD process, whereas the reflected beam is used as the test pulse. The transmitted beam is further split by a beam splitter with a 50:50 $R:T$ ratio. After the splitter, the two beams for the SD process are focused by two cylindrical lenses and overlapped in a glass plate with an overlapping area of $\sim 1\mathrm{mm}\times 13\mathrm{mm}$. Bright sidebands emerge when the two input laser beams overlap spatially and temporally. The first-order SD signal is picked out as the sampling pulse, which is then collimated by a concave cylindrical mirror. Both the high-energy sampling pulse and the test pulse are expanded using two beam expanders. Then they are focused into a wedge-designed nonlinear BBO crystal by two 200-mm focal-length concave cylindrical reflective mirrors. The 21-mm-wide BBO is cut with the angle of 80 deg and the two input beams intersect with a crossing angle of 63 deg in air. Finally, the FOAC signal is produced by SFM process in the BBO crystal, which is imaged and then recorded using a 16-bit sCMOS camera through a 4f lens pair. The sCMOS camera has $2048\times 2048\text{pixels}$, with a pixel size of $11\mu \mathrm{m}\times 11\mu \mathrm{m}$, and nearly single-photon ion detection sensitivity (Tucsen Photonics, Dhyana 95). To facilitate the analysis of the correlation signal, a strip-shaped density filter, with an approximately four orders of magnitude attenuation of the main pulse, and a coated wedge that introduces an attenuated reference replica signal below the original correlation signal are placed behind the BBO crystal. The strip-shaped density filter with a metallic coating has a fixed attenuation ratio about ${10}^4$ for the SFM signal around 400 nm, which has been calibrated before the experiment. The coated wedge would introduce a reference replica signal with about 70 times attenuation due to the back-and-front reflection on the surface of the wedge. Because of the diffraction, the edge effect would influence the signal near the edge of the strip-shaped density filter. However, the density filter is placed right behind the BBO crystal and the correlation signal is imaged from the BBO crystal to the sCMOS sensor by a 4f imaging system. By carefully adjusting the 4f imaging system, the influence of the diffraction effect would be weakened. A bandpass filter with a central wavelength of 400 nm is placed in front of the sCMOS camera to avoid noise from the fundamental incident pulses. The whole setup is compact and economical as a single-shot measurement apparatus.

Fig. 3

Schematic representation of the proof-of-principle experimental setup using FOAC for single-shot TC measurement. BS1 and BS2: two beam splitters. CCM1–CCM3: three concave cylindrical mirrors. DL1 and DL2: two time delay lines. GP: a glass plate for SD signal generation. BE1 and BE2: two beam expanders. DF: a strip-shaped density filter. CW: a coated wedge. L1 and L2: two lenses that form the 4f imaging system. BPF: a bandpass filter.

5.

Experimental Results and Discussion

A femtosecond Ti:sapphire regenerative amplifier ($8\mathrm{mJ}/1\mathrm{kHz}/40\mathrm{fs}$) is used to test the fourth-order autocorrelation method and the single-shot FOAC device at first. A high autocorrelation signal means a high dynamic range of the single-shot measurement. Considering the low-energy transfer efficiency of the SD process, laser pulses of $\sim 8\mathrm{mJ}$ with a diameter of about 10 mm are all guided into the experimental setup. After the first beam splitter, the 2-mJ laser pulse is used as the test pulse and the left 6-mJ is used for sampling pulse generation. Intense SD sidebands are generated when the two input beams intersect each other with a 1.3-deg angle in air and synchronously overlap in both time and space. The pulse energy of the first-order SD signal is measured to be $150\mu \mathrm{J}$ with an efficiency of 2.5%, which can support a high dynamic range single-shot TC measurement. The generated SD signal has a smoother spectrum and cleaner TC than the input pulses. More details about the generation of the sampling pulse based on the SD process can be found in our previous paper.²⁵

The sampling and test pulses are then focused onto a large wedge-designed BBO crystal. The BBO has a central thickness of 1.5 mm to increase the intensity of the correlation signal and to improve the measureable dynamic range at the expense of decreased phase-matching bandwidth. By capturing the spectrum of the sum frequency generation (SFG) signal, the bandwidth of the SFG process is estimated to be about 20 nm. If the test pulse has a broadband spectrum, the phase-matching bandwidth may not be broad enough to cover the whole spectrum in the SFG process with a thicker nonlinear crystal. Fortunately, the spectral bandwidths of the main pulse, the pre- or postpulses, and the ASE background or fluorescence noise usually have the same spectral bandwidth, and the SFG signal intensities of their responses to the phase-matching bandwidth narrowing during SFG process are equal. Then the generated SFG signal with a narrow bandwidth using a thicker nonlinear crystal would have negligible influence on the TC ratio. Because the time window is determined by the crossing angle and the diameter of the BBO, the BBO is designed to have a large aperture of 21 mm and a cutting angle of 80 deg, which supports the phase-matching angle of 32 deg in the crystal. Furthermore, in the experiment, the relatively large cutting angle reduces the noise from SHG signals of both sampling and test pulses.

By adjusting the time delay between the sampling and test pulses, the autocorrelation signal of the main pulse can be observed as a bright blue spot on a white paper. The bright blue spot moves along the horizontal direction as the time delay changes. This is because the overlapping zone between the sampling and main pulses of the test pulse changes continuously with the time delay. The intense correlation signal guarantees a high dynamic range of the measurement, which has to be preprocessed due to the limited dynamic range of the sCMOS camera. Several steps are involved in obtaining a high dynamic range TC measurement. First, the correlation signal from the main pulse of the test pulse is so intense that a strip-shaped density filter is added after the BBO crystal to attenuate the intensity of the main pulse directly. However, some strong prepulses or postpulses can still saturate sCMOS camera. In that case, a coated wedge is added, which will introduce a reference replica signal with about 70 times the attenuation in the shifted area of the sCMOS sensor. As a result, the original authentic intensity of the saturated main pulse and strong satellite pulses can be retrieved with the reference replica. Finally, the autocorrelation signal passes through a bandpass filter and is sent into the sCMOS.

Figure 4(a) shows the fourth-order autocorrelation signal obtained using the sCMOS camera when the exposure time is 1 ms. The intense signal is the original autocorrelation signal of which the strongest signal from the main pulse has already been attenuated by a strip-shaped density filter. The weaker signal line below without saturation is the attenuated replica signal introduced by the front-and-back reflection of the coated wedge, which can be used to obtain the original real intensity of the main pulse and the strong postpulses or prepulses.

Fig. 4

(a) The intensity distribution of the original signal and the replica on the sCMOS. The original signal and the replica are shown in the rectangle area marked with white-dashed lines. The part of the replica signal marked with red lines is zoomed for better visibility in the larger of the two red rectangles. (b) The intensity distribution of the original signal and the replica along the horizontal direction.

The bright correlation signal detected by the sCMOS camera covers an area of $\sim 20\times 1770\text{pixels}$ in the vertical and horizontal directions, respectively, where the time window is encoded into the horizontal direction. The time window can be calculated by $2\times l\times p\times \sin (\theta )/c$, where $l$ is the pixel size of the sCMOS sensor, $p$ is the pixel number relative to the center of the main pulse, $\theta$ is the crossing angle of the sampling pulse and the autocorrelation signal in air, and $c$ is the speed of light in air. As a result, the time window is $\sim 65\mathrm{ps}$ in this experiment and each $11\text{-}\mu \mathrm{m}\text{pixel}$ corresponds to $\sim 37\mathrm{fs}$. After summing up the intensity of the 20 pixels along the vertical direction and subtracting the background noise of the sCMOS, the intensity profile along the horizontal direction is obtained, as shown in Fig. 4(b). Obviously, pixel numbers between 1372 and 1516 or delay times between $-2$ and 3.2 ps are attenuated by the strip-shaped density filter. In the vertical direction, all the 20 pixels for the main pulse are all saturated of the original SFG signal. However, for those prepulses or postpulses in the original SFG signal, only a few pixels get saturated as shown in Fig. 4(a), but not all the 20 pixels are saturated. Therefore, even though the main pulse shows a saturation peak, the pre and postpulses do not have the same peak level, as shown in Fig. 4(b). The same method is used to process the data of the replica signal in Fig. 4(a), and the intensity profile of the weaker replica signal is obtained as shown in Fig. 4(b) (blue solid line). Thus the intensity of the saturated correlation peaks can be retrieved correctly.

The real intensity of the main pulse is obtained by multiplying the attenuation ratio of the strip-shaped density filter and the front-and-back reflection of the coated wedge. Furthermore, two shots of FOAC with shifted times are measured and combined together to further extend the time window. The final TC profile measured by the novel FOAC is shown in Fig. 5 (dotted line). The TC of the kHz laser pulses has a dynamic range of ${10}^8$, and the time window with two shots is extended to $\sim 106\mathrm{ps}$ with 48 and 58 ps in the front and back edges, respectively. The ${10}^{10}$ dynamic range at both ends of time window shows the background of sCMOS without correlation signal, which indicates good capability of the dynamic range measurement. To confirm the reliability of the FOAC results, the TC of the test pulse is also measured using a commercial delay scanning TOAC (Amplitude Technologies Inc., Sequoia-800). Obviously, both the experimental results are in good accordance with each other except for one prepulse at $-30\mathrm{ps}$ with $\sim {10}^{-4}$ intensity, labeled as “a,” which only appeared in the measurement profile using the Sequoia-800. Furthermore, we found a stronger postpulse at the mirror delay time of 30 ps with $\sim 0.7\times {10}^{-2}$ intensity, which is labeled as “A.” This means that the prepulse “a” is a ghost pulse introduced by postpulse “A” during the TOAC measurement by the Sequoia-800. It should be noted that the ghost prepulse “a” is not detected by the proposed single-shot FOAC, which shows much higher measurement fidelity than TOAC. As previously mentioned, this is because the sampling pulse of our single-shot FOAC is generated by a third-order nonlinear process, which has a cleaner TC compared with the sampling pulse generated by SHG in the Sequoia-800 based on TOAC.

Fig. 5

TC results of a Ti:sapphire regenerative amplifier measured using the Sequoia-800 (solid line) and our single-shot FOAC equipment (dashed line).

The time resolution is another important parameter in TC measurement. Although the time step can be as short as 10 fs, the time resolution of a delay-scanning TOAC is limited to hundreds femtoseconds by the large GVM between the test pulse and its SHG sampling pulse. In all previous works, the time resolution of single-shot TOAC or TOCC measurements was always wider than 500 fs due to GVM and the limitation of detectors. Because the sampling pulse has the same central wavelength as the test pulse in this single-shot FOAC, the GVM is not a problem. Ideally, a time resolution of $\sim 37\mathrm{fs}$ can be obtained when considering an $11\mu \mathrm{m}\times 11\mu \mathrm{m}$ pixel size. The spatial resolution of the 1:1 4f imaging system, which is used to map the correlation signal from the SFM crystal to the sCMOS sensor, limits the time resolution of this proof-of-principle experiment to $\sim 160\mathrm{fs}$. By enlarging the main peak pulse in Fig. 5 with a linear intensity scale, the correlation profiles by the Sequoia-800 and by single-shot FOAC are shown in Fig. 6, where the pulse duration of the test pulse is $\sim 40\mathrm{fs}$. A high spatial resolution of the 1:1 4f imaging system with a shorter focal length or larger NA is expected to improve the time resolution of this FOAC. A magnified 4f imaging system can also improve the time resolution; however, the time window will be narrowed at the same time. A wider time window can be obtained with a reduced 4f imaging system and a larger camera sensor.

Fig. 6

Correlation traces by the TOAC and FOAC with a linear plot of intensity.

To further test the dynamic range capability of our method, we also measured the TC of another laser system using the single-shot FOAC, in which the laser pulse with the parameters of $20\mathrm{mJ}/10\mathrm{Hz}/40\mathrm{fs}/800\mathrm{nm}$ is used in the experiment. In comparison to the kHz system, both the obtained SD signal and the test pulse have higher pulse energies of $450\mu \mathrm{J}$ and 4 mJ, respectively. As a result, a higher SFM signal can be obtained, which makes it possible to further enhance the dynamic range. The original correlation signal obtained by the sCMOS is shown in Fig. 7(a), where two strip-shaped density filters are used to attenuate the main peak signal. A 1-mm glass plate is used to introduce a postpulse for the test pulse, the signal of which is also attenuated by a strip-shaped density filter. The coated wedge is unnecessary in this measurement. Figure 7(b) shows the retrieved TC curves obtained by both the single-shot FOAC and the Sequoia-800. By comparing the intensity of the main peak pulse and the sCMOS noise, a dynamic range of ${10}^{11}$ is obtained, which, to date, is the highest dynamic range observed for a single-shot TC measurement. In the experiment, to increase the intensity of the correlation signal, the sampling pulse is not expanded by the beam expander to keep its intensity in the overlapping area with the test pulse. As a result, the diameter is not as large as in the above first experiment and the time window is only about 50 ps. Interestingly, the ghost prepulse “a” introduced by the postpulse “A” measured by the Sequoia-800 is not detected by the FOAC again. To be mentioned, the intensity of postpulse “A” introduced by the 1-mm glass plate is measured to be about $0.5\times {10}^{-3}$ at 10.5 ps. The second postpulse at 21 ps is measured to be about $3.2\times {10}^{-7}$, which is in good agreement with the calculated value about $2.5\times {10}^{-7}$. The intensity of the second postpulse is too weak to be observed.

Fig. 7

The measurement results with a dynamic range of ${10}^{11}$ by the FOAC. (a) The correlation signals on the sCMOS detector. (b) The comparison of the TOAC and FOAC measurement results. The strip-shaped density filters are used in the region of the dashed-line rectangle.

As well as for increasing the correlation signal intensity and improving the detector sensitivity, suppressing the scattering noise is also important for a high dynamic range measurement of ${10}^{11}$. Because the sampling pulse has the same central wavelength as the test pulse in the single-shot FOAC, the correlation signal obtained by SFM has the same central wavelength as the SHG signals of both the sampling and test pulses. Then the noise introduced by the SHG signals of the sampling and test pulses, which cannot be blocked by a spectral filter, needs to be analyzed. It is well known that the SHG process is a second-order optical parametric process that is sensitive to the phase-matching condition. Then a special cutting angle of the BBO is designed to weaken the SHG generation. In the experiment, the crossing angles of the test and sampling pulses with respect to the optic axis of the BBO crystal are 99 deg and 61 deg, respectively, which are very different from the best phase-matching angle, i.e., 29.2 deg. This simple design makes the SHG scattering noise in this single-shot FOAC negligible. In the experiment, while blocking either the sampling pulse or test pulse, the intensity of the other SHG scattering noise is captured by the sCMOS camera. The sCMOS background noise is also obtained by covering the shutter of the sCMOS. The results are shown in Fig. 8 with different types of lines. The scattering noises from the SHG signals of both incident pulses are at the same scale as the background noise of the sCMOS camera. The results clearly prove the capability of ${10}^{11}$ dynamic range measurement using our single-shot FOAC system.

Fig. 8

The detector noise from the sCMOS and scattering noise from the SHG signals.

Finally, the single-shot FOAC is tested using a high TC laser pulse sampled from a PW laser pulse system.³² The sample pulses have a pulse energy of 10 mJ, a repetition rate of 1 Hz, a pulse duration of 40 fs, and a central wavelength of 800 nm. Two strip-shaped filters are included to reduce the main peak correlation signal in the experiment. The attenuation ratio of the filter is so large that only the main pulse can be observed and the information near the main pulse is lost, which would miss dynamic ratio data within 5-ps time window around the main pulse. In the future, we will try to solve this problem by fabricating a step variable density filter. Figure 9(a) shows the original data obtained by the single-shot FOAC. To make the weak signal more visible, the range of the color bar is adjusted to between 100 and 200. The signal is shown in Fig. 9(b). The TC curves of the sample pulse measured by the single-shot FOAC and Sequoia-800 are presented in Fig. 9(c). It can be seen that the two measurements in the time window from $-40$ to 10 ps are quite consistent with each other. A single-shot TC measurement of a PW laser system with a dynamic range of about $2\times {10}^{10}$ and a time resolution of about 160 fs is obtained, which also shows the capability of the ${10}^{11}$ dynamic range. The correlation signal intensity is dependent on the intensities of the two incident pulses in the nonlinear crystal. The intensity profile of the two input beams on the BBO crystal is important for measurement accuracy of the dynamic range. It should be noted that the beam profile of the SD signal for sampling pulse after the third-order nonlinear process is uniform around the focused plane (the surface of the BBO crystal). Since the test pulse is picked out from the edge of the laser beam, the intensity distribution across the beam will not be uniform. The relatively weaker beam focused from the edge part will induce a weakened SFG signal, which may be the reason why there is large difference between the TOAC and FOAC for the data beyond 10 ps. Unfortunately, we did not measure the beam profile of the test beam on the BBO crystal this time. We expect to monitor the beam profiles of the two input beams on the SFG nonlinear crystal using CCD cameras in the future. Then, their intensity distributions will be used to correct the final results.

Fig. 9

The measurement results of the single-shot FOAC and delay-scanning TOAC (Sequoia-800). (a) The correlation signals on the sCMOS detector. (b) The correlation signals on the sCMOS detector when the range of the color bar is adjusted to make the weak signal more visible. (c) The comparison of the TOAC and FOAC measurement results. The strip-shaped density filters are used in the region of the dashed-line rectangle.

6.

Conclusion

We have proposed a simple fourth-order autocorrelation method for single-shot TC measurement with higher time resolution and better fidelity than typical third-order autocorrelation or cross correlation methods. A single-shot FOAC is developed based on the SD process to generate clean sampling pulses. The proof-of-principle experimental results show a dynamic range of $\sim {10}^{11}$, a time resolution of $\sim 160\mathrm{fs}$, and a time window of 65 ps capabilities of this single-shot FOAC. Higher dynamic ranges can be obtained in the future by increasing the thickness of the SFM crystal and improving the sensitivity of the detector. A higher time resolution or a wider time window can be achieved using a magnified or reduced 4f mapping setup in front of the camera. The method and the corresponding single-shot FOAC device will benefit the improvement of PW laser systems and many important ultrahigh intense laser–matter interaction research activities such as the generation and acceleration of protons and ions, laboratory astronomy, fast-ignition inertial confinement fusion, and the generation of secondary sources of high-intensity $\mathrm{\gamma }$ rays.