In previous studies, many optical diagnostic techniques have been developed to measure the parameters of laser-produced underdense plasmas. Optical diagnostics can generally be classified into passive self-emission detection and active probe laser detection. In this study, we focus on the experimental approaches with active probe laser detection. By injecting a probe beam into the plasma region, changes in the phase or intensity of the probe beam reveal plasma information^[1]. Based on this principle, various optical diagnostic methods, such as interferometry^[2], shadowgraphy^[3], and schlieren imaging^[4], have been developed and play essential roles in diagnosing plasma across specific parameter ranges. In order to diagnose the ultrafast process, ultrafast gated devices were commonly used to characterize plasma generated by laser-target interactions, capturing its state at specific moments in time^[5]. In recent years, owing to the ability of optical diagnostics to provide direct insights into the plasmas under specific conditions, researchers have increasingly employed these ultrafast diagnostic devices for plasma-related experiments^[6–9]. However, constrained by the diagnostic detection methods, the experiments could only obtain a few discrete images within single-shot experiments, which limited data collection. Achieving multi-images across multiple time points would have necessitated multiple experimental shots, which could cause variability in experimental conditions and compromise data reliability.

Obtaining plasma physics information as much as possible within single-shot experiments is crucial for diagnosing the laser-produced plasma^[10–12]. Recognizing that an optical streak camera (OSC) is capable of recording the temporal evolution of one-dimensional (1D) spatial emissions along a slit within the entire observation window^[13], we integrated the OSC with a gated optical intensifier (GOI)^[14]. This integrated approach enables the acquisition of critical information on plasma density evolution, plasma velocity, and plasma morphology within single-shot experiments. Furthermore, the GOI provides two-dimensional (2D) data for the OSC, enhancing the completeness of the spatial and temporal diagnostics. This method can be successfully applied in high energy density experiments, such as laboratory astrophysics^[15–17] and inertial confinement fusion studies^[18,19].

In this paper, experiments performed at the Shenguang II (SG II) facility are presented, where a scaled-down plasma jet was generated using nanosecond (ns) drive beams. By employing an OSC and GOIs, we obtained physical information such as jet density, jet velocity, jet morphology, and the continuous evolution of plasma behavior across the entire observation window.

The optical diagnostics are performed at the SG II laser facility. Figure 1 shows a schematic diagram of the designed optical path. The specifications for the optical components and laser parameters are displayed in Table 1. The entire optical system consists of a probe light system, an imaging system, a Nomarski interference system, a shadowgraph system, and three detectors. A probe beam with a wavelength of 527 nm and a duration of 25 ns passes through the region of interest. This probe carrying the plasma information is collected by the first imaging lens (L1) with a focused length F1=300mm, providing a magnification of 2×. The beam is then delivered to the final detectors using the second imaging lens (L2) with F2=250mm. After the imaging system, the probe is divided into two paths. One is for the Nomarski interferometry table, where GOI and OSC are used as the detectors. The other one is for the shadowgraphy table, where GOI is used as the detector. GOIs are used to obtain 2D interferograms and shadowgraphs at different time points, while the OSC is used to obtain 1D spatially and temporally resolved interference images. Additionally, in order to reduce the noise from the laser interaction. A 380 nm long-pass optical filter is placed in the light path to block scattered light from the third-harmonic 351 nm. A narrow filter is also placed after the long-pass optical filter to allow only the probe laser to pass.

The core of the entire optical system lies in the Nomarski interference system^[20]. For incident linearly polarized laser light, after passing through the Wollaston prism, it is split into ordinary (o) and extraordinary (e) beams that are polarized in mutually perpendicular directions. A linear polarizer or a half-wave plate is used to rotate the polarization direction to match the optical axis of the Wollaston prism. The two output beams form a certain angle with each other. After passing through an analyzer, the two beams meet the interference condition of having the same polarization direction, and interference fringes are generated in the region where the two beams overlap. A backlight shadow-like image is formed in the areas where the beams do not overlap. By adjusting the position of the Wollaston crystal in the optical path, the spacing of the interference fringes can be varied. The interference region is then imaged into the field of view of either the OSC or GOI by selecting an appropriate magnification in the imaging light path. Interferometric imaging enables quantitative measurement of spatial electron density distribution through analysis of fringe displacement. In contrast, shadowgraphy was experimentally employed to investigate plasma morphology, where intensity variations in the acquired images are dependent on the second-order derivative of the plasma refractive index.

As mentioned earlier, the spatial distribution of electron density can be inferred from the results of the interferogram. The electron density can be deduced by determining the displacement of interference fringes. In the Nomarski interference system, the displacement of interference fringes corresponds to the change in spatial phase, which in turn is caused by a change in refractive index. This enables the establishment of a relationship between fringe displacement and the plasma refractive index: Δϕ=2πD=∫(kplasma−k0)dl=∫(n−1)ωcdl,(1)where D represents the number of fringe shifts, from before to after the shot. Δϕ is the corresponding phase shift of the fringes, λ denotes the wavelength of the probe beam, and nc represents the critical plasma density corresponding to the probe beam’s wavelength. The plasma refractive index n can then be derived using the electron density formula n2=1−ωp2ω2=1−nenc.(2)

For low-density plasma, where ne/nc≪1, the refractive index n can be simplified using a Taylor expansion as n=1−ne/2nc. Substituting this expression into the phase shift calculation formula, ∫nedl=2Dncλ. Under the assumption of cylindrical symmetry, Abel inversion can be applied to obtain the integrated values, yielding the spatial electron density distribution of the plasma^[21]: ne=1π∫rRd(2Dncλ)dydyy2−r2=1π∫rRdFdydyy2−r2.(3)

For the physical configuration of laser-material interaction, as shown in Fig. 2(a), a cylindrically symmetric plasma forms near the target surface. The probe laser passes along the x-axis through the plasma, so the fringe shift reflects the path-integrated values along the x-axis. For the GOI, a 2D distribution of fringe shifts is obtained, and the cylindrical symmetry of the plasma jet generated by the laser-target interaction implies that the cross-section of the jet is circular. The upper limit of integration required for Abel inversion can be determined from the radius of the circle corresponding to the fringe curvature in the 2D image.

The 1D electron density distribution obtained by the OSC depends on the path integration across the plasma cross-section. Unlike the GOI, the OSC lacks 2D morphological information, and therefore, cannot directly provide the radius R for path integration. Thus, it is assumed that the low-density plasma exhibits spherical symmetry, and the fringe curvature boundary in the OSC image is used as a substitute for R in path integration. The low-density plasma generated in laser-planar target interaction experiments typically exhibits spherical symmetry, satisfying the assumed conditions. The combination of OSC and interferometric imaging enables the acquisition of spatiotemporally resolved plasma density information as a function of spatial position x and temporal evolution t in single-shot laser-target experiments.

To validate the reliability of the Abel inversion code, a numerical benchmark was implemented as follows. 1) A spherical plasma with radius R=1mm is generated by the laser-target interaction. Its electron density distribution follows ne/nc=1−r2, where nc denotes the critical density, with the corresponding fringe shift governed by D(z)=2(1−z2)3/2/3λ. 2) The spatial distribution of fringe shifts D(z) was discretized into varying resolutions (10, 20, and 40 equal parts) and input into the Abel inversion code. Numerical results demonstrate that finer segmentation progressively improves the convergence of the reconstructed electron density ne(z) toward the analytical solution. As shown in Fig. 3, when the segmentation exceeds 40 intervals, the numerical solution aligns closely with the analytical expression, with the discrepancy falling within acceptable limits (Δne/ne<2%).

In the experiment, in order to alter the segmentation, the imaging system’s magnification ratio can be tuned. Increasing the magnification improves segmentation resolution (smaller subdivisions per pixel) but reduces the field of view (FOV). Consequently, experimental configurations necessitate a trade-off between segmentation and FOV size.

This modified optical diagnostic has been applied in recent laboratory astrophysical experiments, where supersonic plasma flow is produced to mimic the ejecta sweeping up the surrounding medium. As shown in Fig. 1, two facing CD planes separated by 4.5 mm are fixed at TCC. The four beams of the SG II laser, with each beam having an energy of 250 J and a pulse width of 1 ns, produce square waves, giving an intensity of 1015W/cm2. Typical results obtained from optical diagnostics are shown in Fig. 4. The GOI is set at 2 ns with an integration window of 120 ps. The OSC captures 1D spatial resolution along the horizontal centerline of the interferogram, as shown in Fig. 4(a). From the curvature of the fringes, it can be observed that a low-density plasma forms near the target point around 1 ns before the zero-time of irradiation; the temporal zero reference (t=0) was synchronized to the trailing edge of the incident laser pulse. At 2.2 ns after irradiation, this low-density plasma expands to the opposite plane target, aligning well with the GOI results.

The OSC image displays arcuate fringes in the central region around 4 ns after irradiation. Since the OSC provides only 1D spatial resolution, it is challenging to intuitively link these arcuate fringes to specific physical phenomena in the laser-plasma interaction. With the 2D imaging capability of the GOI, we can more readily identify the physical source of these arcuate fringes. As shown in Fig. 4(b), around 10 ns after the interaction between the laser and one side of the Cu planar target, knot signals appear in the low-density plasma region. Building upon the work of Lei et al.^[22], we analyzed the formation mechanism of the observed knots; the jet’s internal pressure balance is governed by three mechanisms: ram pressure, thermal pressure, and magnetic pressure, which exhibit distinct gradient directions. At different positions along the jet, transitions between these dominant pressure mechanisms generate anisotropic internal shocks. These separated knots result from anisotropic velocities, forming internal shock waves within the jet. The propagation of these shock waves sweeps material surrounding the jet toward the jet center, forming knots^[23,24]. These arcuate fringes correspond to the time evolution of the knots in 1D horizontal space.

Figure 4(c) shows the results of the backlit interferogram at 2 ns after irradiation, where the interference fringes are bent due to the plasma’s effect. The phase shifts occur as the probe light passes through this region, changing its optical path length, ultimately leading to fringe shifts compared to the non-irradiated state. The low-density plasma boundary appears nearly spherical, which is also the basis for time-evolved density Abel inversion. Figure 4(d) presents the backlit shadowgraphy image at 2 ns after irradiation, where the shadowed contour of the high-density plasma matches that of the interferogram.

In addition to obtaining the plasma morphology evolution through GOI and OSC, we can also calculate the plasma electron density from the movement of the interference fringes. Based on the Abel inversion method previously mentioned for OSC, the bending of the 1D interference fringes along the z-axis observed by OSC reflects changes in the electron density integral along the x-axis at y=0. As the plasma evolves, it gradually expands, and the degree of fringe bending at different positions varies. Using the Abel inversion, we can obtain the spatial electron density of the plasma. The calculation can only be performed at positions where fringe bending occurs, so Fig. 5(a) only shows the electron density inversion from the region where the fringes bend (orange region) to the area where the fringes disappear. The disappearance of interference fringes in the OSC corresponds to the region at x=4.2–6.5mm on the GOI in Fig. 4(c). The Nomarski-interferometry-based imaging method generates interference by overlapping the ordinary ray through the unperturbed region with the extraordinary ray region passing through the probed plasma. When the e-ray traverses the plasma, the fringe shift occurs according to Eq. (1). However, two factors explain the loss of fringes: 1) spatial coherence limit: high plasma density in the probed region induces a fringe shift exceeding the spatially coherent area, resulting in the disappearance of interference fringes; 2) density gradient effect: the steep density gradient within the jet (compared to the outer low-density plasma) produces ultra-dense fringes that are unresolvable, even if spatial coherence is preserved. The evolution of the 1D spatial electron density with time is shown in Fig. 5(b).

Additionally, using the Abel inversion, we can obtain the 2D spatial distribution of electron density at 2 ns, as shown in Fig. 6(a). The region with a density exceeding 4×1019cm−3 corresponds to the areas in Fig. 5(c) where the fringes are denser or where the interference fringes are missing, making the phase wrapped by Fourier transform filtering difficult to resolve. The red dashed line in the figure corresponds to the position of the OSC slit. As shown in Fig. 6(b), the gray area represents the 1D horizontal electron density distribution in the central region, derived from the 2D image obtained by GOI. The red dashed curve quantifies the variation in error bars arising from the position of the OSC slit. The blue solid line represents the plasma density distribution obtained by the Abel inversion from the fringe bending information of OSC at 2 ns, as shown in Fig. 5(b). Both Figs. 6(a) and 6(b) use the left-side target surface as the origin of the spatial coordinates. The horizontal electron density distribution obtained by OSC shows consistency with the results from GOI in terms of magnitude and trend. The low-density plasma electron density obtained by GOI exhibits a peak at 0.29 mm, after which it rapidly decreases. However, no such process is observed in the OSC results. This discrepancy is mainly due to the fact that GOI’s density inversion is based on a cylindrical symmetry assumption, whereas OSC only provides 1D spatial resolution. The electron density is calculated based on the assumption of spherical symmetry, using the bending boundaries of the interference fringes as the radius of the plasma sphere at different time points.

In conclusion, using a combined OSC and GOI as detectors, we measured the plasma density evolution, plasma jet velocity, and jet morphology in a single-shot experiment. In single-shot experiments, GOI complements the 1D information missing in OSC, assisting in the diagnosis of plasma morphology evolution in two dimensions, thus facilitating a more intuitive analysis of plasma evolution. The results from OSC allow for the reconstruction of the continuous plasma evolution process across the entire observation window. This can address the issue encountered with GOI, which requires multiple shots to capture plasma morphology at different time points, and can avoid introducing uncertainties of experimental conditions in different shots. The dual-diagnostic technique combining OSC and GOI proposed in this paper has been validated as a reliable and novel method for probing the continuous evolution of plasma. It could also be applied in laboratory astrophysical experiments to detect previously unexplored transient processes such as the evolution of plasma density during the collisionless shock, offering novel insights into plasma dynamics.