Spatiotemporal Measurement of Nanosecond Pulses Based on Electro-Optic Deflection Diffractive Imaging

Objective As the spatiotemporal distribution of ultrashort pulses affects the energy density of high-energy pulses, spatiotemporal complex amplitude measurement technology has been widely applied in frontier research fields such as inertial confinement fusion. For narrowband nanosecond pulses that cannot achieve high-precision characterization by wavelength-resolved indirect methods, there is an urgent need for single-shot multi-frame spatiotemporal complex amplitude imaging technology capable of achieving high temporal resolution for nanosecond pulses. Methods We propose a single-shot multiplexed angle-encoding diffractive imaging technology for narrowband pulses based on an electro-optic deflection crystal, as shown in Fig. 3(a). The pulse to be measured, denoted as E (x,y,t ), is a nanosecond pulse with a full width at half maximum (FWHM) of 4 ns. The rising edge of the high-voltage pulse voltage is synchronized with the temporal profile of the nanosecond pulse via the electro-optic deflector (EOD). Under different voltage values, the complex amplitudes of the nanosecond pulse at different time slices undergo distinct angular deflections, thereby spatially separating the temporal optical field information. Then, by free-space propagation and encoding modulation, a single-frame diffractive pattern containing superimposed intensity distributions from multiple time slices is recorded on the detector. Based on the single-shot diffractive pattern and angle-encoding multiplexed diffractive imaging algorithm shown in Fig. 2, the complex amplitude optical field information of each time slice can be reconstructed from the multiplexed superimposed diffractive pattern, thus realizing precise measurement of the time slices of the nanosecond pulse. Furthermore, near-field and far-field precise spatiotemporal distributions of the nanosecond pulse can be obtained through optical field propagation. Results and Discussions The recorded diffractive patterns are shown in Fig. 4. Figure 4(a) displays the intensity distribution without high-voltage application, while Fig. 4(b) presents the pattern under the application of the ultrafast high voltage power supply, showing spatial deflection along the direction corresponding to linear refractive index variation of the crystal. Each spatial position corresponds to the diffractive pattern intensity at different time slices. Under high-voltage application, the multiplexed superimposed diffractive pattern in Fig. 4(b) enables the reconstruction of amplitude and phase distributions for ten modes within the nanosecond pulse. The reconstructed amplitude and phase profiles are presented in Figs. 5(a) and 5(b) respectively. The temporal resolution between frames is 0.4 ns, with the amplitude of the optical field at different time slices corresponding to distinct spatial positions. Within the time range from-2.0 to 1.6 ns, the energy variation follows a Gaussian distribution. Figures 5(a1)‒ (a10) reveal significant differences in spatial intensity distributions across time slices, allowing quantitative analysis of spatiotemporal distortion in the optical field. Corresponding phase information for each time slice is shown in Figs. 5(b1)‒ (b10). These phase reconstructions permit detailed examination of wavefront evolution during propagation, enabling identification and characterization of wavefront distortion phenomen Based on the reconstruction results, the amplitude distributions at different spatial cross-sections are further calculated by adopting the free-space propagation equation, enabling analysis of energy flux variations during high-energy pulse propagation. Figures 6(a) ‒ (c) display the pulse propagation at t=-2.0 ns, t=-0.4 ns, and t= 1.6 ns respectively. Each frame is separated by 200 mm, showing propagation from z= 0 to 1800 mm. The sequence clearly resolves the transition from field focusing to divergence, with high-frequency components at the focal plane accurately reconstructed. Thus, this method enables precise computational imaging of both near-field and far-field distributions for nanosecond pulses at different time slices. To further evaluate the spatial resolution and phase measurement accuracy of the proposed method, we select a standard amplitude resolution target (USAF1951) and a phase step target as test samples for precise optical field reconstruction, as shown in Fig. 7. Figure 7(a) displays the reconstructed amplitude resolution target, where Group 4 Element 4 is clearly resolved, indicating a spatial resolution better than 22.1 µm. Figure 7(b) presents the one dimensional intensity profile along the red dashed line marked in Fig. 7(a). Figure 7(c) shows the reconstructed phase step target. The measured phase difference between regions A 1 and A2 averages 1.17 rad, deviating from the designed value (1.2 rad) by less than 2.5%. For vortex beams with phase singularities, the optical fields are reconstructed in experiments by employing both SS-MAEUPI and Ptychography methods. Figures 8(a) and 8(b) show the amplitude distributions reconstructed by SS-MAEUPI and ptychography respectively, while Figs. 8(c) and 8(d) display their corresponding phase distributions. Comparison with the scanning method indicates that SS-MAEUPI achieves accurate phase reconstruction precision for optical fields with phase singularities. Conclusions Based on multiplexed encoding diffractive imaging combined with an electro-optic deflection crystal, we propose a single-shot multiplexed angle-encoding diffractive imaging technology for narrowband pulses. This method deflects the temporal information of narrowband nanosecond pulses to different spatial positions, and then reconstructs the complex amplitude information of different time slices by combining the multiplexed complex amplitude iterative algorithm. In the experiment, the amplitude and phase measurements of ten time slices of 4 ns pulses are realized, with a temporal resolution better than 0.4 ns. Furthermore, the changes in pulse energy and wavefront are precisely analyzed. Additionally, it is verified that the spatial resolution is better than 22.1 µm, with the phase measurement error of less than 2.5%. Therefore, this method can be adopted to analyze the distortion of energy and wavefront of high-energy nanosecond pulses during propagation, providing an effective diagnostic technology for the transient changes of high-power density physical phenomena. It has broad application prospects in power density improvement of narrowband high-energy pulses and imaging research on ultrafast phenomena.