Single-shot 3D characterization the spatiotemporal optical vortex via a spatiotemporal wavefront sensor (STWFS)

The advent of spatiotemporal wave packets (STWPs), represented by spatiotemporal optical vortices (STOVs), has paved the way for the exploration in optics and photonics. To date, despite considerable efforts, a comprehensive and efficient practical means to characterizing wave packets with such complex structures is still lacking. In this study, we introduced a new method designed to achieve high-precision and high-throughput spatiotemporal wave packet measurements using a user-friendly set up. This method is based on a quadriwave lateral shearing interferometric wavefront sensor that utilizes wavelength division multiplexing, termed the “spatiotemporal wavefront sensor (STWFS).” Using this method, we have fabricated a compact prototype with 295 * 295 spatial pixels * 36 wavelength channels of 0.5 nm spectral resolution in a single frame. This STWFS enabled, for the first time, single-shot self-referenced spatiotemporal three-dimensional (3D) optical field characterizations of STOV pulses with transverse orbital angular momenta L of 1 and 2, and obtained the dynamic visualization of the focused propagation of STOV pulses. Furthermore, the STWFS provides a 1.87 nm (0.95%) root mean square (RMS) absolute accuracy for spatiotemporal phase reconstruction. This achievement represents the highest performance compared with other three-dimensional spatiotemporal metrology methods. As a spatiotemporal optical field characterization method, the STWFS offers ultrafast 3D diagnostics, contributing to spatiotemporal photonics and broader applications across different fields, such as light-matter interactions and optical communications.

💡 Research Summary

The paper introduces a novel single‑shot, self‑referenced method for three‑dimensional (3‑D) characterization of spatiotemporal optical vortices (STOVs), termed the spatiotemporal wavefront sensor (STWFS). STOVs are a class of spatiotemporal wave packets (STWPs) that carry transverse orbital angular momentum (OAM) and have attracted interest for applications ranging from ultrafast imaging to optical communications. Existing metrology techniques either require multiple shots, external reference beams, or suffer from limited spatial/spectral resolution and high computational load, making them unsuitable for low‑repetition‑rate, high‑power laser systems.

The STWFS combines a quadriwave lateral shearing interferometer with wavelength‑division multiplexing achieved via a two‑dimensional diffraction grating and a rotated narrow‑bandpass filter (NBPF). The incoming broadband pulse is diffracted into multiple orders (Mx, My = ±1, ±3, ±5), each passing through the NBPF at a slightly different incidence angle, which shifts its central wavelength. After a propagation distance that fully separates the sub‑pulses, a second 2 × 2 grating inside the wavefront sensor creates four laterally sheared copies of each spectral channel, generating an array of interferograms on a single camera. Because each wavelength is mapped to a distinct spatial region, the interferograms can be cropped and processed independently.

Phase retrieval uses a Fourier‑transform integration (FTI) algorithm to obtain the relative phase across the sheared wavefronts for each wavelength. Since this yields only inter‑spectral relative phases, an absolute spectral phase is measured at a single spatial point using frequency‑resolved optical gating (FROG). The absolute phase is then stitched to the relative phases, producing a full 3‑D data cube (x, y, λ). An inverse Fourier transform converts the spectral data into the time domain, delivering the complete electric‑field distribution E(x, y, t). The system records 295 × 295 spatial pixels and 36 wavelength channels (0.5 nm resolution) in a single frame, achieving a reconstruction speed of about one second per data set.

Experimental validation employed a Ti:sapphire laser (central wavelength ≈ 800 nm) and a 4f spatial‑spectral pulse shaper with a spatial light modulator (SLM) to generate STOV pulses with topological charges L = 1 and L = 2. The STWFS measured the spectrally resolved intensity and phase, which matched independent spectrometer measurements (RMS error ≈ 3.6 %) and the phase programmed on the SLM (RMS error ≈ 0.95 %). The system also visualized the focused propagation dynamics of the STOVs in real time. Compared with other 3‑D metrology methods (TERMITES, FALCON, CASSI, BBSSP, etc.), the STWFS uniquely satisfies all three criteria—single‑shot, self‑referenced, and high‑accuracy—while offering low computational complexity (≈ 0.3 % phase residual) and a compact footprint (20 × 10 × 10 cm).

The authors acknowledge that absolute spectral phase still requires a separate FROG measurement, but suggest that future integration of FROG within the STWFS or advanced multi‑point phase‑retrieval algorithms could eliminate this dependency. Moreover, by increasing the number of NBPF channels and optimizing the grating design, the spectral channel count could be scaled to several hundred, enabling characterization of even more complex STWPs.

In summary, the STWFS provides a high‑precision, high‑throughput, and user‑friendly platform for ultrafast 3‑D optical field diagnostics. Its ability to capture the full spatiotemporal electric field of STOVs in a single shot opens the door to closed‑loop adaptive control of spatiotemporal wave packets, benefiting fields such as strong‑field physics, nonlinear optics, metasurface engineering, and high‑capacity optical communications.