An optical vortex, characterized by a helical phase structure of the form
Photonics Research, Volume. 13, Issue 6, 1776(2025)
Perfect spatiotemporal optical vortices Spotlight on Optics
Recently, spatiotemporal optical vortices (STOVs) with transverse orbital angular momentum have emerged as a significant research topic. While various STOV fields have been explored, they often suffer from a critical limitation: the spatial and temporal dimensions of the STOV wavepacket are strongly correlated with the topological charge. This dependence hinders the simultaneous achievement of high spatial accuracy and high topological charge. To address this limitation, we theoretically and experimentally investigate a new class of STOV wavepackets generated through the spatiotemporal Fourier transform of polychromatic Bessel–Gaussian beams, which we term as perfect spatiotemporal optical vortices. Unlike conventional STOVs, perfect STOVs exhibit spatial and temporal diameters that are independent of the topological charge. Furthermore, we demonstrate the generation of spatiotemporal optical vortex lattices by colliding perfect STOV wavepackets, enabling flexible manipulation of the number and sign of sub-vortices.
1. INTRODUCTION
An optical vortex, characterized by a helical phase structure of the form
Recently, spatiotemporal optical vortices (STOVs) defined in the space-time domain have garnered increasing attention due to their ability to carry unique transverse OAM of light [16–19]. The development of STOVs can be traced back to early predictions [20,21] and has recently been experimentally demonstrated through both nonlinear [22] and linear methods [23,24]. The successful generation of STOV wavepackets has catalyzed further exploration into spatiotemporal topology [25,26], harmonic generations [27–29], and other forms of matter waves [30]. This progress has led to the emergence of novel spatiotemporal optical wavepackets [16,17], including spatiotemporal Bessel [31,32], crystal [33], and Laguerre and Hermite Gaussian wavepackets [34]. However, the beam radii of these conventional optical vortices—whether spatial vortex beams or STOV wavepackets—strongly depend on their topological charge number, which can hinder their applications in many cases. For instance, this dependence presents challenges in coupling STOVs into a single optical fiber for mode-division multiplexing [35,36], in the angular momentum transfer to particles for optical trapping and manipulation [37], and in the OAM-dependent divergence that accompanies the increase in the mode index for optical transmission [38].
Consequently, the concept of perfect optical vortices has been proposed to overcome the above limitations, as their beam radius is independent of the topological charge number [39,40]. This feature introduces an unprecedented paradigm for applications in ultra-secure image encryption [41], high-dimensional quantum teleportation [42], trapping particles [43], and information encoding and transmission [38]. Very recently, Ponomarenko
Sign up for Photonics Research TOC Get the latest issue of Advanced Photonics delivered right to you!Sign up now
In this work, we report the experimental generation of perfect spatiotemporal optical vortices, where the ring size in both space and time remains independent of the topological charge. We theoretically and experimentally demonstrate that the proposed perfect STOV wavepackets are the spatiotemporal Fourier transforms of polychromatic Bessel–Gaussian beams based on space-time duality. Experimental results are in excellent agreement with theoretical predictions. Furthermore, we show that the spatiotemporal collision of two perfect STOVs produces STOV lattices, where the number of sub-vortices and symbols can be freely controlled.
2. THEORETICAL ANALYSIS AND NUMERICAL SIMULATIONS
The perfect STOV wavepacket in the spatiotemporal domain (
In the spatial domain, spatially perfect vortex beams can be generated through the Fourier transform of spatial Bessel beams [46]. Motivated by this, the perfect STOV can be generated by the Bessel Gaussian mode spatial frequency–frequency domain (
The above equation represents the complex amplitude of perfect STOV with topological charge of
Equations (1)–(3) suggest that perfect STOV can be synthesized via spatiotemporal Fourier transform by employing a spatiotemporally coupled polychromatic Bessel–Gaussian seed beam. Figures 1(a)–1(d) present the numerical simulation results for the generation of perfect STOV wavepackets at different free-space propagation distances. The simulation uses a spatial–spectral Bessel–Gaussian beam with a topological charge of
Figure 1.Perfect spatiotemporal optical vortex (STOV) wavepackets. (a)–(d) 3D iso-intensity profiles of a perfect STOV of
Previous research has demonstrated the generation of spatiotemporal Laguerre–Gaussian and spatiotemporal Bessel–Gaussian wavepackets, where the spatial and temporal diameters are dependent on the topological charge [31,32,34,47]. As shown in Fig. 1(e), numerical simulations reveal that the spatial and temporal widths of spatiotemporal Laguerre–Gaussian and spatiotemporal Bessel–Gaussian wavepackets increase with increasing topological charge. In contrast, the spatial and temporal diameters of perfect STOV wavepackets remain constant, regardless of the topological charge. This is one of the main features and advantages of perfect STOVs.
3. EXPERIMENTAL SETUP
Figure 2 exhibits the experimental setup for perfect STOV generation and characterization. The mode-locked input laser, with a spectral bandwidth of approximately 20 nm centered at 1030 nm, is split into a probe pulse and an object pulse. The probe pulse passes through a pulse compressor consisting of a pair of parallel gratings and a right-angle prism and is then de-chirped to a Fourier-transform-limited pulse. The object pulse is directed into a folded 2D ultrafast pulse shaper that consists of a reflective grating, a cylindrical lens, and a phase-only reflective SLM (Holoeye GAEA-2,
Figure 2.Experimental setup for synthesizing and characterizing perfect STOV wavepackets. The setup includes three sections: a holographic pulse shaper, a time delay line system for fully measuring the 3D profile of the generated perfect STOV wavepacket, and a pulse compressor system. The computer-generated hologram (CGH) embedded on the SLM comprises two parts of the phase: (1) the phase distribution of a spatial–spectral Bessel–Gaussian mode; (2) a phase-only diffraction grating for controlling the spatial–spectral amplitude modulation. M, mirror; BS, beam splitter; CL, cylindrical lens.
The modulated beam is reflected and recombined, then it is focused by a spherical lens (
4. EXPERIMENTAL RESULTS AND DISCUSSION
Figure 3(a) presents the intensity iso-surface and sliced phase patterns of experimentally generated perfect STOV wavepackets with typical topological charges of
Figure 3.Theoretical and experimental results for the generated perfect STOV wavepacket and its comparison with the spatiotemporal Laguerre–Gaussian wavepacket. (a) and (b) Reconstructed intensity iso-surface and sliced phases (
To evaluate the performance of perfect STOVs, we conducted an experimental comparison with single-ring spatiotemporal Laguerre–Gaussian beams [34] of
The properties of the perfect STOV wavepackets are further verified by comparing with those of spatiotemporal Laguerre–Gaussian wavepackets. In addition to their unique characteristics of constant sizes, perfect STOVs could offer additional degrees of freedom in controlling their spatial and temporal dimensions. By adjusting the parameter
In the first case, as shown in Figs. 4(a1) and 4(a2), the initial two perfect STOV wavepackets separated in time are generated first by applying linear phases with opposite slopes to perfect STOV wavepackets with the same spatial and temporal diameters (
Figure 4.Spatiotemporal collision of perfect STOVs with time-varying transverse OAM. (a1)–(c1) Measured iso-intensity profile of the collision of two perfect STOVs with the same spatial and temporal diameters and different topological charges of
Compared with other methods using different parameters for controlling the radius of the vortex ring [48] or using the combination of conical and helical phase for generating perfect STOVs [49], our method has the advantage of rigorously satisfying the spatiotemporal Fourier transform conditions both mathematically and physically while having a much simpler and straightforward experimental configuration. This is achieved by the spatiotemporal holographic shaping method to modulate the complex spatiotemporal optical field [33].
5. CONCLUSION
In conclusion, a perfect spatiotemporal optical vortex with spatiotemporal sizes independent of the topological charges is generated experimentally by the spatiotemporal Fourier transform of the polychrome Bessel–Gaussian beam. The properties of the perfect STOVs are verified through comparison with spatiotemporal Laguerre–Gaussian wavepackets. Furthermore, we show the spatiotemporal collision of two perfect STOV wavepackets by introducing a linear phase in the time dimension, where the spatiotemporal collision of two perfect STOVs with different diameters leads to the phenomenon of spatiotemporal vortex reconnection, resulting in STOV lattices consisting of spatiotemporal sub-vortices with a controllable number and sign. These perfect spatiotemporal optical vortices may be used to facilitate optical communications, particle trapping, and tweezing among other potential applications.
APPENDIX A: NUMERICAL PROPAGATION OF PERFECT STOV WAVEPACKETS IN THE ANOMALOUS DISPERSIVE MEDIUM
The spatiotemporal evolution dynamics of a wavepacket propagating in a dispersive medium can be numerically studied by the angular spectrum propagation theorem by means of the fast Fourier transformation method, given by [
Figure 5.Numerical simulation for the spatiotemporal evolution dynamics of the generated perfect STOV wavepacket of
APPENDIX B: SPATIOTEMPORAL INTENSITY AND PHASE DISTRIBUTIONS OF THE PERFECT STOV AND SPATIOTEMPORAL LAGUERRE–GAUSSIAN WAVEPACKETS
Figure
Figure 6.Reconstructed intensities and phases of generated perfect STOVs with different
Figure 7.Reconstructed intensities and phases of generated spatiotemporal Laguerre–Gaussian wavepackets with
[50] G. P. Agrawal. Nonlinear Fiber Optics(2012).
Get Citation
Copy Citation Text
Haihao Fan, Qian Cao, Xin Liu, Andy Chong, Qiwen Zhan, "Perfect spatiotemporal optical vortices," Photonics Res. 13, 1776 (2025)
Category: Physical Optics
Received: Jan. 8, 2025
Accepted: Apr. 14, 2025
Published Online: Jun. 3, 2025
The Author Email: Qiwen Zhan (qwzhan@usst.edu.cn)
CSTR:32188.14.PRJ.555236