New Photonic State-Optical Tornado
The famous poet Su Shi wrote in his poemInscription on the Wall of Xilin Temple:When viewed horizontally, they appear as ridges; when viewed from the side, they appear as peaks. They vary in height and distance. It can be observed that unexpected results may arise when we consider different perspectives.
Recently, Professor Zhan Qiwen and his Nanophotonics team made a significant breakthrough in the study of optical orbital angular momentum (OAM). They successfully filled a gap by analyzing the spatiotemporal vortices of OAM with controllable transverse orbital angular momentum. This research, led by Professor Zhan, is part of the Future Optics International Laboratory team at USST, under the guidance of Academician Zhuang Songlin and Academician Gu Min.
The spatiotemporal vortex has transversely controllable orbital angular momentum (OAM), which reveals another new degree of freedom for photonic orbital angular momentum (OAM). It has great potential and application value in research in the fields of optical communication, optical information processing, micro- and nano-optics, biosensing, as well as chiral nanomaterials photonics and plasmonic devices.
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Background
Electromagnetic radiation possesses both energy and momentum. As one of the important members of the electromagnetic radiation family, light has been proven by scientists to have linear momentum along its propagation direction (i.e., the z-axis in the spatial Cartesian coordinate system). In addition to linear momentum, scientists have also demonstrated that light possesses angular momentum. One is the spin angular momentum (SAM) related to the spin of photons, which is related to the polarization properties of light. The other is the orbital angular momentum (OAM) related to the angular phase distribution of photons. As shown in Figure 1, it represents a schematic diagram of the spin angular momentum (SAM) and orbital angular momentum (OAM) that light possesses during longitudinal propagation.
Fig.1Schematic of the spatial distribution of SAM and OAM
In general, angular momentum is along the direction of light propagation (i.e., longitudinal), while in 2015 scientists at the Planck Experimental Research Centre in Germany proposed that it is equally possible to have transverse spin angular momentum (SAM) in the direction of relative light propagation. A schematic mechanical description of the generation of longitudinal SAM and transverse SAM is shown in Figure 2 below. This property has a wide range of applications in many fields, e.g., these two degrees of freedom allow us to probe the spin states of atoms, molecules and quantum dots.
Fig.2 Schematic mechanical description of longitudinal SAM and transverse SAM
From the research in 2015, it is known that light not only has longitudinal SAM but also transverse SAM. So, a question arises as to whether orbital angular momentum (OAM) also possesses such properties. In the usual research, scientists often refer to OAM as the longitudinal orbital angular momentum along the direction of light propagation. In this paper, a definite answer is given that OAM also has transverse characteristics. However, due to the complex physical properties of spatiotemporal vortices, it has strong spatiotemporal coupling (i.e., the pulse distribution varies with spatial position) and there is no reliable way to generate it in general experimental conditions. In some special cases, such as tight focusing, evanescent waves in finite waveguides, and nonlinear effects, it can exist. However, in these extreme cases, the zero OAM component occupies a large portion of the transverse OAM, which imposes significant limitations on the study of transverse OAM.
In this paper, the authors demonstrate the existence of transverse orbital angular momentum (OAM) using an indirect proof method based on the conservation of angular momentum in the Fourier transform from the spatial-temporal domain to the spatial-frequency-frequency domain. They analyze the spatiotemporal vortex generated by the transverse OAM in a three-dimensional wave packet and compare it to the spin angular momentum (SAM) in the transverse direction. The authors show that the magnitude of the transverse OAM in the three-dimensional spatiotemporal vortex can be controlled in a simpler way compared to the transverse SAM, making it a controllable parameter. This finding may lead to new applications, and the method proposed in this paper can be applied to other spectra and different wave fields.
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Innovative research
3.1 OAM of spatial plane vortices and spatiotemporal plane vortices
Fig.3 Schematic of space-plane vortex longitudinal and space-time-plane transverse OAMs.
As shown in Figure 3a, it represents a schematic diagram of a three-dimensional vortex wave packet in the common spatial plane, accompanied by longitudinal OAM. The authors made an imaginative transformation, which is to rotate the spatial three-dimensional vortex wave packet shown in Figure 3a around the x-axis by 90 degrees, to obtain a three-dimensional vortex wave packet with transverse OAM. (We can also understand it in this way: the z-axis direction in Figure 3b can be treated as a time axis t.) In this way, the three-dimensional vortex wave packet is generated in the spatiotemporal (x-t) plane, and the corresponding spiral phase surface of the vortex optical field is in the spatiotemporal plane. Therefore, its orbital angular momentum (OAM) is transverse, indicated by the red arrow in Figure 3b. The authors also provide a theoretical explanation for the existence of transverse OAM using the principles of quantum mechanics in the supplementary materials. (Here, the direction of transverse OAM is towards the y-axis position, but it can also be towards the negative direction of the y-axis, which is mainly related to the rotation direction of the spiral phase. This is usually expressed in terms of positive and negative topological charges. Here the authors use a topological charge of 1.)
3.2 Generation of spatiotemporal vortices
Fig.4 Experimental setup flowchart for generating spatiotemporal vortices.
As shown in Fig. 4, the experimental setup flowchart for generating spatiotemporal vortices is depicted. The authors demonstrated the generation of spatiotemporal vortices using a spatial frequency-domain approach. It is seemingly impossible to directly generate a spiral phase for spatiotemporal vortex pulses in the spatiotemporal plane. However, interestingly, the authors utilized the Fourier transform to achieve the conversion. By performing a 2D Fourier transform, the spatiotemporal plane can be transformed into the spatial frequency-domain and frequency-domain, while conserving the angular momentum during this process. (The theoretical derivation for this part is explained in detail in the original paper and supplementary information.) This provides a favorable experimental condition for proving the existence of spatiotemporal vortices, as the Fourier transform can be realized using optical components.
In the experiment, the incident light (blue arrow) is a chirped mode-locked pulse with a duration of approximately 3 ps. Firstly, the incident light passes through the first lens and then undergoes a spatial-frequency Fourier transform by passing through a diffraction grating and a cylindrical lens. The transformed optical field is incident on a spatial light modulator (SLM) loaded with a spiral phase with a topological charge of 1. The reflected light (red arrow) undergoes an inverse Fourier transform by passing through a diffraction grating and a cylindrical lens, resulting in the generation of a chirped spatiotemporal vortex at the output. By loading the SLM with spiral phases of different topological charges, the generation of spatiotemporal vortices with controllable transverse orbital angular momentum can be achieved.
3.3 Detection of spatiotemporal vortices
The generation of spatiotemporal vortices was achieved using a clever method that involved a Fourier transform from the spatial-temporal domain to the spatial-frequency-frequency domain. However, it is important to demonstrate that the spatiotemporal vortices generated using this indirect method possess transverse orbital angular momentum (OAM). One common method to detect vortices is through coherent detection, where cross-shaped interference fringes are observed when the vortex beam interferes with a plane wave. The number of cross-shaped fringes is related to the value of the orbital angular momentum. Figure 5 shows the detection images of spatial plane vortices with different topological charges (1 and 2) interfering with spherical waves and plane waves, respectively.
Fig.5 Patterns of spatial plane vortex light coherently detected with spherical and plane waves
The authors used the principle of Michelson interferometry to detect the spatiotemporal vortex. As shown in Figure 6, the detection setup for the spatiotemporal vortex is illustrated.
Fig.6 Flowchart of coherent detection of spatiotemporal optical vortices
In the experimental setup shown in Figure 6, the chirped spatiotemporal vortex is overlapped with a short reference pulse (~90 fs) at a certain angle to generate interference fringes. It is important to note that the chirped spatiotemporal vortex is intentionally longer than the reference pulse to ensure that the fringe pattern represents the spatial phase profile of the thin temporal slice. The resulting interference fringes provide information about the spatial phase distribution of the spatiotemporal vortex. The global coherence results are presented in Figure 7.
Fig.7 Coherence results of spatiotemporal vortex detection with topological charge number 1
In the experimental setup shown in Figure 6, by adjusting the angle between the spatiotemporal vortex and the reference beam, vertical fringes can be formed. The presence and evolution of these vertical fringes can demonstrate the transverse orbital angular momentum of the spatiotemporal vortex. The evolution of the vertical fringe pattern can be understood as follows. As shown in Figure 7a, different vertical line positions (1, 2, 3, 4, 5) represent different phase surfaces. When the reference beam scans through, coherent fringes appear due to the phase gradient in the spatiotemporal vortex. Distortion occurs at the central singularity position due to the change in the phase gradient. The regions on both sides of the singularity exhibit symmetric transformations. Figure 7b shows the results of theoretical coherent simulation, and Figure 7c shows the results of experimental measurement.
Finally, the authors also measured higher-order spatiotemporal vortices and reconstructed the three-dimensional phase distribution of the spatiotemporal vortex. The simulation results are in good agreement with the experimental measurements.
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Applications and Outlook
The authors discuss the generation and detection of spatiotemporal vortices with controllable transverse orbital angular momentum. They propose a method that is both innovative and applicable. The tunable transverse OAM of the spatiotemporal vortex is believed to have potential applications, such as increasing data capacity in optical communications.
In addition, in an interview with the American Physical Society, the author mentioned their interest in the next research steps. It may take some time for researchers to test the practical applications of these fundamental research findings. However, they speculate that this new optical state could be used to improve the transmission of large amounts of data with higher security, among other potential applications. The author also expressed a desire to better understand how this state of light interacts with materials in space and time.
At the end of the interview, Professor Zhan Qiwen's statement carries profound meaning. He said, We don't know yet? But the sky's the limit.
The research achievement titled Generation of spatiotemporal optical vortices with controllable transverse orbital angular momentum was published in the prestigious optical journal Nature Photonics, a sub-journal of Nature, which is one of the world's top optical journals. The authors of the paper are Andy Chong, Chenhao Wan, Jian Chen, and Qiwen Zhan.
