It is well known that light has spin angular momentum (SAM) determined by polarizability and orbital angular momentum (OAM) determined by the spatial distribution of the optical field. These two angular momentum of light are both independent of each other and there are interactions, can be produced through a certain form of coupling between each other, this process is called spin-orbit coupling. Spin-orbit coupling of light widely exists in the strong focusing field and non-uniform or anisotropic medium in the light and matter interaction, in the light of the spin Hall effect, spin-controlled beam shaping, precision metrology, optical tweezers, and other applications of great significance. For a long time, the mutual coupling between the spin angular momentum and the longitudinal orbital angular momentum in space has been a common concern. Due to the complex properties of spacetime vortices, little research has been reported on the mutual coupling of spin-orbitals associated with transverse orbital angular momentum. In recent years, thanks to some pioneering research works on spacetime vortices, such as controllable generation methods, propagation properties in free space and dispersive media, conservation of transverse orbital angular momentum in second-harmonic generation, and partially coherent spacetime vortices, spacetime vortices have been provided with exploitable means of generating, manipulating, and observing spacetime vortices. For such a new type of transverse orbital angular momentum, spin-orbit mutual coupling can be expected to appear as a new phenomenon.
Recently, the nanophotonics team led by Prof. Qiwen Zhan at the University of Shanghai for Science and Technology has made important progress in the field of spacetime vortex research, demonstrating a new type of spin-orbit coupling effect between longitudinal spin angular momentum and transverse orbital angular momentum through the study of tightly-focused circularly-polarized spacetime vortices. These peculiar spin-orbit coupling phenomena are expected to generate new effects and functions in light-matter interactions. The results were published in ACS Photonics under the title Spin-orbit coupling within tightly focused circularly polarized spatiotemporal vortex wavepacket and selected as the cover article (Fig. 1).
Fig.1 Journal Cover
In this work, the researchers found that the transversely polarized component of the strongly focused circularly polarized spatiotemporal vortex focal field carries both the transverse and longitudinal orbital angular momentum, and the longitudinal orbital angular momentum is evolved from the longitudinal spin angular momentum under the strong focusing condition, as shown in Fig. 2. Due to the strong coupling effect between the transverse orbital angular momentum and the longitudinal orbital angular momentum, which leads to a significant deflection of the pointing of its spatiotemporal phase singularity, the tilting angle of the spatiotemporal phase singularity can be conveniently controlled by modulating the pulse width of the wave packet.
Fig.2 Intensity and phase distributions of the x-polarized and y-polarized components of the focal field
For the longitudinally polarized component of the focal field, the spatiotemporal phase singularity structure is more complex, undergoing a continuous evolution from pure longitudinal orbital angular momentum to pure transverse orbital angular momentum. At the exact center of the wave packet, the phase singularity trajectory forms a closed knot containing both longitudinal and transverse orbital angular momentum, as shown in Fig. 3.
Fig.3 Intensity, phase singularity trajectory and phase distribution of the z-polarized component of the focal field
As for the polarization distribution of the focal field, as shown in Fig. 4, the focal field is close to circularly polarized in the xy-plane because the intensities of its x-polarized and y-polarized components are approximately equal and the relative phase difference between them is π/2. The focal field is mainly elliptically polarized in the xt-plane and yt-plane because the intensity of the z-polarized component is obviously smaller than that of the x-polarized and y-polarized components. However, at the center of the focused wave packet, the focal field is linearly polarized along the 2-direction near the center because the intensity of the x-polarized and y-polarized components is 0, while the intensity of the z-polarized component is larger.
Fig.4 Polarization distribution of the focal field
When interacting with structural materials, these unique features of the novel spin-orbit coupling may produce significantly different responses, especially if the sample is selectively responsive to certain specific polarization states. In addition, richer spin-orbit interactions will be found when factors such as chromatic aberration and aberration of the focusing system are taken into account. These unique spin-orbit mutual coupling effects provided by strongly focused circularly polarized spacetime vortices have potential applications in optical manipulation, photon emission with tailored properties, light-matter interactions, and plasma physics.
