Understanding of transverse spin angular momentum in tightly focused linearly polarized vortex beams

Nonlinear spin-orbit coupling in optical thin films

Tunable generation of vortex beams holds relevance in various fields, including communications and sensing. In this paper, we demonstrate the feasibility of nonlinear spin-orbit interactions in thin films of materials with second-order nonlinear susceptibility. Remarkably, the nonlinear tensor can mix the longitudinal and transverse components of the pump field. We observe experimentally our theoretical predictions in the process of second-harmonic generation from a thin film of aluminum gallium arsenide, a material platform widely spread for its role in the advancement of active, nonlinear, and quantum photonic devices. In particular, we prove that a nonlinear thin film can be used to produce vector vortex beams of second-harmonic light when excited by circularly-polarized Gaussian beams.

Topological state transitions of skyrmionic beams under focusing configurations

The recent emerging appearance of optical analogs of magnetic quasiparticles, i.e., optical skyrmions constructed via spin, field, and Stokes vectors, has garnered substantial interest from deep-subwavelength imaging and quantum entanglement. Here, we investigate systematically the topological state transitions of skyrmionic beams constructed by the Stokes vectors in the focusing configuration. We theoretically demonstrated that in the weak focusing, the skyrmion topological number is protected. Whereas, in the tight focusing, a unique topological transformation with skyrmion number variation is exhibited for the optical skyrmion, anti-skyrmion, and 2nd-order skyrmion structures. The significant difference between the topological state transitions of these two cases originates from the transformation from the paraxial optical system to the nonparaxial optical system, and the approximate two-dimensional polarization structure to the three-dimensional polarization structure. The results provide new insights into the topological state transitions in topological structures, which promote applications in information processing, data storage, and free-space optical communications.

Hall Effect at the Focus of an Optical Vortex with Linear Polarization

The tight focusing of an optical vortex with an integer topological charge (TC) and linear polarization was considered. We showed that the longitudinal components of the spin angular momentum (SAM) (it was equal to zero) and orbital angular momentum (OAM) (it was equal to the product of the beam power and the TC) vectors averaged over the beam cross-section were separately preserved during the beam propagation. This conservation led to the spin and orbital Hall effects. The spin Hall effect was expressed in the fact that the areas with different signs of the SAM longitudinal component were separated from each other. The orbital Hall effect was marked by the separation of the regions with different rotation directions of the transverse energy flow (clockwise and counterclockwise). There were only four such local regions near the optical axis for any TC. We showed that the total energy flux crossing the focus plane was less than the total beam power since part of the power propagated along the focus surface, while the other part crossed the focus plane in the opposite direction. We also showed that the longitudinal component of the angular momentum (AM) vector was not equal to the sum of the SAM and the OAM. Moreover, there was no summand SAM in the expression for the density of the AM. These quantities were independent of each other. The distributions of the AM and the SAM longitudinal components characterized the orbital and spin Hall effects at the focus, respectively.

Spin-orbit interactions of a circularly polarized vortex beam in paraxial propagation

Spin-orbit interactions (SOIs) of circularly polarized beam and circularly polarized vortex beam during paraxial propagation in a radial gradient-index (GRIN) fiber are analyzed using the generalized Huygens-Fresnel principle and the GRIN fiber's ABCD matrix. SAM is only associated with polarized light helicity and OAM is only associated with topological charge m. SAM and OAM do not crosstalk or convert between each other; SOIs did not occur at the GRIN fiber's focal plane. SOIs of partially coherent circularly polarized beam and partially coherent circularly polarized vortex beam in the GRIN fiber are also studied and show the same characteristics as the perfectly polarized beam.

Effect of optical spatial coherence on localized spin angular momentum density in tightly focused light [Invited]

Optical coherence is one of the most fundamental characteristics of light and has been viewed as a powerful tool for governing the spatial, spectral, and temporal statistical properties of optical fields during light-matter interactions. In this work, we use the optical coherence theory developed by Emil Wolf as well as the Richards-Wolf's vectorial diffraction method to numerically study the effect of optical coherence on the localized spin density of a tightly focused partially coherent vector beam. We find that both the transverse spin and longitudinal spin, with the former induced by the out-of-phase longitudinal field generated during strong light focusing and the latter induced by the vortex phase in the incident beam, are closely related to the optical coherence of the incident beam, i.e., with the decrease of the transverse spatial coherence width of the incident beam, the magnitude of the spin density components decreases as well. The numerical findings are interpreted well with the two-dimensional degrees of polarization between any two of the three orthogonal field components of the tightly focused field. We also explore the roles of the topological charge of the vortex phase on enhancing the spin density for the partially coherent tightly focused field. The effect of the incident beam's initial polarization state is also discussed.

Linear and angular momentum properties induced by radial- and azimuthal-variant polarized beams in a strongly focused optical system

Optical linear and angular momenta have attracted tremendous research interest in recent years. In this paper we theoretically investigate the electromagnetic fields and linear and angular momentum properties of tightly focused radial- and azimuthal-variant vector input beams. Calculations show that a uniform 3D optical cage can be achieved when the optical degree of freedom of polarization in the radial direction is introduced. Furthermore, the distributions of linear and angular momenta in the focal volume are revealed. Moreover, we numerically investigate the gradient, scattering, and total forces as well as spin and orbital torques on a Rayleigh particle generated by the optical cage. It is found that there are two equilibrium positions before and after the focal plane, both of which can achieve stable 3D particles capture. Most importantly, the longitudinal spin and orbital torques show the same patterns but in opposite directions in the two equilibrium positions, thus, the unwinding of the double helix can be expected to be achieved by virtue of this special optical torque.

Optical trapping of Rayleigh particles based on four-petal Gaussian vortex beams

The intensity distribution of four-petal Gaussian vortex (FPGV) beams through a focused optical system and the radiation force acting on a Rayleigh dielectric sphere is obtained based on the extended Huygens-Fresnel principle and the Rayleigh scattering theory. We mainly study the trapping of high and low refractive index Rayleigh particles by FPGV beams and the effect of the topological charge m on the radiation force. The results show that the specific distribution of the incident beam can be controlled by a reasonable choice of topological charge m. The multiple locations in a beam of light where particles of different refractive indices can be captured will be found. On the other hand, when m changes, the number of particles captured and the locations where they can be captured change accordingly. Therefore, the flexibility to simultaneously capture multiple Rayleigh particles with different refractive indices with a single beam at different locations in the focal plane can be achieved using the FPGV beam.

Simulation and Experiment of the Trapping Trajectory for Janus Particles in Linearly Polarized Optical Traps

The highly focused laser beam is capable of confining micro-sized particle in its focus. This is widely known as optical trapping. The Janus particle is composed of two hemispheres with different refractive indexes. In a linearly polarized optical trap, the Janus particle tends to align itself to an orientation where the interface of the two hemispheres is parallel to the laser propagation as well as the polarization direction. This enables a controllable approach that rotates the trapped particle with fine accuracy and could be used in partial measurement. However, due to the complexity of the interaction of the optical field and refractive index distribution, the trapping trajectory of the Janus particle in the linearly polarized optical trap is still uncovered. In this paper, we focus on the dynamic trapping process and the steady position and orientation of the Janus particle in the optical trap from both simulation and experimental aspects. The trapping process recorded by a high speed camera coincides with the simulation result calculated using the T-matrix model, which not only reveals the trapping trajectory, but also provides a practical simulation solution for more complicated structures and trapping motions.