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We investigate the spin angular momentum (SAM) of double-index cylindrical vector beams in tight focus. Such a set of beams is a generalization of the conventional cylindrical vector beams since the polarization order is different for the different transverse field components. Based on the Richards-Wolf theory, we obtain an expression for the SAM distribution and show that if the polarization orders are of different parity, then the spin Hall effect occurs in the tight focus, which is there are alternating areas with positive and negative spin angular momentum, despite linear polarization of the initial field. We also analyze the orbital angular momentum spectrum of all the components of the focused light field and determine the overwhelming angular harmonics. Neglecting the weak harmonics, we predict the SAM distribution and demonstrate the ability to generate the focal distribution where the areas with the positive and negative spin angular momentum reside on a ring and are alternating in pairs, or separated in different semicircles. Application areas of the obtained results are designing micromachines with optically driven elements.

Cylindrical vector beams and vortex beams, two types of typical singular optical beams characterized by axially symmetric polarization and helical phase front, possess the unique focusing property and the ability of carrying orbital angular momentum. We discuss the formation mechanisms of such singular beams in few-mode fibers under the vortex basis and show recent advances in generating techniques that are mainly based on long-period fiber gratings, mode-selective couplers, offset-spliced fibers, and tapered fibers. The performances of cylindrical vector beams and vortex beams generated in fibers and fiber lasers are summarized and compared to give a comprehensive understanding of singular beams and to promote their practical applications.

Super-resolution optical microscopy, which gives access to finer details of objects, is highly desired for fields of nanomaterial, nanobiology, nanophotonics, etc. Many efforts, including tip optimization and illumination optimization etc., have been made in both near-field and far-field super-resolution microscopy to achieve a spatial resolution beyond the diffraction limit. The development of vector light fields opens up a new avenue for super-resolution optical microscopy via special illumination modes. Cylindrical vector beam (CVB) has been verified to enable resolution improvement in tip-scanning imaging, nonlinear imaging, stimulated emission depletion (STED) microscopy, subtraction imaging, superoscillation imaging, etc. This paper reviews recent advances in CVB-based super-resolution imaging. We start with an introduction of the fundamentals and properties of CVB. Next, strategies for CVB based super-resolution imaging are discussed, which are mainly implemented by tight focusing, depletion effect, plasmonic nanofocusing, and polarization matching. Then, the roadmap of super-resolution imaging with CVB illumination in the past two decades is summarized. The typical CVB-based imaging techniques in fields of both near-field and far-field microscopy are introduced, including tip-scanning imaging, nonlinear imaging, STED, subtraction imaging, and superoscillation imaging. Finally, challenges and future directions of CVB-illuminated super-resolution imaging techniques are discussed.

Cylindrical vector beam (CVB) is a structured lightwave characterized by its topologically nontrivial nature of the optical polarization. The unique electromagnetic field configuration of CVBs has been exploited to optical tweezers, laser accelerations, and so on. However, use of CVBs in research fields outside optics such as condensed matter physics has not progressed. In this paper, we propose potential applications of CVBs to those fields based on a general argument on their absorption by matter. We show that pulse azimuthal CVBs around terahertz or far-infrared frequencies can be a unique and powerful mean for time-resolved spectroscopy of magnetic properties of matter and claim that an azimuthal electric field of a pulse CVB would be a novel way of studying and controlling edge currents in topological materials. We also demonstrate how powerful CVBs will be as a tool for Floquet engineering of nonequilibrium states of matter.

Function expansion of fiber sensor is highly desired for ultrasensitive optical detection and analysis. Here, we present an approach of multifunctional fiber sensor based on Fano resonances and localized surface plasmon resonance (LSPR) excited via cylindrical vector beam with ability of refractive index (RI) sensing, nano-distance detection, and surface enhanced Raman spectroscopy (SERS). Silver (Ag)-nanocube modified microfiber is theoretically proved to enable to detect RI of the nearby solids and gases based on Fano resonances with a sensitivity of 128.63 nm/refractive index unit (RIU) and 148.21 nm/RIU for solids and gases, respectively. The scattering spectrum of the Ag nanocube has the red-shift response to the varies of the nano-distance between the nanocube and the nearby solid, providing a detection sensitivity up to 1.48 nm (wavelength)/nm (distance). Moreover, this configuration is theoretically verified to have ability to significantly enhance electric field intensity. Radially polarized beam is proved to enhance the electric field intensity as large as 5 times in the side-face configuration compared with linear polarization beam. This fiber-based sensing method is helpful in fields of remote detection, multiple species detection, and cylindrical vector beam-based detection.

The exponentially escalating global bandwidth demands have propelled mode‐division multiplexing technologies as critical enablers for enlarging optical communication capacity. Leveraging spatially orthogonal photonic eigenmodes of circularly symmetric structured light beams, such as orbital angular momentum (OAM) and cylindrical vector beam (CVB) modes, enables the parallel multiplexing of large‐scale digital signals within a single physical channel. This thus significantly expands data transmission density and advances next‐generation optical communications and networks forward. This review aims to achieve a comprehensive overview of mode (de)multiplexing technologies using OAM/CVB modes, which are mainly categorized into beam splitter combinations, multiorder diffractive gratings, optical coordinate transformations, angular dispersion lenses, multilayer cascaded modulations, and multidimensional mode hybrid (de)multiplexing. Insights into their current capabilities and limitations are included. We conclude by analyzing the challenges and prospects of this promising field, paving the way for future developments and innovations. This review presents a comprehensive overview of mode (de)multiplexing technologies using circularly symmetric structured light beams, encompassing strategies of beam splitter combinations, multiorder diffractive gratings, optical coordinate transformations, angular dispersion lenses, multilayer cascaded modulations, and multidimensional hybrid (de)multiplexing. Insights into their current capabilities, challenges, and prospects of this promising field are included, establishing a foundation for future advancements and innovations.

Elements of micromachines can be driven by light, including structured light with phase and/or polarization singularities. We investigate a paraxial vectorial Gaussian beam with multiple polarization singularities residing on a circle. Such a beam is a superposition of a cylindrically polarized Laguerre–Gaussian beam with a linearly polarized Gaussian beam. We demonstrate that, despite linear polarization in the initial plane, on propagation in space, alternating areas are generated with a spin angular momentum (SAM) density of opposite sign, that manifest about the spin Hall effect. We derive that in each transverse plane, maximal SAM magnitude is on a certain-radius circle. We obtain an approximate expression for the distance to the transverse plane with the maximal SAM density. Besides, we define the singularities circle radius, for which the achievable SAM density is maximal. It turns out that in this case the energies of the Laguerre–Gaussian and of the Gaussian beams are equal. We obtain an expression for the orbital angular momentum density and find that it is equal to the SAM density, multiplied by −m/2 with m being the order of the Laguerre–Gaussian beam, equal to the number of the polarization singularities. We consider an analogy with plane waves and find that the spin Hall affect arises due to the different divergence between the linearly polarized Gaussian beam and cylindrically polarized Laguerre–Gaussian beam. Application areas of the obtained results are designing micromachines with optically driven elements.

Nowadays, the well-known cylindrical vector beams (CVBs) – the axially symmetric beam solution to the full-vector electromagnetic wave equation – are widely used for advanced laser material processing, optical manipulation and communication and have a great interest for data storage. Higher-order CVBs with polarisation order greater than one and superpositions of CVBs of various orders (hybrid CVBs) are especially of interest because of their great potential in contemporary optics. We performed a theoretical analysis of the transformation of first-order CVBs (radially and azimuthally polarised beams) into hybrid higher-order ones using phase elements with complex transmission functions in the form of the cosine or sine functions of the azimuthal angle. Binary multi-sector phase plates approximating such transmission functions were fabricated and experimentally investigated. The influence of the number of sectors and a height difference between neighbouring sectors, as well as the energy contribution of the different components in the generated hybrid higher-order CVBs were discussed in the context of polarisation transformation and vector optical field transformation in the focal region. The possibility of polarisation transformation, even in the case of weak focusing, is also demonstrated. The simple structure of the profile of such plates, their high diffraction efficiency and high damage threshold, as well as the easy-to-implement polarisation transformation principle provide advanced opportunities for high-efficient, quickly-switchable dynamic control of the generation of structured laser beams.

It is known that in the cross-section of a high-order cylindrical vector beam (CVB), polarization is locally linear. The higher the beam order, the higher the number of full rotations of the vector of local linear polarization when passing along a contour around the optical axis. It is also known that both in the input and in the focal planes, the CVB has neither the spin angular momentum (SAM), nor the orbital angular momentum (OAM). We demonstrate here that near the focal plane of the CVB (before and after the focus), an even number of local subwavelength areas is generated, where the polarization vector in each point is rotating. In addition, in the neighboring areas, polarization vectors are rotating in different directions, so that the longitudinal component of SAM vectors in these neighboring areas is of the opposite sign. In addition, after the beam passes the focus, the rotation direction of the polarization vector in each point of the beam cross-section is changed to the opposite one. Such spatial separation of the left and right rotation of the polarization vectors manifests so that the optical spin Hall effect takes place.

It is shown, theoretically and numerically, that the distributions of the longitudinal energy flow for tightly focused light with circular and linear polarization are the same, and that the spot has circular symmetry. It is also shown that the longitudinal energy flows are equal for optical vortices with unit topological charge and with radial or azimuthal polarization. The focal spot has a minimum diameter (all other characteristics being equal), which is measured based on the intensity of an optical vortex with azimuthal polarization. The diameter of the focal spot calculated from the energy flow for light with circular or linear polarization is slightly larger (by a fraction of a percentage). The magnitude of the diameter based on the intensity plays a role in the interaction of light with matter, and the magnitude of the diameter based on the energy flux affects the resolution in optical microscopy which is crucial in sensorial applications.