The generation of vector beams using metasurfaces is crucial for the manipulation of light fields and has significant application potential, ranging from classical physics to quantum science. This paper introduces a novel dielectric metasurface composed of quarter‐wave plate (QWP) meta‐atoms, known as a QWP metasurface, designed to generate focused vector beams (VBs) of Bell‐like states under right circularly polarized illumination. The propagation phase imparted on both the co‐ and cross‐polarized components of the output field constructs hyperbolic and helical phase profiles with topological charge l _p , whereas the Pancharatnam–Berry (PB) phase acts only on the cross‐polarized component to construct another helical phase profile with topological charge l _g . Thus, the co‐ and cross‐polarized components form two orthogonal vector vortex (VV) modes with topological charges l _p and l _p + l _g , respectively. When the parameter conditions are satisfied by matching the incident polarization chirality σ and topological charges l _p and l _g , the focused VBs of Bell‐like states are generated by simultaneously manipulating the two VV modes, in contrast to existing QWP metasurfaces. The polarization states of the generated VBs are manipulated using the initial orientation angle θ ₀ of the meta‐atom. Overall, this research provides an innovative strategy for metasurface design, enhancing the functionality of metasurface devices for a broader range of application scenarios.

Metasurfaces of quarter-wave-plate (QWP) meta-atoms exhibit high flexibility and versatility in light-field manipulations; however, using them to generate multi-channel focused vector beams is challenging. This study proposes dielectric metasurfaces comprising two interleaving sets of QWP meta-atoms. Their parameters are adjusted based on the pre-set orders of the target vector beams to manipulate higher-order Poincaré beams and vortex superpositions in multiple channels. The metasurface phase profiles include hyperbolic, vortex, and gradient phases for focusing wavefronts, generating circularly polarized vortices, and deflecting vortices into two cross-polarization and one co-polarization channel. Four metasurface samples were designed to generate different order higher-order Poincaré beams in different channels, demonstrating the feasibility of QWP meta-atoms metasurface for manipulation of complicated vector light fields. Theoretical analysis, simulations, and experiments all demonstrate the feasibility of the proposed metasurfaces. Thus, this study is significant for compact, integrated, and multifunctional nanophotonic platforms with applications in high-capacity communication, image processing, quantum entanglement, and quantum communication.

We study theoretically the single-electron triangular zigzag graphene quantum dot in three typical in-plane electric fields. The far-infrared absorption spectra of the dot are calculated by the tight-binding method and then the optical selection rules are identified by contrast with the corresponding energy spectra. Our result shows that there exist the remarkable optical selection rules due to the C3 symmetry of the dot. When the electric field possesses also the C3 symmetry, there are only two absorption peaks in the absorption spectra. As the C3 symmetry of the system is damaged by the electric fields, both the intensity of the strongest peak and the number of the forbidden transitions decrease gradually. Moreover, the polarization causes the decrease of the peak intensities and even new forbidden transitions. Our findings may be useful for the application of graphene quantum dots to electronic and optoelectronic devices.

Metasurface-based longitudinal modulation introduces the propagation distance as a new degree of freedom, extending the light modulation with metasurfaces from 2D to 3D space. However, relevant longitudinal studies have been constrained to designing the metasurface of half-wave plate (HWP) meta-atoms and generating either non-focused or two-channel vortex and vector beams. In this study, we propose a metasurface composed of quarter-wave plate (QWP) meta-atoms to generate the longitudinal multi-channel focused vortex and vector beams. The metasurface consists of two interleaved sub-metasurfaces of QWP meta-atoms. For each sub-metasurface, the helical and hyperbolic phase profiles are designed independently in the propagation and geometric phases to generate focused co- and cross-polarized vortices with corresponding topological charges. Under the illumination of x-linearly polarized light, the metasurface generates two circularly polarized vortices, two linearly polarized vortices, and one vector beam on five focal planes. Theoretical analysis and simulation results demonstrate the feasibility of the proposed QWP metasurface. Our study presents a significant advancement in the development of integrated and multifunctional optical devices and systems, with significant potential applications in light–matter interaction, laser processing, and optical communication.