Nanoscale lattices of arbitrary orders are generated by truncated spiral metasurfaces combining geometric and dynamic phases.

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.

Based on the fact that the half-width of the Fourier transform is inversely proportional to that of a symmetrical primary decay function, the half-width of the intensity profiles of light scattered from self-affine fractal random surfaces in the whole $k_{\perp }$ region is studied. The primary function, whose Fourier transform is the intensity profile, is approximated with a simple mathematical decay function by equating their half-widths and maximums. The expression obtained for the half-width of the scattered intensity profiles reduces to the present results in the two extreme cases with the scattering roughness factors being either very small or very large. For a complete verification, we perform a simulation of the light scattering, in which self-affine fractal random surfaces are generated with an algorithm that is an analogy to the formation of laser speckles. The simulated and theoretical results conform well.

The derived two-dimensional autocorrelation function of speckles in the deep Fresnel region shows that it is related to the scattering of rough surface with the scattered intensity profile acting as the aperture function. We propose the method that is convenient for measuring surface parameters from the normalized autocorrelation function of speckles acquired with a microscopic imaging system. In experiment, a multi-scale behavior of the speckles has been identified, which is compatible with fractal character. With the speckle intensity data, we calculate the normalized autocorrelation function of the speckles and extract the roughness, the lateral correlation length and the roughness exponent of the random surface samples by fitting the expression to the autocorrelation function data. Comparison of the results with an atomic force microscopic measurements shows that our method has a satisfying accuracy.

Metasurfaces with orthogonal nano-slit pairs arranged on spirals are proposed to generate vector beams (VBs) of Bell-like states and slanted polarizations. The design of the metasurfaces is based on the theoretically derived parameter condition for manipulation of the two vector vortex modes, which is satisfied by matching the three parameters of rotation order m , the spiral order n , and incident polarization helicity σ . The linear polarization states of the VBs are controlled by the initial orientation angle φ 0 of slit pairs. VBs of satisfying quality are experimentally obtained, with the analytical and simulated results validated.

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.