Multichannel focused higher-order Poincaré sphere beam generation based on a dielectric geometric metasurface.

Focused vector beams (VBs) are important topic in the areas of light field manipulation. Geometric metasurfaces provide a convenient platform to facilitate the generation of focused VBs. In this study, we propose a dielectric geometric metasurface to generate multichannel focused higher-order Poincaré sphere (HOP) beams. With identical meta-atoms of half-wave plate, the metasurface comprises two sub-metasurfaces, and each of them includes two sets of rings related to Fresnel zones. For meta-atoms on each set of rings, the hyperbolic geometric phase profile is configured so that the mirror-symmetrical position-flip of the off-axis focal point is enabled under the chirality switch of the illuminating circular polarization. With the design of helical geometric phase profiles for the two sets of rings, a sub-metasurface generate two HOP beams at the symmetrical two focal points. The performance of the two sub-metasurfaces enables the metasurface with four sets of rings to generate the array of four HOP beams. The proposed method was validated by theoretical analyses, numerical simulation and experimental conduction. This research would be significant in miniaturizing and integrating optical systems involving applications of VB generations and applications.

Metasurfaces for generating higher-order Poincaré beams by polarization-selective focusing and overall elimination of co-polarization components.

Focused higher-order Poincaré (HOP) beams are of particular interest because they facilitate understanding the exotic properties of structured light and their applications in classical physics and quantum information. However, generating focused HOP beams using metasurfaces is challenging. In this study, we proposed a metasurface design comprising two sets of metal nanoslits for generating coaxially focused HOP beams. The nanoslits were interleaved on equispaced alternating rings. The initial rings started at the two adjacent Fresnel zones to provide opposite propagation phases for overall elimination of the co-polarization components. With the designed hyperbolic and helical profiles of the geometric phases, the two vortices of the opposite cross-circular-polarizations were formed and selectively focused, realizing HOP beams of improved quality. Simulations and experimental results demonstrated the feasibility of the proposed metasurface design. This study is of significance in the integration of miniaturized optical devices and enriches the application areas of metasurfaces.

Generation of spatiotemporal optical vortices in ultrashort laser pulses using rotationally interleaved multispirals.

Ultrashort optical vortex pulses carrying spatiotemporal orbital angular momentum (OAM) have inspired versatile applications such as the micromachining of integrated quantum chips and discoveries such as optical toroidal structures and OAM-carrying X-waves. Generating high-quality ultrashort vortices with controllable topological charges remains a crucial issue. Thus, we propose a rotationally interleaved multispiral to generate such vortices. A multispiral comprises multiple identical spirals rotated around the center in the equal-azimuthal interval and interleaved in equal-radius increments; this structure overcomes the previous structural asymmetry of the single spiral and improves the vortex quality. Accordingly, we conducted theoretical analyses, numerical simulations, and experimental investigations that demonstrated the feasibility of multispirals in generating the ultrashort vortices with symmetric distributions and flexibly controlling the topological charges. The proposed study is significant for broader applications involving ultrashort vortices and extensive investigations in related areas such as research on electron vortices, plasmonic vortices, and other matter vortices.

Arbitrary superposition of plasmonic orbital angular momentum states with nanostructures.

A kind of plasmonic nanostructure is proposed that can generate the arbitrary superposition of orbital angular momentum (OAM) states in surface plasmons (SPs), which is achieved by combining the segmented spirals with nanoslit pairs. The structures can independently modulate both the phase and amplitude of SP waves, and thus enable the superposition of two OAM states with arbitrary topological charges (TCs) as well as free control of their relative amplitudes. Superposed states distributed over the entire Bloch sphere and hybrid superposed states with different TCs were constructed and experimentally demonstrated. This work will offer more opportunities for multifunctional plasmonic devices.

Generation of vector beams of Bell-like states by manipulating vector vortex modes with plasmonic metasurfaces.

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 φ0 of slit pairs. VBs of satisfying quality are experimentally obtained, with the analytical and simulated results validated.

Flexible generation of higher-order Poincaré beams with high efficiency by manipulating the two eigenstates of polarized optical vortices.

Vector beams contain complex polarization structures and they are inherently non-separable in the polarization and spatial degrees of freedom. The spatially variant polarizations of vector beams have enabled many important applications in a variety of fields ranging from classical to quantum physics. In this study, we designed and realized a setup based on Mach-Zehnder interferometer for achieving the vector beams at arbitrary points of higher-order Poincaré sphere, through manipulating two eigenstates in the Mach-Zehnder interferometer system with the combined spiral phase plate. We demonstrated the generation of different kinds of higher-order Poincaré beams, including the beams at points on a latitude or longitude of higher-order Poincaré sphere, Bell states for |l| = 1 and |l| = 2, radially polarized beams of very high order with l = 16, etc. Vector beams of high quality and good accuracy are experimentally achieved, and the flexibility, feasibility and high efficiency of the setup are demonstrated by the practical performance.

Optical lattices and optical vortex arrays in clustered speckles.

Clustered speckle, optical lattices, and their optical vortex array are subjects of interest in optical wave manipulation. In this study, disordered optical lattices and vortex arrays with different unit structures were found in the clustered speckles generated by a circularly-distributed multi-pinhole scattering screen when it was illuminated by coherent light. These structures included hexagonal lattices, kagome lattices, and honeycomb lattices. Moreover, optical lattices with asymmetric units generated by modulation of phases with non-integer multiples of 2π were discussed. Theoretical analysis and numerical calculations demonstrated that optical lattices in clustered speckles in the observation plane were generated by the phase modulations of the random scattering screen. The lattice type depended on the number of 2π multiples of the summed phase difference between the pinholes. Additionally, the conditions for the formation of periodical optical lattices and their vortex arrays were given. Different optical lattices and their vortex arrays appearing simultaneously in the clustered speckle were difficult to generate using the common multi-beam interference system. This phenomenon is of great significance in the study of the orbital angular momentum of photons and other fields.

Metasurface of deflection prism phases for generating non-diffracting optical vortex lattices.

A functional metasurface of both transparent medium slices and multiple deflection prisms is proposed, where phase retardations for generating non-diffracting vortex lattices are integrated and encoded as rotation angles of nano-apertures. Under plane-wave illumination, the transmitted waves from the thin flat metasurface act analogously as multiple beams, each with a designed propagating direction and pre-scribed phase shift, that generate an optical lattice within their overlapping region of space. By altering the design parameters of the metasurface, lattice type and size can be controlled. Both numerical simulations and experiments were conducted, verifying the possibility of the proposed method and the non-diffracting properties of the generated vortex lattices.

Generation of a plasmonic radially polarized vector beam with linearly polarized illumination.

Polarization state of a wave field can be manipulated through the plasmonic metasurface consisting of orthogonal nanoslit pairs; the output polarization angle is independent of the incident linearly polarized light and is highly dependent on the orientations of nanoslit pairs. We combine the Archimedes spiral with the nanoslit pairs to compensate for the Pancharatnam-Berry (PB) phase induced by the orientation of nanoslits, as well as achieve the radially polarized vector beam (RPVB) under the illuminations of different linearly polarized lights. Experiments are performed to successfully realize the RPVB, and the results are in excellent agreement with the numerical simulations.

Radially polarized plasmonic vector vortex generated by a metasurface spiral in gold film.

Vector vortices with spatially varying polarization are interesting phenomena and have motivated many recent studies. A vector vortex in the wavefield of a surface plasmon polariton (SPP) may be extended to the sub-wavelength scale, which would be more significant. However, the formation of vector vortices requires the polarization state to possess components parallel to the surface of metal films. In this study, we generated radially polarized vector plasmonic vortices using the metasurface spiral of orthogonal nanoslit pairs. We theoretically derived the x and y component expressions in the central point area of the spiral and obtained a doughnut-shaped intensity distribution with radial polarization. The Jones matrix of the metasurface spiral was generated to describe the polarization characteristics. The results were validated by performing finite-difference time-domain simulations. In addition, we used a Mach-Zehnder interferometer system to extract the intensity and phase distributions of different components of the SPP field. The experimental doughnut-shaped radially polarized vector vortex was consistent with the theoretical and simulated results.

Spatiotemporal evolutions of ultrashort vortex pulses generated by spiral multi-pinhole plate.

We use the spiral multi-pinhole plate to generate ultrashort vortex pulses and study their spatiotemporal evolutions involving intensity, phase, orbital angular momentum, and energy current. In the experiment, a Mach-Zehnder-type interferometer is employed to perform the investigation of ultrashort vortices. Combining the experimental results and the theoretical analyses, we discuss the spatiotemporal evolutions of ultrashort vortex pulses in femtosecond regime. The results show that the distribution of orbital angular momentum in the cross-section of the vortex pulse is maintained almost invariable in the pulse duration, while both the intensity and the energy current obey a Gaussian-like distribution. With time evolution, the phase contour lines of such vortex pulses rotate around the propagation axis.

Experimental solution for scattered imaging of the interference of plasmonic and photonic mode waves launched by metal nano-slits.

Using an L-shaped metal nanoslit to generate waves of the pure photonic and plasmonic modes simultaneously, we perform an experimental solution for the scattered imaging of the interference of the two waves. From the fringe data of interference, the amplitudes and the wavevector components of the two waves are obtained. The initial phases of the two waves are obtained from the phase map reconstructed with the interference of the scattered image and the reference wave in the interferometer. The difference in the wavevector components gives rise to an additional phase delay. We introduce the scattering theory under Kirchhoff's approximation to metal slit regime and explain the wavevector difference reasonably. The solution of the quantities is a comprehensive reflection of excitation, scattering and interference of the two waves. By decomposing the polarized incident field with respect to the slit element, the scattered image produced by slit of arbitrary shape can be solved with the nanoscale Huygens-Fresnel principle. This is demonstrated by the experimental intensity pattern and phase map produced by a ring-slit and its consistency with the calculated results.

Measurement of surface parameters from autocorrelation function of speckles in deep Fresnel region with microscopic imaging system.

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.

Generation of second-order vortex arrays with six-pinhole interferometers under plane wave illumination.

We propose a method based on six-pinhole interferometers to generate vortex arrays with topological charge 2, only with plane wave illumination. The six-pinhole interferometer is composed of two concentric symmetrical three-pinhole interferometers with different radial distances of the pinholes and a relative rotation of 60 deg from each other. In the Fourier domain, the vortices with second-order topological charge are generated when the radial distances of the two three-pinhole interferometers satisfy some certain ratios. Due to the symmetry of the six-pinhole interferometer, such vortices are distributed at the vertices of some symmetrically distributed regular hexagons. The experimental results obtained in a focal-to-focal system show satisfactory coincidence with the calculations.

Manipulating the Generation of Photonic Moiré Lattices Using Plasmonic Metasurfaces.

The generation of moiré lattices by superimposing two identical sublattices at a specific twist angle has garnered significant attention owing to its potential applications, ranging from two-dimensional materials to manipulating light propagation. While macroscale moiré lattices have been widely studied, further developments in manipulating moiré lattices at the subwavelength scale would be crucial for miniaturizing and integrating platforms. Here, we propose a plasmonic metasurface design consisting of rotated nanoslits arranged within N + N' round apertures for generating focused moiré lattices. By introducing a spin-dependent geometric phase through the rotated nanoslits, an overall lens and spiral phase can be achieved, allowing each individual set of round apertures to generate a periodic lattice in the focal plane. Superimposing two sets of N and N' apertures at specific twist angles and varying phase differences allows for the superposition of two sublattices with different periods, leading to the formation of diverse moiré patterns. Our simulations and theoretical results demonstrate the feasibility of our proposed metasurface design. Due to their compactness and tunability, the utilization of metasurfaces in creating nanoscale photonic moiré lattices is anticipated to find extensive applications in integrated and on-chip optical systems.

Quarter-Wave Plate Metasurfaces for Generating Multi-Channel Vortex Beams.

Metasurfaces of quarter-wave plate (QWP) meta-atoms have exhibited high flexibility and versatile functionalities in the manipulation of light fields. However, the generation of multi-channel vortex beams with the QWP meta-atom metasurfaces presents a significant challenge. In this study, we propose dielectric metasurfaces composed of QWP meta-atoms to manipulate multi-channel vortex beams. QWP meta-atoms, systematically arranged in concentric circular rings, are designed to introduce the modulations via the propagation phase and geometric phase, leading to the generation of co- and cross-polarized vortex beams in distinct channels. Theoretical investigations and simulations are employed to analyze the modulation process, confirming the capability of QWP meta-atom metasurfaces for generating the multi-channel vortex beams. This study presents prospective advancements for the compact, integrated, and multifunctional nanophotonic platforms, which have potential applications in classical physics and quantum domains.

Generation of high-order optical vortices with asymmetrical pinhole plates under plane wave illumination.

We propose a novel and simple method for generating optical vortex with high topological charge (TC), merely using an asymmetrical pinhole plate illuminated by plane wave. N pinholes are arranged along a particular spiral line around the plate origin, with constant azimuth angle increment and varied radial distances. The radial differences introduce a constant variation of m/N wavelength to the optical paths from the N pinholes to the observation plane origin, and this increases the phases of the transmitting waves by progressively 2mπ/Nand totally 2mπ. We numerically calculate the transmitted light field according to the Fresnel diffraction theory, and find the vortex with TC m around the observation plane origin. The experimental verifications are performed using some self-made asymmetrical pinhole plates fabricated by a femtosecond laser, with the high TC vortices both generated and detected in a Mach-Zehnder type interferometer. The experimental results coincide with the theoretical simulations well.

Tetrad phase vortex structure in scattered SPP field produced by silver nano-ring-slit under linearly polarized illumination.

We report the tetrad phase vortex structure in the scattered surface plasmon polariton (SPP) field produced by a silver nano-ring-slit with linearly polarized illumination. In the experiment, Mach-Zehnder type interferometer is constructed in which a microscopic objective (MO) is used to collect and image the scattered SPP field, and the phase map is extracted by Fourier transform of the interference intensity. To explain the formation of the tetrad phase vortices in the central area of the ring, we propose an empirical model for the ring-slit-excited SPP source field by trial calculations with the Huygens-Fresnel principle for SPP propagations. It is shown that the azimuthal variation of the amplitude of the source SPP is roughly a half of a constant base, and the variation of the phase is a little greater than π/2. The intensity and the phase distributions of the SSP field calculated with the formulations of this model phenomenologically conform the experimental results.

Evolutions of speckles on rough glass/silver surfaces with film thickness.

This paper reports experimental studies on speckles produced by the rough silver films. The speckles on the rough glass/silver surfaces are measured with a microscopic imaging system. The structures of speckle patterns have the characteristics of fractals and multi-scaled sizes. We find that with the increase of the silver film thickness, the contrast of the speckles increases, and the intensity probability density functions gradually transit to exponential decay. We calculate the global and the local correlation functions of the speckle patterns, and find that both the fractal exponent and correlation length of the small-sized speckles decrease with the thickness of the silver films. We use the mechanisms of rough dielectric interface scattering and random surface plasmon waves to give the preliminary explanations for the evolutions of the speckles.

Experimental study on the existence and properties of speckle phase vortices in the diffraction region near random surfaces.

We design an optical setup to extract phase vortices in which the interference intensity of reference light wave and speckle fields produced by random screens with different roughness values in the diffraction region near random screens is obtained. Random screens with different roughness are used as samples. Fourier transform is used to extract speckle phase vortices from the interference intensity, and the experimental results show that the phase vortices can be produced when the roughness of the screen is large enough, and they even may appear on the surface. The density of phase vortices would become larger with an increase of the distances in the diffraction region near the random screen. When the distance is certain, the density of phase vortices becomes larger with the increase of roughness. These results would be helpful for understanding the formation of phase vortices.