Vortex beams are widely used in optical capture^[1–3], microscopy^[4,5], optical fiber communications^[6,7], quantum information^[8,9], and other fields because of their orbital angular momentum associated with the spiral wavefront. However, the diameter of the vortex beam is easily affected by the topological charge, which will greatly limit the applications of vortex beams. For example, optical tweezers often require a larger topological charge and a smaller spot diameter in particle manipulation, while the topological charge is proportional to the diameter^[10]. The number of multiplexed vortex beams in optical fiber coupling will also be limited in the field of optical fiber communications^[11,12]. However, the cross-sectional spot diameter of the perfect vortex beam is independent of topological charges and will be able to overcome this problem well^[13]. The perfect vortex beam is generated by Fourier transforming a Bessel–Gaussian beam^[14], which is achieved by using a thin convex lens. Traditionally, modulating perfect vortex beams and their beam array patterns can be generated through optical devices such as digital micro-mirror devices (DMDs)^[15], spatial light modulators^[16], spiral phase plates^[17], and axicons^[18], which increases the complexity of the optical system. Therefore, there is an urgent requirement for miniaturized devices to generate high-resolution beams.

Metasurfaces are ultrathin optical components composed of subwavelength unit arrays. Compared with traditional optical devices, metasurfaces can achieve precise control of the amplitude, phase, and polarization of light waves by adjusting the geometric shape and arrangement of each unit on the surface^[19,20]. In recent years, metasurface optical devices have promoted the development of wave plates^[21,22], holograms^[23,24], structured beams^[25,26], and modulation of beam arrays. There are related studies on the use of plasma to generate focused three-dimensional perfect vortex beam metasurfaces^[27], and the use of efficient broadband dielectric metasurfaces to generate ultraviolet vortex metasurfaces^[28]. Metasurface technology for beam arrays has also been reported. For example, a transmissive all-dielectric metasurface was used to generate a Bessel beam array with high uniformity and high resolution through a Dammann grating^[29]. These provide theoretical and experimental foundations for perfect vortex beams and the arrays with subwavelength high-power density. At present, there are few reports on the generation of perfect vortex beams with high reflection efficiency through all-dielectric reflective metasurfaces^[30,31]. In addition, most methods for generating perfect vortex beams are based on axicons, and the resulting ring width is relatively wide, and the optical power density on the ring is relatively weak.

In this paper, we propose an all-dielectric reflective metasurface made of rectangular nanoantennas as a launch device for perfect vortex beams. The encoding of the metasurface is achieved through a Pancharatnam–Berry (PB) phase-specific design that combines the phase distribution of the Bessel beam kinoform (BBK), spiral phase plate, and Fourier transform lens. The structural size of the all-dielectric reflective metasurface is 95μm×95μm. The regulation of different topological charges and ring diameter of the perfect vortex beam can be achieved under the wavelength of 1550 nm. The generation of a four-channel one-order perfect vortex beam array is achieved by introducing a Dammann grating. We have experimentally verified the metasurface device, which is consistent with the simulation results. This technology will greatly facilitate particle micromanipulation and play a huge role in multiplexing information, optical fiber communications, and other fields.

Figure 1 shows a schematic diagram of a reflective metasurface device for generating the perfect vortex beam. Upon irradiation of each anisotropic structure with right-handed circularly polarized (RCP) light, the reflected beam contains a perfect vortex beam with orthogonally polarized components induced by the PB phase, as well as a diverging beam with original spin components. The PB phase delay is determined by the rotation angle of the nanocells, independent of the incident light wavelength and the size of the structural unit. The basic unit of the metasurface structure consists of a three-layer bread structure composed of Si/SiO2/Si (SOI), as shown on the right in Fig. 1. Silicon is crystalline silicon. The thickness of the top silicon layer h=500nm and the lattice constant of the single crystal cell P=950nm. The length and width of the nanocells are optimized using the time-domain finite-difference (FDTD) method with periodic boundary conditions in the x and y directions, and a perfectly matched layer in the z direction. The incident wavelength is 1550 nm, which corresponds to the refractive index n=3.535611+0.001475i for Si, with a small absorption coefficient. Realizing a geometric phase perfect vortex beam metasurface, the anisotropic structure should be a perfect half-wave plate, i.e., φx−φy=π. We perform parametric scans from 250 to 850 nm for length and width, respectively, with a scan interval of 5 nm. For x-polarized light (y-polarized light) incident on the structure, its transmittance Tx(Ty) and phase distribution φx(φy) with respect to the length and width of the nanocells are shown in Figs. S1(a)–S1(d) in the Supplement 1. Here, the length L=670nm and width W=270nm of the single crystal cell are selected. The phase delay of the nanocells with the rotation angle is shown in Fig. S1(e) in the Supplement 1, which verifies the correctness of the PB phase. The maximum cross-polarization reflectivity efficiency is 90.17% at 1550 nm. The cross-polarization reflection efficiency is the incidence of a right-handed circularly polarized beam, which is converted to the reflectivity of a left-handed circularly polarized (LCP) beam. The cross-polarization conversion efficiency can reach 99%. The calculation expression is RLCP/RLCP+RRCP. Figure S1(f) in the Supplement 1 depicts the variation of cross-polarization and co-polarization reflectivity efficiency with normal light incidence with wavelength from 1500 to 1600 nm, and the polarization conversion efficiency is greater than 90% in this band. Therefore, the designed metasurface has a broad working band of 100 nm, including S-band, C-band, and L-band.

In order to realize the generation of perfect vortex beams as well as perfect vortex beam arrays, we start from the basic perfect vortex beam generation method. The perfect vortex beam can be generated by introducing a Fourier transform into the light field through a thin convex lens on the Bessel–Gaussian beam. Here, the BBK method can be utilized to convert the fundamental mode Gaussian beam into a perfect vortex beam. BBK is the diffractive optical element (DOE) based on Bessel beam phase modulation, which is mainly used to efficiently generate annular vortex beams. The perfect vortex beam generated by BBK has the advantages of high energy and a narrow bright ring, and is suitable for applications such as high-resolution microscopy and optical tweezers. The complex amplitude distribution of the l-order perfect vortex beam with spot radius r0 is given by E(r,φ)=F(r)eilφ,(1)where F(r) is the amplitude distribution, characterizing the presence of an amplitude spike at r=r0; φ is the azimuthal angle and l is the topological charge.

The generation of perfect vortex beams requires superposition of the phase profile of the BBK and the phase profile of the thin convex lens, and the phase distribution [shown in Fig. 2(a)]. The phase profile of the perfect vortex beam is φ(x,y)=φBBK+φlens.(2)

Here, the phase profile of the BBK is φBBK=sgn[Jl(2πr0r)]eilφ,(3)where Jl(·) is the l-order Bessel function, r0 is the parameter associated with the perfect vortex beam, φ is the azimuthal angle, and l is the topological charge. The phase profile consists of two parts: radial and angular, where the vortex term represents the angular component. sgn[Jl(2πr0r)] is the radial component. They determine the vortex structure of the beam and the Bessel-like profile of the beam, respectively, forming a ring-shaped intensity distribution in Fourier space.

The phase profile of a thin convex lens is φlens=−π(x2+y2)λf,(4)where λ is the wavelength of the incident light and f is the focal length of the generated perfect vortex beam. The phase of a Fourier lens enables the light field to complete an accurate Fourier transformation in the Fourier plane (focal plane).

In this paper, we combine the perfect vortex beam phase profile with a Dammann grating to produce perfect vortex beam arrays. The even-numbered Dammann grating is used, which has better uniformity of each diffraction order than the odd-numbered Dammann grating. According to the principle of the Dammann grating, the diffraction angle is θ=arcsin(mλp),(5)where m is the diffraction order and p is the grating period.

The distance between adjacent diffraction order spots is Δd=D2tan[arcsin(NA)]tan(arcsinmλp),(6)where D is the diameter of the metasurface. In this paper, the diameter size of the metasurface is D=95μm; NA is the numerical aperture, NA=0.15. It can be found that the grating period p can dynamically adjust the distance between neighboring spots through this equation. Decreasing p can increase the spot distance and reduce the interference between the spots. In this paper, the Dammann grating period is carefully designed with px=py=9.5μm, which is the smallest period that can be designed based on the structure of the metasurface. Therefore, the metasurface can be composed of 10 such periods of Dammann gratings, that is, D=10×p. We utilize this method to generate 2×2 perfect vortex beam arrays. The structure size of the metasurface is 95 µm, the single unit cell P=950nm, and the metasurface structure can be composed of 100 nanocells. According to the inflection point coordinate of 0.5 for even-type Dammann gratings, the position of the phase mutation point is at the 50th nanocell.

The perfect vortex beam based on the Dammann grating can be generated by the superposition of the phase profile of the Dammann grating and the phase profile of the perfect vortex beam, as shown in Fig. 2(b), and the phase profile can be represented as φarray(x,y)=φBBK+φlens+φDamman.(7)

According to the metasurface designed with geometric phase, the rotation angle θ of the structure is half of the phase profile, and the anisotropic structural units are arranged into a spatially non-uniform array at a specific rotation angle to obtain the corresponding perfect vortex beam phase profile. Here, we study the effect of different topological charges l on the generation of perfect vortex beams by the FDTD method, as shown in Fig. 3, where the focal length is f=300μm. Focused field distributions in the x–y plane and transmission field distributions in the x–z plane with topological charges l=−3,−2,−1,1,2,3 are studied, respectively. It can be seen that the ring diameter and the ring width keep a constant value of 93.4674 and 7.0351 µm at f=300μm, despite the topological charge changes. The intensity uniformity calculation formula of the perfect vortex beam is Q=1−(Imax−Imin)/(Imax+Imin). The uniformity of the perfect vortex beams with different topological charges is approximately above 0.9. It can be seen from the transmission field that at the near-field position, the Gaussian beam passes through the metasurface, resulting in a Bessel beam that begins to propagate forward and evolves into a perfect vortex beam at z=300μm. Here, we can see that the ring diameter of the Bessel beam is related to the topological charge and increases with the increase of the topological charge. In addition, the perfect vortex beam is interfered by a spherical wave. The simulations show that perfect vortex beams with l=1,2,3 appear as one, two, and three petals, respectively. The interfering petals are equal to the topological charge. The perfect vortex beams with opposite topological charges have different rotational orientations of their interfering petals, as shown in Figs. 3(m)–3(r). We numerically calculate the effect of different topological charges l on the perfect vortex beam using the Fresnel diffraction integral, as shown in Fig. S3 in the Supplement 1. It can be seen that the numerical calculation results of Fresnel diffraction are completely consistent with the simulation results, and the ring diameters of the perfect vortex beams are also completely equal. For perfect vortex beams with different topological charges, we calculate their OAM spectra and find that perfect vortex beams with different topological charges can achieve a mode purity as high as one. The results are shown in Fig. S8 in the Supplement 1.

The ring diameter control of the perfect vortex beam is different from the control through the axial period of the axicon, which can be controlled by the diameter parameter r0 in Eq. (3). We set r0 as 0.04, 0.06, 0.08, and 0.1, and the distributions of the focusing field and the x–z plane electric field are shown in Figs. 4(a)–4(h). It can be seen from the simulation that as r0 increases, the ring radius gradually increases. The ring diameters are 31.186, 55.2764, 73.3668, and 93.4674 µm, respectively, which is almost linear growth, as shown in Fig. 4(i). The light intensity distribution is greater than 0.9, which directly reflects the high-reflection efficiency of the perfect vortex beam metasurface designed as shown. In the x–z plane electric field distribution, when the ring diameter is small, the longitudinal focal depth of the Bessel beam is longer than when the ring diameter is large, so it will cause the diffraction ring at the edge of the focused field to appear when r0 is small. At the same time, we also numerically calculate the effect of different diameter parameters r0 on the perfect vortex beam using the Fresnel diffraction integral, as shown in Fig. S4 in the Supplement 1. The simulation results are completely consistent with the theoretical calculation results.

The Dammann grating can be used to control the perfect vortex beam array and realize multi-channel perfect vortex beams. We generate a 2×2 perfect vortex beam array by superimposing the perfect vortex beam phase profile with the Dammann grating phase profile. The effects of different topological charges and Dammann grating periods on the perfect vortex beam array are studied. The Dammann grating period p can directly affect the spacing of the perfect vortex beams. The larger the period p, the smaller the distance between the perfect vortex beams. Figures 5(a)–5(d) show the phase distributions for l=−1, p=9.5μm, l=1, p=9.5μm, l=−1, p=19.5μm, and l=1, p=19.5μm, respectively, and Figs. 5(e)–5(h) show the focusing field distributions corresponding to the phase distributions. Here, r0=0.04 and focal length f=300μm. The diffraction angle of the perfect vortex beam array is 9.28°, and the spot distance is 100 µm when p=9.5μm. The diffraction angle of the perfect vortex beam array is 4.53°, and the spot distance is 49.74 µm by calculation when p=19.5μm. The intensity uniformity of the four perfect vortex beams is about 0.4. This is because the superposition of the Dammann grating phase interferes with the distribution of edge intensity. The perfect vortex beam is the light spot with a dark center and bright surroundings. The phase mutation points modulated by the Dammann grating often form phase mismatch areas at the annular bright spots, which will cause discontinuous bright spots and uneven light spots in the ring structure. The correctness of generating perfect vortex beams by a Dammann grating is verified through simulation. The results of the ring characteristics and topological charge characteristics of the perfect vortex beam array can be found in Figs. S9 and S10 in the Supplement 1. It is further proved that the light intensity distribution is uneven, but the topological charge is consistent.

To verify the correctness of the simulation results, we designed and built a reflective metasurface test device, as shown in Fig. 6(a). The experimental device is composed of the 1550 nm laser light source, which is converted into collimated right-handed circularly polarized light through a linear polarizer and a quarter-wave plate. Since the designed metasurface is geometrically phase modulated, when we convert the light beam into left-handed circularly polarized light, there will be no phenomenon on the structure, and only the reflected light spot of the incident light beam irradiating the structure will appear. Through pinhole filtering, the aperture of the pinhole is 50 µm. The light beam passes through a 20× objective lens with an NA of 0.4 and converges on the metasurface. In order to observe the generated perfect vortex beam, the reflected light is collected again through a 20× objective lens. Finally, the perfect vortex beam is collected by the charge-coupled device (CCD). Another set of quarter-wave plates and linear polarizers is used to distinguish the original polarization state from the cross-polarization state.

The perfect vortex beam experimental results collected by the reflective perfect vortex beam experimental device we built based on Fig. 6(a) are shown in Figs. 6(b)–6(g). The collected experimental results have been subjected to the corresponding image processing. Figures 6(b)–6(g) show the intensity distribution results of fixed diameter parameter r0=0.1, focal length f=300μm, and topological charges of 1, −1, 2, −2, 3, and −3, respectively. The diameter of the perfect vortex beam does not change with the change of topological charge through experimental testing. Usually, the vortex beam with perfect characteristics is presented by the Fourier plane of the lens. During the experiment, the perfect vortex beam must be at the designed focus f=300μm to show a “perfect” result. Once it passes the focus, the effect of the perfect vortex beam will disappear. To further verify the effect of the perfect vortex beam array, we set the diameter parameter r0=0.04, the focal length f=300μm, the topological charge l=1, and the period p=9.5 and 19.5 µm, respectively. It can be seen from the collected experimental results that the period p will affect the spacing of the perfect vortex beam array. Due to the influence of the incident light, the collected perfect vortex beam has stray light spots, but the physical properties such as the ring diameter and diffraction angle are almost consistent with the simulation results in Fig. 5. In addition, the results in Figs. 6(h)–6(i) further verify the influence of the diameter parameter r0 on the perfect vortex beam. Figure 6(j) shows the scanning electron microscope (SEM) results of the prepared metasurface sample, and Fig. 6(k) shows the local SEM magnified view of the center of the sample. Electron beam lithography is used to prepare the metasurface samples, and the detailed processing flow is shown in Fig. S5 in the Supplement 1. Figure 6(l) is a comparison of the ring diameter data of the simulation and the experiment. It can be seen from the figure that the diameter of the simulation ring is almost equal to that of the experimental ring, and the error is no more than 0.5 µm. There are two possible reasons for this error. The first is the error caused by processing, and the second is the error introduced by the displacement platform during the experiment. Figure 6(m) shows the comparison results of the ring width between the experiment and the simulation. It can be seen that the simulated ring width is 6.02 µm, while the experimental ring width is within the range of 4.84 to 7.61 µm, with an error not exceeding 1.6 µm. The sources of error lie in the incident light intensity in the experiment and the changes in the front and back positions of the CCD. Figures 6(n)–6(q) show the interference results of perfect vortex beams with topological charges of −3, −2, +2, and +3 with spherical waves. The experimental setup is shown in Fig. S11 in the Supplement 1. We can see that the number of petals separated by interference corresponds to the topological charge result, and the handedness of the petals represents their positivity or negativity. The dotted line in the figure represents the number of interfering petals. Here, the metasurface sample was experimentally tested, and it was found that a highly efficient perfect vortex beam can be obtained at the front end of another set of wave plates and linear polarizers, with a polarization conversion efficiency of 89.91%, shown in Table 1. The experimental data of polarization conversion efficiency are shown in Fig. S6 in the Supplement 1.

In summary, we propose and demonstrate a beam generator based on an all-dielectric reflective metasurface composed of rectangular nanoantennas. Combined with the Bessel beam kinoform, the phase distribution of the spiral phase plate and the Fourier transform lens is based on the geometric phase to achieve multi-parameter control of the perfect vortex beam and its multi-channel beam array. We have proved that the topological charge has no effect on the ring diameter, and the diameter parameter r0 can be used to control the beam diameter. In addition, combined with the Dammann grating, the generation of four-channel perfect vortex beams is achieved, and the beam uniformity is about 40%. The designed reflective metasurface has a polarization conversion efficiency of 89.81%. This work has good consistency in theory, numerical analysis, and experiment. We believe that the designed compact reflective perfect vortex beam will have potential applications in optical fiber communications, particle manipulation, quantum information, and so on.