Creating perfect composite vortex beams with a single all-dielectric geometric metasurface

Bolun Zhang; Zheng-da Hu; Jicheng Wang; Jicheng Wang; Jingjing Wu; Sang Tian

doi:10.1364/OE.475158

1. Introduction

Vortex origins from a natural physical phenomenon in ocean. Analogously, the concept of optical vortex beam (OVB) also exists in the field of optics, whose wavefront features a doughnut intensity profile and a spiral phase distribution characterized by a spatial phase-dependent factor exp(ilθ), where l denotes the topological charge (TC), and θ is the azimuth angle [1,2]. So far, it has been generally reported that an OVB carrying orbit angular momentum (OAM) with infinite orthogonal eigenmodes is able to develop the information capacity of a single photon unboundedly, which raises a brand-new degree of freedom for applications in optical communication and manipulation [3–7]. Despite the precedence, the highly TC-dependent annular intensity profile makes it difficult to spatially superimpose the OVBs with different TCs in practical fields, such as coupling them into a single air-core fiber [8,9]. In order to overcome the limitation, perfect vortex beam (PVB) has been introduced as an ideal model of OVB, in which the annular intensity profile maintains constantly no matter how TC changes [10]. At first, conventional optical devices such as axion lens [11], spatial light modulator (SLM) [12], interferometer [13], and digital micro-mirror device [14] were utilized for the generation of PVB. Nevertheless, these methods generally require a series of bulky photonic elements, confronting with various inevitable obstacles in miniaturization and integration.

Metasurface, a two-dimensional (2D) metamaterial constructed by numerous artificial subwavelength meta-atoms, has been listed as a superior candidate for manipulating light arbitrarily in recent years [15–19]. Based on their remarkable advancement in flexibility and compactibility over macroscopic optical components, metasurfaces have brought tremendous vitality for integrating multiple functionalities into a single photonic device, leading to the development of various novel metasurface-based applications, for instance, metalenses [20–23], meta-holograms [24–26], high-resolution imaging [27–29], and vortex beam generators [30,31]. Recently, several attempts have been made to create the PVB with metasurfaces. In 2017, Wu et al. demonstrated an approach of implementing three geometric metasurfaces as substitutes for a spiral plate, an axion lens, and a Fourier transform lens to generate the PVB, while the complexity of its design still remained to be reduced [32]. In 2018, Zhang et al. originally merged the phase profiles of the three bulky optical elements into one plasmonic metasurface, thus simplified the platform availably [33]. Subsequently, more and more strategies have been proposed to further optimize and multifunctionalize the PVB-based metasurface system, so far it has been still a challenge to balance the trade-off between the generation efficiency and operating bandwidth. On the other hand, although the “perfect” characteristic of the PVB has brought an excellent convenience for spatially superposing various OVBs, it also leads to the impossibility to directly distinguish the PVBs with different TCs, producing an inconvenience in information reprocessing and utilization [34–40]. Hence, it is exigent to update the PVB with a more functional metasurface platform.

In this paper, we originally propose an advanced type of the PVB designated as perfect composite vortex beam (PCVB), which can be efficiently generated by a single all-dielectric geometric metasurface in a broadband region. The so-called PCVB is mainly featured with a rosette-like intensity pattern in the focal plane, whose petals are intensively connected with the TC, while the radius maintaining “perfect”. The extra degree of freedom is totally developed by introducing the concept of composite vortex beam (CVB) into our metasurface design. Based on finite-difference time-domain (FDTD) method, we also discuss the generation of the PCVBs with various sizes and rotation angles. To further confirm the practicability of our work, we demonstrate a PCVB s’ coaxial array and detect their optical angular force for manipulating a metallic nanoparticle. We desire our work can open a new gate for various practical applications in optical communication, quantum information processing, and optical spanners.

2. Design and theory

As an ideal model of the OVB, the transverse complex amplitude distribution of the PVB can be expressed as [10]

(1)$$E({r,\theta } )= \delta ({r - {r_0}} )\textrm{exp}({il\theta } )$$

where (r, θ) are the polar coordinates in the beam cross section, δ(r) is the Dirac delta function, and r₀ is the radius of the annular intensity pattern. Since it has been extremely difficult to realize such an ideal model in experiment, a more practical way for generating a PVB is to directly perform the Fourier transform over a high-order Bessel-Gaussian beam (BGB) operating a Fourier transform lens [16,17]. In this case, Eq. (1) can be rewritten as

(2)$$E({r,\theta } )= {i^{l - 1}}\frac{{{w_g}}}{{{w_0}}}\textrm{exp}\left[ { - \frac{{{{({r - {r_0}} )}^2}}}{{{w_0}}}} \right]{J_l}\left( {\frac{{2{r_0}r}}{{{w_0}^2}}} \right)\textrm{exp}({il\theta } )$$

where w_g is the waist of the input BGB, w₀ is the waist of the BGB in the rear focal plane, and J_l is the l^th order modified Bessel function of the first kind. Otherwise, since the BGB has been ordinarily emerging as a product of a Laguerre-Gaussian beam (LGB) with an axion lens, the PVB can also be generated by coaxially passing a LGB through an axion lens and a Fourier transform lens in order [32], as shown in Fig. 1(a). Among which, the transverse complex amplitude distribution of the LGB can be expressed as [4]

(3)$$\begin{aligned} L{G_{plz}} &= \sqrt {\frac{{2p!}}{{\pi ({p + |l |} )!}}} \frac{1}{{w(z )}}{\left[ {\frac{{\sqrt 2 r}}{{w(z )}}} \right]^{|l |}}\textrm{exp} \left[ { - \frac{{{r^2}}}{{{w^2}(z )}}} \right]L_p^{|l |}\left[ {\frac{{2{r^2}}}{{{w^2}(z )}}} \right]\textrm{exp} ({il\theta } ) \\ &\times \textrm{exp}\left[ {\frac{{ik{r^2}z}}{{2({{z^2} + z_R^2} )}}\left] {\textrm{exp}} \right[ - i({2p + |l |+ 1} )ta{n^{ - 1}}\left( {\frac{z}{{{z_R}}}} \right)} \right] \end{aligned}$$

where p is the number of the radial nodes, w(z) = w₀√1 + (z/z_R)² is the beam radius at z, w₀ is the beam radius at z = 0, z_R = πw₀²/λ is the Rayleigh range of the Gaussian envelop, λ is the beam wavelength, L_p^|l| is the Laguerre polynomial, and k = 2π/λ is the wavenumber. As a result, the concept of the CVB can be introduced by superposing multiple LG modes with specific polarization states, which can be described as [41]

(4)$$\left| {LG} \right\rangle _{sup} = \mathop \sum \nolimits_{pl,\sigma }^N c_{pl}e^{i\delta _{pl}}\left| {LG_{pl},\sigma } \right\rangle $$

where |LG > _sup is the transverse complex amplitude distribution of the CVB, N is the total number of the superposition modes, σ represents the circular polarization state, as well as c_pl and δ_pl are the amplitude coefficient and initial phase, respectively. It can be clearly seen that, comparing with the LGB, the CVB definitely possesses more degrees of freedom according to the physical principle suggested in Eq. (4). Thus, it is desired to create a “PCVB” with the same “perfect” characteristic as a typical PVB, while performing more diversity and flexibility based on the identical methodology mentioned above as shown in Fig. 1(b).

Fig. 1. Analogy of the generation schemes between the PVB and PCVB. (a) Schematic illustration of the conventional approach for generating a PVB with a series of bulky optical elements. (b) Schematic illustration of our proposed approach for generating a PCVB based on the same optical setup.

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To numerically demonstrate the above-proposed scheme with a single all-dielectric geometric metasurface, we first extract the phase profiles of the CVB, axion lens, and Fourier transform lens for combining them as the metasurface phase as shown in Fig. 2(a). The phase profiles of the three optical components can be described as

(5)$${\varphi _{CVB}}({x,y} )= \textrm{arg}(\left| {LG} \right\rangle _{sup})$$

(6)$${\varphi _{axion}}({x,y} )={-} \frac{{2\pi }}{\lambda }\sqrt {{x^2} + {y^2}} \cdot NA$$

(7)$${\varphi _{lens}}({x,y} )={-} \frac{\pi }{{\lambda f}}({{x^2} + {y^2}} )$$

where (x, y) are the Cartesian coordinates, NA is the numerical aperture of the axion lens, and f is the focal length of the Fourier transform lens. The basic unit-cell of the designed metasurface is shown in Fig. 3(a), which contains a H = 600 nm height crystalline silicon (c-Si) rectangular nanopillar arranging spatially on a sapphire substrate with a nominal lattice constant of P = 400 nm. The selection of the antenna height H = 600 nm was referred to the normal thickness of spin-coated silicon on substrate (SOS) layer. The selection of the lattice constant P = 400 nm was referred to former metasurface-based PVB works for gaining a desirable high diffraction efficiency in the near infrared region via optimizing the length and width of the nanopillar. Since the high refractive index and low loss of the c-Si strongly governs the functionality of the nanostructure [37,42], our metasurface can lead a great transmission to the subsequent simulations. As a result, for a normally incident circularly polarized light, the geometry-dependent-only Pancharatnam-Berry (PB) phase (or geometric phase) covering from 0 to 2π will be fully yielded by the rotating anisotropic rectangular nanopillars [17,20,27], which can be expressed as

(8)$${\varphi _{PB}}({x,y} )= 2\theta ({x,y} )= {\varphi _{CVB}}({x,y} )+ {\varphi _{axion}}({x,y} )+ {\varphi _{lens}}({x,y} )$$

where θ is the orientation angle of the nanopillar with respect to the fast axis. Eventually, the helical wavefront of the input circularly polarized beam will be converted into the opposite helicity, reconstructing a cross-polarized PCVB in the predesigned focal plane as shown in Fig. 2(b). It can be clearly seen that the rosette-like appearance of the proposed PCVB is actually caused by the singular phase distribution of the CVB. The way we superimposing the LG modes leads to several dividing lines with phase shift across the spiral phase distribution, which are corresponding to the dark parts of the intensity pattern. These dividing lines cut the whole phase distribution into the normally-distributed pieces of cake with only two phases: π and 2π. As a result, this special kind of binary spiral phase distribution will rebuild the incident wavefront, focusing a rosette-like intensity pattern in the focal plane.

Fig. 2. Schematic principal illustrations of generating the PCVB using a single all-dielectric metasurface. (a) Phase profile of the predesigned metasurface as a superposition of the CVB, axion lens, and Fourier transform lens. (b) Schematic illustration for generating the PCVB based on the geometric metasurface. For a RCP beam, the metasurface partly converts it into the opposite helical state, reconstructing a PCVB in the focal plane.

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Fig. 3. Optical properties of the optimized building block. (a) Schematic illustrations of the unit-cell of the metasurface, which contains a c-Si rectangular nanopillar with the height of H = 600 nm, length of L = 186 nm, and width of W = 122 nm arranging spatially on a sapphire substrate with a nominal lattice constant of P = 400 nm. The nanopillar is locally rotated by an azimuth angle of θ with respect to the fast axis according to the PB phase. (b) Magnetic field distributions normally excited by the x- (left) and y- polarized incident light (right) at 780 nm, which suggest a π phase delay between the two components. (c) Distribution of the calculated phase for the x- and y- polarized light, as well as their difference as a function of the wavelength ranging from 600 nm to 900 nm. (d) Distribution of the transmittance of the cross- and co-polarized components, as well as the PCE as a function of the wavelength in the same range.

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In order to realize a broadband generation of the proposed PCVB within the modulation of the PB phase, each nanopillar scatterer of the metasurface array should act as a broadband half-wave plate with a relatively high transmission efficiency across the entire operating waveband [35–37]. To ensure this primary prerequisite, we implement FDTD method to optimize the structural parameters of the nanopillar, where periodic boundary conditions (PBCs) are applied in the x and y directions for simulating a periodic array, and perfect matched layers (PMLs) are adopted to the propagation z direction for eliminating the nonphysical reflections. Besides, the corresponding complex refractive index of the materials except for c-Si are all taken from [43]. The refractive index of c-Si is taken from our experiment data. As shown in Fig. 3(a), the length and width of the nanopillar are optimized to be L = 186 nm and W = 122 nm, which can exhibit an extremely high polarization conversion efficiency (PCE) from 750 to 830 nm in Fig. 3(c), while preserving a phase retardation close to π between the x- and y- polarization components in Fig. 3(d). It is worth mentioning that the PCE discussed here can be defined as: PCE = |t_cross|²/(|t_co|²+|t_cross|²), the transmittance for circularly polarized light can be calculated as |t_cross|² = 1/4[t_xexp(iφ_x)- t_yexp(iφ_y)]² and |t_co|² = 1/4[t_xexp(iφ_x)+ t_yexp(iφ_y)]², where t_x, t_y, φ_x, φ_y are the amplitude and phase shifts of the complex amplitude transmission coefficients for linearly polarized light along the x and y axis, respectively [35]. As a result, our designed all-dielectric geometric metasurface can achieve an extremely high polarization conversion efficiency more than 100% over a broadband range from 750 to 830 nm, as well as the transmittance of the cross-circularly-polarized light can reach over a relatively high value of 0.6 during the broadband range and the highest value of 0.84 at 780 nm. Moreover, the two waveguide-like modes suggested in the magnet field distributions in Fig. 3(b) further unveil the physical mechanism behind the π phase delay, demonstrating the optimized nanopillar as a highly efficient half-wave plate.

3. Result and discussion

According to the above discussions, we first demonstrate the broadband generation of the PCVBs in a near-infrared region by carrying on the FDTD simulations, where PML boundary conditions are applied in the x, y, and z directions. For simplicity, it is only considered superposing two LG modes with the same circular polarization state at z = 0 in this section. Therefore, Eq. (5) can be rewritten as

(9)$${\varphi _{CVB}}({x,y} )= \textrm{arg}({{c_{{p_1}{l_1}}}{e^{i{\delta_{{p_1}{l_1}}}}}|{L{G_{{p_1}{l_1}} \rangle} + {c_{{p_2}{l_2}}}{e^{i{\delta_{{p_2}{l_2}}}}}} |L{G_{{p_2}{l_2}}}} \rangle )$$

where p₁ = p₂ = 0, l₁ = l₂ = l, c_l₁ = c_l₂ = 1, and δ_l₁ = δ_l₂ = 0. As a result, Fig. 4 shows the numerically simulated intensity profiles of the PCVBs with the TCs ranging from l = 1 to l = 3 at different focal distances of 20 µm, 18.7 µm, and 17.6 µm corresponding to the free-space wavelengths of 730 nm, 780 nm, and 830 nm, respectively, which are simply generated by three 24 µm × 24 µm sized radial metasurfaces of NA = 0.2. It can be directly seen that each intensity profile is able to be characterized as a 2D axisymmetric rosette-like annular pattern, whose petals are distributed uniformly along the circumferences of the annular intensity patterns. It is also seen that, with the increasement of the TCs, the petals are varying as two times of the TCs, while the radiuses of the annular intensity patterns are nearly remaining “perfect”. Based on the results, the TC of the proposed PCVB can be directly read by its intensity profile instead of implementing the interference with a co-propagating Gaussian beam [35], which provides a giant convenience for topological information coding and multiplexing.

Fig. 4. Numerically simulated rosette-like intensity patterns of the generated PCVBs with various TCs ranging from l = 1 to l = 3 (from left to right) at different wavelengths of 730 nm, 780 nm, and 830 nm (from top to bottom) using three 24 µm × 24 µm sized radial metasurfaces of NA = 0.2. The focal distances are f = 20 µm, 18.7 µm, and 17.6 µm, respectively. Scale bar: 5µm.

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Then we demonstrate the generation of several PCVBs with various sizes at the central wavelength of 780 nm by simply adjusting the numerical apertures of the metasurfaces, as shown in Fig. 5. It can be clearly seen that, with the numerical apertures ranging from NA = 0.1 to NA = 0.3, the radiuses of the PCVBs increase as well, which are proportional to the numerical apertures of the metasurfaces. Additionally, it can also be seen that with the enlargement of the beam sizes, the intensity patterns gradually become more divergent, which may be affected by the relative sizes between the generated PCVBs and metasurfaces. Therefore, it is critical to balance the trade-off between the numerical aperture and fabrication size of the metasurface for generating a high-quality PCVB with a proper size. As a result, we mainly select NA = 0.2 as a compromised choice in this manuscript.

Fig. 5. Numerically simulated rosette-like intensity patterns of the generated PCVBs with various TCs ranging from l = 1 to l = 3 (from left to right) at the central wavelength of 780 nm using the metasurfaces with different numerical apertures of NA = 0.1, 0.2, and 0.3 (from top to bottom). Scale bar: 5µm.

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Additionally, we further discuss the generation of the PCVBs with various rotation angles and orientations, which are shown in Fig. 6. It can be clearly seen that, comparing with the contrast group of δ_l₁ = δ_l₂ = 0, the PCVBs with different TCs of l = 1, l = 2, and l = 3 are rotated anticlockwisely by about 60°, 30°, and 20° when δ_l₁ = 2/3π and δ_l₂ = 0, respectively, while being rotated clockwisely when δ_l₁ = 0 and δ_l₂ = 2/3π. The results generally indicate that the initial phases essentially represent the contributions of different superposition modes to the rotation of the PCVB, in which the positive and negative TCs of l₁ and l₂ are corresponding to the anticlockwise and clockwise orientations, respectively. As a result, the initial phases of the CVB and the rotation angle of the PCVB α can be approximately inferred as

(10)$$\alpha = \frac{{{\delta _{{l_1}}} - {\delta _{{l_2}}}}}{{2l}}$$

where the operational sign of the result solely denotes the rotation orientation. Thus, via simply designing the initial phases of the metasurface, the rotation of the PCVB is supposed to be controlled arbitrarily.

Fig. 6. Numerically simulated rosette-like intensity patterns of the generated PCVBs with various TCs ranging from l = 1 to l = 3 (from left to right) at the central wavelength of 780 nm using the metasurfaces with different initial phased of δ_l₁ = δ_l₂ = 0, δ_l₁ = 2/3π and δ_l₂ = 0, as well as δ_l₁ = 0 and δ_l₂ = 2/3π (from top to bottom) under the numerical aperture of NA = 0.2. Scale bar: 5µm.

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To further explore the superiority of our design in practical applications, a coaxial array composed of multiple axially-distributed PCVBs is also demonstrated here. As shown in Fig. 7(a), the phase profiles for generating the PCVBs are merged into a single array phase, which can be described as

(11)$$\begin{aligned} {\varphi _{array}} &= \textrm{arg}\left( {\mathop \sum \nolimits_{i = 1}^N \textrm{exp}(i{\varphi_{PCVB,i}}} \right))\\ &= \textrm{arg}\left( {\mathop \sum \nolimits_{i = 1}^5 \textrm{exp}(i({{\varphi_{CVB,i}} + {\varphi_{axion}} + {\varphi_{lens,i}}} )} \right)) \end{aligned}$$

where the number of the PCVBs N = 5. As a result, Fig. 7(b) shows that for a normally incident right-circularly polarized (RCP) light at 780 nm, a series of left-circularly polarized (LCP) PCVBs with various TCs ranging from l = 1 to l = 5 can be generated at different focal distances of f₁ = 16 µm, f₂ = 17 µm, f₃ = 18 µm, f₄ = 19 µm, and f₅ = 20 µm, respectively. Different from the multi-channel non-axial array and coplanar coaxial array demonstrated in the former work [38,44,45], our coaxial non-coplanar design greatly expands the degree of freedom along the propagation direction, alleviating the influence of the beam interference limited by array size on beam quality. Besides, the one-to-one correspondence between the TC and intensity profile, as well as the “perfect” characteristic of the PCVB also develop the proposed design as a more functional platform for information multiplexing and processing. Additionally, to further manifest the limitations of the prior approaches for vortex beam generation and optical vortex distinction, here we list a table for briefly manifesting the advancement of our work compared with the reported similar works, as shown in Table 1. It can be clearly seen that compared with those complicated metasurface platforms such as split-square-ring metasurfaces [30,31], waveguide-like metasurfaces [46], and 3D metasurface, our all-dielectric geometric metasurface is more easily to design and fabricate, while performing a better operating efficiency over a broadband wavelength range. Besides, compared with those typical vortex beam generators [30,31,46] and composite vortex beam generator [41], our vortex beam generator for generating the PCVB is more likely to be a superior candidate for various future OAM-based applications according to our demonstration. Furthermore, compared with those prior complicated approaches for optical vortex (OV) distinction such as holography-based method [47] and deep-learning-based method [48], our proposed PCVBs can be directly distinguished through observation, owing to their easy-to-directly-detect feature from the TC-dependent intensity petals. As a result, our metasurface-based PCVB generator is desired to perform great potential in optical communication and information processing in the possible future.

Fig. 7. Schematic illustrations of generating the coaxial array of the PCVBs using a single all-dielectric metasurface. (a) Phase profile of the array phase as a superposition of multiple PCVBs. (b) Schematic illustration of generating the coaxial array composed of multiple PCVBs with various TCs ranging from l = 1 to l = 5 using the metasurface of NA = 0.2 at 780 nm, where the numerically simulated results can be obtained at different focal lengths of f₁ = 16 µm, f₂ = 17 µm, f₃ = 18 µm, f₄ = 19 µm, and f₅ = 20 µm, respectively. Scale bar: 5 µm.

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Table 1. Comparison of previous similar works with our work

View Table

Last but not least, we calculate the optical angular forces of the PCVBs for demonstrating its capability of manipulating particles. As shown in Fig. 8(a), an Ag particle with radius of 0.2 µm is placed at x = −5 µm in the focal plane of f = 18.7 µm. Therefore, for a normally incident RCP light of 780 nm, the generated LCP PCVBs with different TCs of l = 1, l = 2, and l = 3 will exert an optical force on the Ag particle, respectively. Using the optical force calculation toolbox based on Maxwell stress tensor (MST) available in FDTD software, thus the force of nanoparticles in the light field can be calculated by integrating the MST on the particle surface. The time-average force exerted on the particle can be expressed as

(12)$$\langle F \rangle = \smallint \left\{ {\frac{\varepsilon }{2}Re[{E \cdot n} ]{E^\ast } - \frac{\varepsilon }{4}({E \cdot {E^\ast }} )n + \frac{\mu }{2}Re[{\mu ({H \cdot n} ){H^\ast }} ]- \frac{\mu }{4}({H \cdot {H^\ast }} )n} \right\}ds$$

where ɛ and µ are the relative permittivity and relative permeability of the medium among the particle under test, and n is the normal unit perpendicular to the integration area ds. As a result, we numerically test the optical angular forces of the PCVBs from 0° to 180° by clockwisely rotating the particle around the origin every 90°, 45°, and 30°, respectively, as shown in Fig. 8(b)-(d). The results are shown in Fig. 8(e)-(g), it can be clearly seen that the particle is only forced when it is placed on the petals of the intensity patterns, which suggests that our PCVB-based metasurface can be utilized as an optical spanner for manipulating nanoparticles.

Fig. 8. Optical angular force of the proposed PCVBs. (a) Schematic illustration of detecting the optical force of the PCVBs on an Ag particle. (b)-(d) Schematic illustrations of the relative positions between the Ag particle and the intensity patterns of the PCVBs with different TCs ranging from l = 1 to l = 3 (from left to right) with the same numerical aperture of NA = 0.2 at 780 nm, where the particle is rotated clockwisely every around the origin every 90°, 45°, and 30°, respectively. (e)-(g) Simulated optical angular force of the PCVBs with various TCs ranging from l = 1 to l = 3, correspondingly. Scale bar: 5 µm.

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4. Conclusion

In summary, we have originally proposed a new category of PVB called PCVB, whose “perfect” intensity profile exhibits a rosette-like appearance composed of several TC-related petals. The extra degrees of freedom are genetically inherited by introducing the concept of CVB into the conventional methodology for generating a PVB. Following the trend of miniaturization and integration, we demonstrate the proposed scheme by implementing a single geometric metasurface instead of utilizing bulky optical devices. Based on the numerical simulations with FDTD method, our design is demonstrated to perform a great functionality of generating the PCVBs with various operating wavelengths, diameters, as well as rotation angles for superposition and manipulation. Benefit from the design flexibility and fabrication simplicity, it is desired to experimentally achieve a PCVB-based metasurface platform with even more diversity and superiority in the future.

Funding

National Natural Science Foundation of China (11811530052, 11904136, 62105126); Intergovernmental Science and Technology Regular Meeting Exchange Project of Ministry of Science and Technology of China (CB02-20); Natural Science Foundation of Jiangsu Province (BK20210454); State Key Laboratory of Millimeter Waves (K202238); Graduate Research and Innovation Projects of Jiangsu Province (SJCX20_0763).

Disclosures

The authors declare no conflicts of interest.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Refence	Metasurface type	Vortex beam Generation	Operating Efficiency	OV distinction
[30]	Split-square-ring metasurface	Typical vortex Beam	0.97 at 16 GHz	No
[31]	Split-square-ring metasurface	Typical vortex Beam	More than 80% at 0.86 THz	No
[41]	Geometric Metasurface	Composite vortex Beam	7% at 630 nm	No
[46]	Waveguide-like metasurface	Typical vortex Beam	Maximum coupling efficiency of 16%	No
[47]	3D metasurface	-	Less than 2.5% at 633 nm	Holography- based
[48]	-	-	-	Deep-learning -based
Our work	Geometric metasurface	Perfect composite Vortex beam	PCE of 100% over 750-830 nm	Direct observation

Creating perfect composite vortex beams with a single all-dielectric geometric metasurface

Abstract

Corrections

1. Introduction

2. Design and theory

3. Result and discussion

4. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (8)

Tables (1)

Equations (12)

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