Volumetric Generation of Optical Vortices with Metasurfaces - ACS

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Volumetric generation of optical vortices with metasurfaces Lingling Huang, Xu Song, Bernhard Reineke, Tianyou Li, Xiaowei Li, Juan Liu, Shuang Zhang, Yongtian Wang, and Thomas Zentgraf ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.6b00808 • Publication Date (Web): 03 Jan 2017 Downloaded from http://pubs.acs.org on January 3, 2017

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Volumetric generation of optical vortices with metasurfaces Lingling Huang1*, Xu Song1, Bernhard Reineke2, Tianyou Li1, Xiaowei Li3, Juan Liu1, Shuang Zhang4, Yongtian Wang1†, Thomas Zentgraf2‡

2. 3.

1. School of Optoelectronics, Beijing Institute of Technology, Beijing, 100081, China Department of Physics, University of Paderborn, Warburger Straße 100, D-33098 Paderborn, Germany Laser Micro/Nano-Fabrication Laboratory, School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China 4. School of Physics & Astronomy, University of Birmingham, Birmingham, B15 2TT, UK

Abstract: Recent advances in metasurfaces, i.e., two-dimensional arrays of engineered nanoscale inclusions that are assembled onto a surface, have revolutionized the way to control electromagnetic waves with ultrathin, compact components. The generation of optical vortex beams, which carry orbital angular momentum, has emerged as a vital approach to applications ranging from high-capacity optical communication to parallel laser fabrication. However, the typically bulky elements used for the generation of optical vortices impose a fundamental limit toward on-chip integration with sub-wavelength footprints. Here, we investigate and experimentally demonstrate a three-dimensional volumetric optical vortices generation based on the light-matter-interaction with a high-efficiency dielectric metasurface. By employing the concepts of Dammann vortex gratings and spiral Dammann zone plates, a 3D optical vortex arrays with micrometer spatial separation is achieved from visible to near-infrared wavelengths. Importantly, we show that the topological charge distribution can be spatially variant and fully controlled by the design. Keywords: Dielectric Metasurface, Vortex Array, Orbital Angular Momentum

* † ‡

Email: [email protected] Email: [email protected] Email: [email protected]

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Flat optics have attracted great interest for being a promising alternative to control light waves by implementing ultrathin planar elements, namely metasurfaces, with spatially varying phase response instead of relying on phase accumulation along optical paths [1-3]. The main advantage of such tailored metasurfaces is that large phase shifts can be realized by nanostructures with thicknesses much less than the wavelength of light, and thus metasurface can be easily integrated into multifunctional on-chip optoelectronic systems [4-6]. Particularly, one type of such metasurfaces, referred to as geometric metasurfaces (GMs) that are based on a Pancharatnam-Berry phase change principle, provide fascinating dispersion-less and helicity-dependent phase properties [7-9]. The desired phase profile of the wave is directly encoded in the azimuthal orientation of the locally imprinted meta-atom [9-10]. The recent advances in flat optics with metasurfaces have shown the ability to overcome the limitations of conventional optics with a wide range of applications in wave front engineering [11-17], information processing [18], and spin controlled photonics [19-21]. In principle, the phase profiles of nearly any optical components including lenses [11-13], wave plates [14], holograms [15-16], as well as elements capable of bending light in unconventional ways [17] could be designed on the basis of plasmonic or dielectric metasurfaces [22-23]. An important application for metasurfaces is the control and modification of optical beam profiles, and in particular the generation of orbital angular momentum (OAM) for light, which is pivotal in terms of both fundamental physics and practical applications. The optical vortex beam that possesses a helical phase front and a doughnut-shaped intensity in the focus spot [24-25] has received increasing attention for its various applications, ranging from optical manipulation of microscopic particles and biological cells [26] to free-space optical communication system [27]. Such a beam is characterized by an azimuthal phase dependence exp(ilφ), i.e., the OAM in the propagation direction has the discrete value of lh per photon, where l is the topological charge of the beam [24]. Various techniques have been reported for the generation of optical vortices, such as utilizing spiral phase plates, spatial light modulators, cylindrical mode converter and computer-generated holograms [25]. However, bulky macro-scale interference-based generation methods through hologram-coding or phase-shifting have imposed a fundamental physical limit for realizing the vortex beam at a chip-scale footprint. In 2 ACS Paragon Plus Environment

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recent studies, metasurfaces with phase-modification capability were used for optical vortex generation, which showed potential for significant size reduction of the optical elements [4,9,28-30]. However, those vortex plates were so far restricted to create only limited number of vortices with specific topological charges [4,9,28-30], whereas spatial multiplexing would be required to attain additional topological charges [28]. As the various values of OAM of optical vortex beams result in different orthogonal eigenmodes they have gained great attention for optical multiplexing to facilitate a dramatic increase in transmission capacity by exploring the spatial freedom of light waves [27,31-33]. Especially, it has been shown that the use of vortex beams with an OAM basis can increase the tolerance of quantum key distribution systems to eavesdropping [34]. A number of schemes have been proposed for the parallel processing of vortex beams, including free space multiplexing and demultiplexing of OAM eigenstates [35], chip-scale generation and transmission of OAM-carrying beams on silicon-integrated circuits through whispering gallery mode resonators [31-32] and waveguide-based interconnected resonant micro-ring fibers [33]. However, these approaches are resonant and therefore highly dispersive in nature, leading to a narrow bandwidth down to several nanometers. In addition, these techniques are not suitable for achieving a truly three-dimensional (3D) parallel processing of vortex beams with a more compact footprint. In this letter, we propose and experimentally demonstrate the generation of a three-dimensional volumetric vortex array with independently controllable topological charges that is based on a single ultrathin dielectric metasurface. With 3D vortex array we mean that a sequence of coaxial beam profiles in longitudinal propagation direction will be present for the 2D diffraction orders in each transverse plane. We employ the concepts of Dammann vortex grating (DVG) [36-37] and spiral Dammann zone plate (SDZP) [38] together with a lens factor to generate the metasurface phase profile with sub-wavelength pixel size. Figure 1 illustrates the generation and reconstruction procedure of such a 3D vortex array. The metasurface consists of Silicon nanofins patterned on top of a glass substrate. Each nanofin acts as a pixel of the entire diffractive metasurface element that generates the required continuous local phase discontinuity for circularly polarized (CP) light at normal incidence. The generated 3D vortex array with 3 ACS Paragon Plus Environment

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spatially variant topological charges is designed to appear within the Fresnel range of the metasurface. Specifically, the topological charge in each node of the generated 3D lattice can be determined by a simple formula mLx+nLy+qLz, where m, n and q represent the diffraction orders in x, y, and z directions, and Lx, Ly and Lz are the intrinsic base topological charges in transverse and longitudinal directions, respectively (Methods Section). The design technique allows for a well-defined, quantized, and fully controllable spatially variant topological charge distribution. Importantly, such metasurface-based vortex generators can achieve truely 3D vortex arrays over a large volume with high uniformity. Furthermore, the geometric nature of the phase profile (based on a Pancharatnam-Berry-Phase) enables the reconstruction of the vortices over a broad spectral bandwidth in the near infrared and visible wavelength range. Importantly, the metasurface can be designed to possess the remarkable capability of vortex beam detection. The flexibility of our approach enables on-chip parallel processing to 3D micro- and nano-fabrication [39], and offers the possibility of ultrahigh-capacity and miniaturized nanophotonic devices for harnessing angular momentum multiplexing and mode sorting [40-41].

Results: The design principle of the vortex plate is schematically shown in Figure 2. The phase distribution is obtained from the combination of an optimized Dammann Vortex Grating, a Spiral Dammann Zone Plate, and a lens factor, as shown in Figure 2(a) (Methods Section). The DVG is

specially designed to create a two-dimensional vortex

array in the x-y plane with uniform energy distribution among the designated diffraction orders. This is accomplished by integrating the blazing grating with a spiral phase pattern with intrinsic base topological charge of Lx and Ly in orthogonal directions, whereas each period is divided into equal segments for multi-level continuous phase optimization with a simulated annealing algorithm to achieve better uniformity. Each diffraction order (m, n) in the transverse focal plane is characterized by an equal-energy optical vortex of topological charge mLx+nLy. The SDZP can achieve a sequence of coaxial vortices in the focal volume. Indeed, a SDZP is essentially a Dammann zone plate (DZP) into which a spiral phase structure with intrinsic base topological charge of Lz is nested. In analogy to the Dammann grating concept, by modulating the phase transition points in one period in 4 ACS Paragon Plus Environment

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radial direction of the SDZP, the light energy can be redistributed uniformly into several longitudinal coaxial vortices at the desired orders. In addition, a lens factor is also nested into the final phase mask to simplify the generation scheme of the vortex array, because traditionally one has to insert a lens behind the SDZP. Thus a sequence of coaxial focused vortices carrying a topological charge of qLz for qth order can be generated longitudinally in the proximity of geometric focus, by combining the SDZP together with the lens factor. Note here the vortex located at the geometrical focal position of the lens is defined as zeroth order, whereas the vortices extending along the positive z direction are defined as positive orders and vice versa. Therefore, through overlapping these three phase profile of the DVG, the SDZP and the lens factor together, the final phase plate can be formed, which has the capacity to generate 3D vortex array with topological charge distribution obeying the rule of mLx+nLy+qLz. Numerical simulations show the transverse and longitudinal coaxial vortices intensity distributions in both the focal plane (in x-y plane) and the meridian plane (in y-z propagation plane) for each single DVG (Figure 2b) and SDZP (Figure 2c), respectively. The effect of the lens factor, which converges the scattered light from the SDZP into separate longitudinal coaxial positions in the neighbourhood of focus volume, is schematically illustrated by Figure 2d. With such a design an M×N×Q 3D vortex array can be achieved by combining an M×N DVG and a 1×Q SDZP together with a lens factor, where M, N, and Q are numbers of total diffraction orders along three orthogonal orientations, respectively. To verify the concept of our design methodology, a 5×5 DVG with intrinsic base topological charge Lx= Ly =2, a 1×5 SDZP with Lz=2 and a lens factor with focal length f=800 µm are chosen for experimental demonstration. The detailed design principle can be found in the Methods Section. The vortex plate is realized by utilizing a dielectric geometric metasurface to encode the generated phase profile following the above design. The metasurface is composed with designed pattern of silicon nanofins on top of a glass substrate (Figure 3). Each single Si nanofin can be considered as a dielectric resonator. Its orientation dependent interaction with CP light generates the desired geometric phase discontinuity of Φ=2σθ in the cross-polarized scattered field, where σ=±1 corresponds to the helicity of right- (RCP) and left circularly polarized (LCP) incident light, and the azimuthal angle θ of the 5 ACS Paragon Plus Environment

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nanofin with respect to the laboratory frame [9]. It is well known that a half wave plate can fully convert a circularly polarized beam into the opposite handedness as the result of a phase delay of π between the fast and slow axes. Hence, to achieve high conversion efficiency between the two circular polarization states, we carry out a 2D parameter optimization using a rigorous coupled wave analysis method to optimize the size parameters of the nanofins. The lattice constant of the nanofin array was fixed to be 600 nm, and the length L to be 400 nm. The parameters for width and height of the Si nanofins are swept to find the optimum parameters for half-wave plate functionality at the operation wavelength of λ=780 nm. For the refractive index of amorphous silicon (α-Si) at 780 nm a value of n=3.9231+0.1306i was used. The simulated conversion efficiency and phase difference δ between the fast and slow axes are shown in Figure 3(b). Note that the conversion efficiency is defined as the ratio of the cross polarization efficiency to the total transmission efficiency composed of both co-polarization and cross polarization. The optimized values for the height h and width w of the Si nanofins are chosen as 450 nm and 140 nm, respectively, resulting in a high conversion efficiency of 57.2% and a phase delay of π at 780 nm. For the experimental proof of the concept, we fabricate the dielectric metasurface sample by standard electron beam lithography and reactive ion etching of Silicon (for details see Methods Section). The vortex plate contains 666×666 pixels, with a lattice constant of 600 nm. The fabricated Si nanofins have a size of 410×175×466 nm3 (L×w×h), which are close to our designed values (Figure 3c). For the characterization of the metasurface we first simulate the intensity distribution of vortex array in x-y plane at different focal planes along the z direction (Figure 4). The numerical calculations are performed by using a Fresnel diffraction method. From the intensity plots one can clearly observe that the characteristic beam profile for each vortex exhibits an annular intensity distribution in the cross section, and a characteristic dark spot with zero intensity in the center. Furthermore, an entire set of 5 focal planes along the z direction is achieved, whereas the 5×5 in-plane vortices on each plane are spatially variant. For further discussion we take the zeroth-order focal plane at z=815µm for λ=780 nm as an example. According to the rule of mLx+nLy+qLz, we can easily determine that the distributions of topological charges should be symmetric about 6 ACS Paragon Plus Environment

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the diagonal line of such a 5×5 array with q=0. As an illustration, the topological charges in the first row can be calculated as [−8, −6, −4, −2, 0] by setting m=[−2, −1, 0, 1, 2], n=−2, q=0 . Each focused vortex beam shows quite distinct doughnut-shaped intensity distribution with a different radius. Similarly, the topological charge distribution at other focus planes can be calculated with the same method. Experimentally we use a setup as shown in Figure 5(a). A linear polarizer (P) and a quarter-wave plate (QWP) are positioned in front of and after the sample to prepare and select the desired circular polarization state for the illumination and transmission. Due to the sub millimetre size of the reconstructed vortex array, a 20× (NA=0.45) magnifying microscope objective is positioned right after the sample to collect the transmitted light and image it onto a CCD camera. The depth and spatial distribution of the 3D vortex lattice can be analysed by adjusting the 3D precision translation stage where the sample is mounted on. Thus, different focal planes can be imaged separately on the camera to obtain a series of 2D images, allowing the verification of the 3D vortex array located at the corresponding node of the 3D lattice. Although the metasurface is designed for a wavelength of λ=780 nm (for which the metasurface functions as a half wave plate to efficiently enhance the conversion efficiency), it can also work at other wavelengths due to the dispersion-less phase property based on the Pancharatnam-Berry phase principle. We demonstrate this broadband effect by measuring the corresponding beam profiles for wavelengths of λ=633 nm and λ=785 nm at the q=0, 1, 2 planes (Figure 5(b)-(c)). We observe that the vortices with topological charge equal to zero shift their positions from the center diagonal line to the secondary diagonal and third diagonal, respectively. The imperfection in OAM image quality captured by CCD is the result of the overlap between different spectra in the coaxial planes and a possibly slight experimental misalignment for the collection with objective lens. Note that the coupling is mainly coming from the suppression and redistribution of all the other diffraction orders from the SDZP in longitudinal direction. While there is only negligible coupling between the transverse diffraction orders from the DVG. Nevertheless, the experimental results show good agreement with the numerical predictions in Figure 4. More detailed measurement results


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and a movie for evolution demonstration of such 3D vortex array can be found in the Supplementary Material. The metasurface can also be used for measuring the topological charge of a vortex beam (Figure 6). Light from the He-Ne laser with λ=633 nm is collimated and expanded through an objective and pinhole. By using a spatial light modulator (SLM), which is uploaded with a fork shaped phase profile (see inset of Figure 6) to generate the vortex beam of desired topological charge. When a b-charged vortex beam is selected as the incident beam, the topological charges of the 5 × 5 vortex arrays on those five coaxial planes can be determined by mLx+nLy+qLz+b (Figure 7). When the topological charge of the vortex array at a certain order is zero, the vortex will be annihilated, and the dark core disappears. Instead, a central bright spot appears which can serve as the criteria for detection of the topological charge. For the experiment we utilized a vortex beam with topological charge of l=−4 to detect the corresponding vortices in the five coaxial planes. Thus, the corresponding vortex with l=4 would be quenched to be a bright focal point, as indicated by the green dashed lines in Figure 7. All the other vortices would acquire extra OAM of bh . The experimental results confirm our theoretical expectations. The detailed results for incident vortex beam carrying different topological charges of l=0, −2, −4, and −6 can be found in the Supplementary Material.

Discussion: For many applications, it is often crucial to discern different OAM states with high fidelity. For the generation of such 3D volumetric vortex arrays based on the scheme proposed, we proofed that such metasurface design is quite robust against fabrication errors, which can faithfully reproduce the same 3D array with slightly different energy efficiencies to the original ones by adding a limited range of random phase noise. For the experimental detection, the fidelity of the OAM is often limited by the complexity of the experimental setup. While in our scheme, both the wavelength and the angle of incidence are precisely controlled. Even for oblique incidence, the gradient phase generated by the metasurface will only bend the light trajectory of each diffraction orders, but will not change the OAM modes with extra fractional topological charge error. In addition, due to the dispersion-less property of the Pancharatnam-Berry phase principle, such dielectric metasurfaces can generate exact phase profiles as desired, to ensure the high fidelity in 8 ACS Paragon Plus Environment

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the case of wavelength deviation. Other subtle effects in the experiment are almost negligible. Eventually, the fidelity of the OAM states will keep high, and the produced states are in good agreement with simulations. Our presented generation mechanism of volumetric vortex arrays is an efficient and simple method for generating spatially variant vortex beams. Besides the 3D vortex array generation, the metasurface possesses the remarkable capability of topological charge detection for vortex beams. The experimental results show that the overall 5 × 5 × 5 vortex arrays are tuneable by simply changing the OAM of the incident beam. Furthermore, the design process for larger numbers of 3D vortex arrays are almost the same, but there are some restrictions in both the underlying physics and the numerical optimization process. The maximum number of such 3D vortex arrays are determined by the design parameters of the DVG and the SDZP (e.g. period, focal length, spatial separation, numerical aperture). However, both the energy efficiency and uniformity of each vortex beam would decrease accordingly. Nevertheless, for a fixed number, the increase of pixel numbers and reduce of pixel size of metasurface will greatly improve the resolution of the vortices. In addition, it should be noted that the energy distribution of each vortex located in the corresponding node of the 3D lattice can be adjusted to be proportional rather than equally through multilevel continuous phase optimization in each segment of the metasurface plate. Therefore, it can provide greater freedom in applications such as 3D parallel laser fabrication.

Conclusion: In summary, we propose and experimentally demonstrate a kind of volumetric optical vortices with spatially variant topological charges. The concept was realized by an ultrathin dielectric geometric metasurface with chip-scale footprint as small as 400 µm2. The dielectric metasurface with Si nanofins can work effectively as a half wave plate at the operation wavelength of 780 nm which leads to a high efficiency for the Pancharatnam-Berry-phase effect. Such distinguished spatial separability of vortex beam carrying different OAM modes can potentially applied to chip-level high-efficiency high-capacity OAM communication, multi-channel optical trapping devices, and 3D parallel laser fabrication.


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Methods Space variant vortex array design: The generation of the 3D vortex arrays is a combination of optimized 2D Dammann vortex gratings (DVG), spiral Dammann zone plates (SDZP), and a lens factor. A phase distribution can be obtained from each of the three parts and the final phase mask is the overlap of these three parts rather than using separated elements. The transmission function of a one dimensional vortex grating can be expressed by Fourier series as follows: ∞

2π x) (1) Λx m =−∞ Where Lx is the intrinsic base topological charge in x direction, φ is the azimuthal angle, TVG =

∑c

m

exp(imLxϕ ) exp(im

Λx is the period of the grating, and cm is the Fourier coefficient for the mth refraction order. Therefore, this forked-shaped grating can generate a row of optical vortices in the x-y plane with different topological charges, determined by mLx. Due to such a property, the vortex grating has often been used as an effective optical element that can easily generate and detect 1D topological charges of vortex beams. The vortex grating can be extended into two dimensions by the nest of two orthogonal vortex gratings. According to Eq. (1), the transmission function of 2D vortex gratings can be written as: ∞

TVG 2 D =

∑c

m

m =−∞ ∞

exp(imLxϕ ) exp(im

∞ 2π 2π x) × ∑ cn exp(inLyϕ ) exp(in y) Λx Λy n =−∞

∞

2π 2π x+n y )]exp[i (mLx + nLy )ϕ ] = ∑ ∑ cmn exp[i (m Λx Λy m =−∞ n =−∞

(2)

where Ly, Λy, and cn represent the intrinsic base topological charge, period, and the Fourier coefficient of nth diffraction order in y direction, respectively. The generation of 2D vortices by utilizing binary optics elements with phase 0 and π has been well discussed [36]. However, a binary phase structure dramatically reduces the diffraction efficiencies in higher orders. Here, the Dammann phase modulation is applied for uniform optimization with simulated annealing method. To further increase the total 10 ACS Paragon Plus Environment

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diffraction efficiency, we use a different method by optimizing the phase distribution in each small segment. For our 5 × 5 DVG, we set the period of the vortex grating to Λx=Λy=6 µm and divide them into 10 × 10 equal segments with lattice constant of 600 nm for multi-level continuous phase optimization and calculate the maximum diffraction efficiency among these equal-energy orders. The intrinsic base topological charge in x and y axes are set to be Lx=Ly=2. After optimization, the total efficiency η can reach 73.61%. The optimized DVG phase profile can be found in Figure 2(b). Now each order (m, n) is characterized by an equal-energy optical vortex of topological charge mLx+nLy, and the generation range is greatly expanded, as schematically shown in Figure 2(b). Furthermore, spiral Dammann zone plates can achieve a sequence of coaxial vortices in the focal volume, whose transmission function can be expressed as [38] ∞

TSDZP =

∑c

q

q =−∞

exp[iq (

2π 1 − ( ρ sin α )2 + Lzϕ )] Λξ

(3)

where (ρ, φ) are normalized polar coordinates at the entrance pupil plane, α=arcsin(NA) is the maximum aperture angle related to numerical aperture NA of a focusing objective, and Lz is the intrinsic base topological charge of the SDZP. When Lz=0, the SDZP degenerates into a DZP and Λξ is the period in ξ of the DZP, where ξ＝ 1 − ( ρ sin α ) 2 . cq is the Fourier coefficient of the qth order, which related to the phase transitional points in one period. Similarly to the design concept of Dammann grating, by optimizing the values of these transitional points in the SDZP, the light energy can be redistributed into several coaxial vortices at the desired orders. In fact, these transitional points could be obtained directly from the conventional Dammann grating, since it has been well optimized. Once the desired focus number and focus spacing are given, the transmission function TSDZP versus (ρ, φ) can be obtained. Here, we design a 1 × 5 SDZP with transition points of [0, 0.03863, 0.39084, 0.65552, 1] in one normalized period, and we set Λξ=5.2 nm, α=0.2447 with the focal length f= 800 µm, the pixel numbers of the metasurface to be 666×666, and lattice constant to be 600 nm. Thus, the generated coaxial vortex of the qth order is carrying a topological charge of qLz with incidence of a uniform plane-wave beam if the base charge Lz of an SDZP is nonzero (an integer or a fraction). The resulting phase profile is shown in Figure 2(c).


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By overlapping the optimized 2D DVG and SDZP together, we obtain the Fourier series as follows: ∞

∞

∑ cmn exp{i[(m

∑

m =−∞ n =−∞ ∞

∞

∞ 2π 2π x+n y ) + (mLx + nLy )ϕ ]}× ∑ cq exp[iq(2πξ / Λξ + Lzϕ )] Λx Λy q =−∞

∞

2π 2π = ∑ ∑ ∑ cmnq exp{i[m x+n y +q(2πξ / Λξ )]}exp[i (mLx + nLy +qLz )ϕ ] Λx Λy m =−∞ n =−∞ q =−∞

(4)

Where cmnq can be optimized to be equal in the desired diffraction orders by the product of cmn and cq. The first exponential term determines the spatial location of the optical vortices while the second term determines the vortex carrying OAM with topological charges of mLx+nLy+qLz for each (m, n, q)th order. Since the SDZP usually needs to be located in front of a lens to distribute the vortices longitudinally in the proximity of geometric focus. To simplify the reconstruction scheme of such 3D vortex array, a lens factor is also nested into the phase distribution, which can be written as: exp[ − ik( f 2 + r 2 − | f |)]

(5)

Where k=2π/λ is the wave vector, r = x 2 + y 2 is the radius, and f is the focal length of lens. We set λ=780 nm as operation wavelength, and set f =800 µm to be consistent with the design of SDZP, so that the two can achieve a redistribution of the coaxial vortices. Through overlapping these three phase profile of the DVG, the SDZP and the lens factor, the final 3D vortex phase plate is generated. The transverse spacing between any two adjacent orders of the vortex arrays in either x or y direction is obtained from the DVG as ∆x = (Nx /2sinα) λ, ∆y = (Ny /2sinα) λ, where Nx and Ny are corresponding period numbers inside the aperture of the lens factor, NxΛx = NyΛy =2kNA. The axial spacing along z direction is obtained from the SDZP, and it is expressed as ∆z=(Nξ /(1-cosα)) λ, where Nξ =(1-cosα)/ Λξ is the period number in ξ.

Fabrication: The dielectric metasurface shown in Figure 3 was fabricated on an ITO coated float glass substrate. On this substrate a 470 nm thick layer of hydrogenated amorphous silicon was deposited by a physical enhanced chemical vapor deposition (PECVD) process. For depositing the silicon layer a 2% silane/argon mixture was used at 150 °C. Subsequently, 12 ACS Paragon Plus Environment

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a standard electron beam process was used for patterning a PMMA mask on the surface. After development of the PMMA mask a 50 nm Cr layer was deposited by electron beam evaporation. Then the resist and the Cr layer was removed in an acetone bath. Only at the patterned areas small Cr rectangles remains on the surface of the silicon layer. Eventually, this Cr pattern was used as an etching mask for the reactive ion etching (RIE). In this process, a mixture of 20 sccm SF6, 12 sccm O2 and 12 sccm Argon (at 20 mbar pressure and 300 W RF power) was used for etching. The O2 gas was used for a sidewall passivation during the etching to obtaining high anisotropy in the etching rate. After the RIE process the Cr mask was removed by wet etching solution that contains perchloric acid and ceric ammonium nitrate.

Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: XXXXXX. Detailed optimization process of metasurface parameters, experimental investigation of 3D vortex array, and verification of spatially variant topological charges are included.

Acknowledgement L.H., J.L. and Y.W. acknowledge the financial support by the NSFC Major Projects of International Cooperation and Exchanges (No. 61420106014). L.H. and X.S. acknowledge the financial support by NSFC Project (No. 61505007). L.H. and X.L. acknowledge the financial support by NSFC Project (No. 51675049). B.R. and T.Z. acknowledge the financial support by the Deutsche Forschungsgemeinschaft DFG (Grant Nos. ZE953/7-1 and GRK 1464/2 A08). The authors would like to acknowledge the continuous support from Cedrik Meier by providing the electron beam lithography system. Author contributions L.H. and T.Z. proposed the idea, L.H. and X.S. conducted pattern designs and numerical simulations, B.R. fabricated the samples, L.H., X.S. and T.L. performed the 13 ACS Paragon Plus Environment

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measurements, L.H., X.S., B.R., S.Z. and T.Z. prepared the manuscript. L.H., Y.W. and T.Z. supervised the overall projects. All the authors analysed the data and discussed the results. Additional information Competing financial interests: The authors declare no competing financial interests.


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Figure Caption Figure 1. Illustration of the generation and reconstruction procedure of 3D vortex array based on dielectric metasurface. Each Si nanofin plays the role of a pixel of diffractive element, which can generate the required continuous local phase profile with normal incidence of CP light. The reconfigured 3D vortex array with spatially variant topological charges is designed to appear within the Fresnel range.

Figure 2. Design principle of the three-dimensional vortex plate. The phase distribution of the 3D vortex plate can be obtained from the combination of an optimized Dammann Vortex Grating, a Spiral Dammann Zone Plate, and a lens factor. For Dammann Vortex Grating, it can generate 2D vortex array in focal plane; and the Spiral Dammann Zone Plate together with a lens factor can generate coaxial space variant vortex array longitudinally along z direction. Figure 3. Design of the dielectric metasurface. (a) The schematic structure of dielectric metasurface. It consists of Si nanofin array patterned on glass substrate. The orientation angle ϕ of the individual nanofin is carrying the desired phase discontinuity. The period of the nanofin array is fixed to be 600 nm, and the length to be 400 nm. The parameters of width and height are swept to achieve half-wave plate at λ=780 nm. (b) Simulated 17 ACS Paragon Plus Environment

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cross polarization conversion efficiency and phase difference δ by sweeping the parameters of width and height of Si nanofin. The operation wavelength is fixed at 780 nm. (c) Schematic of the sample design and scanning electron microscopy images of the fabricated sample (top view and oblique view).

Figure 4. Simulation results of 3D vortex array of each coaxial plane for λ=780 nm. The green dashed lines indicate the positions where the topological charges are equal to zero.

Figure 5. Experimental investigations of 3D vortex array at two different wavelengths. (a) The experiment set up for capturing an image of the 3D vortex array. Different focus planes can be obtained by tuning the distances between the objective and the vortex plate. Experimental results of vortex array at three different z positions for q=0, 1, 2, respectively, with an incident wavelength of (b) λ=633 nm and (c) λ=780 nm, respectively. The entire set of images can be found in the Supplementary Material. The green dashed lines indicate the location, where the topological charges are equal to zero.

Figure 6. Experimental set up for the detection of topological charges of the vortex array. The spatial light modulator (SLM) uploaded with fork phase profile is used to generate the vortex beam of desired topological charge as incidence beam for the metasurface. After passing through the metasurface sample the 3D vortex array is measured by imaging to a CCD camera (MO-microscopy objective; BS-beam splitter; P-Polarizer; W-quarter wave plate).

Figure 7. Experimental verification of the space variant topological charges of the 3D vortex array. Simulations results (top row) and experimental results (bottom row) for an incident vortex beam with l=−4 and λ=633 nm for different coaxial observation planes along z direction. The corresponding vortex array with l =4 would be quenched to singularity points for vortices located on the green dashed lines.


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3D vortex array m×Lx+n×Ly+q×Lz

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Simulations

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Figure for TOC 284x191mm (63 x 63 DPI)


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Volumetric Generation of Optical Vortices with Metasurfaces - ACS

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