 Research
 Open access
 Published:
Dielectric metasurface zone plate for the generation of focusing vortex beams
PhotoniX volumeÂ 2, ArticleÂ number:Â 10 (2021)
Abstract
Vortex beams carrying orbital angular momentum have important applications in high dimensional optical information processing, manipulations of tiny particles, superresolution imaging and so on. Among various optical components, metasurface represents an ideal platform for realizing vortex beams with multiple optical functionalities due to its strong ability in manipulating the phase, polarization and amplitude of light. A metasurface combing the functions of a lens and a vortex beam generator can greatly shrink the size of many optical systems. Here, we alternatively propose a new metasurface design based on the concept of a Fresnel zone plate to generate, focus the vortex beams, and perform onaxis interference between different vortex beams. These functions are experimentally demonstrated through encoding the spiral phase profiles into the odd and even zones of a dielectric metasurface. The proposed vortex beam generation strategy employs the advantages of both the Fresnel zone plate and the metasurface, and may open new routes for highdimensional optical information processing.
Introduction
In 1992, Allen et al. proposed that a LaguerreGaussian beam with a helical phasefront exp(il Î¸) carries orbital angular momentum (OAM) of lÄ§ per photon [1], where l is the topological charge which determines how fast the phase changes along the azimuthal angle Î¸, Ä§ is the reduced Planckâ€™s constant. Since then, vortex beams (VBs) with OAM have attracted increasing attention for their various applications in particle manipulations [2, 3], high dimensional information processing [4,5,6], optical metrology [7, 8], etc. Although conventional devices including spiral phase plates [9], spatial light modulators [10] and so on have been widely used to generate optical VBs, however, they are usually bulky and thus limit the miniaturization of corresponding optical systems. To some extent, this constraint can be circumvented by using metasurfaces which are composed of spatially variant subwavelength metaatoms [11]. In last few years, metasurface technologies have been successfully applied to realize various planar optical components, such as metalenses [12,13,14,15], holograms [16,17,18,19,20,21,22], vortex beam generators [23,24,25,26,27,28,29,30,31,32,33,34,35], pulse shaper [36] and so on. Recently, metasurface devices were also applied to the areas of quantum information. For example, metasurface chips for quantum entanglement states generation and reconstruction [37,38,39], cold atoms generation [40], high dimensional quantum source [41] were experimentally demonstrated.
Among various design strategies, the metasurfaces based on dynamic phase and geometric PancharatnamBerry (PB) phase are usually used to design optical components with high efficiency. For dynamic phase metasurface [11, 14], the phase modulation at specific wavelength is usually implemented by changing the geometrical size of the metaatoms. For the PB phase metasurface [23], the spatially dependent phase of transmitted or reflected light can be achieved by changing the orientation angle of the anisotropic metaatoms. The metasurface VB generators can directly impart a spiral phase factor exp(ilÎ¸) to the electric field of the incident light. In addition to generating VBs, metasurfaces are capable of integratingÂ multiple functions into a single optical chip. For example, simultaneously generating and focusing of VBs were realized by using the phase profiles of a conventional lens [28,29,30,31,32,33,34,35]. A plasmonic metasurface VB generator working in the visible region has low optical efficiency [28]. In order to further improve optical efficiency, both alldielectric [30] and the metaldielectric hybrid [33,34,35] metasurfaces have been proposed. In the microwave regime, which is not the focus of this work, the generation of high efficiency VBs also attract quite a lot of attentions [27, 31, 32].
Like metasurfaces, the Fresnel zone plate [42, 43] is another kind of planar optical devices. By imparting the predefined surface profiles into the two sets of neighboring rings of the Fresnel zone plates, one can control the propagation of electromagnetic waves by using optical diffraction effect. In this work, it is expected that the metasurface based Fresnel zone plate can be used for generating, focusing VB and even preform other optical functions. In the proof of concept experiment, the dielectric metasurface (Fig.Â 1a), consisting of polarizationindependent silicon nitride (SiN_{x}) metaatoms, are employed to generate the focusing VBs with OAM. In addition, we also demonstrated that the HermiteGaussian beam can be synthesized by generating two VBs with opposite OAM values and performing the onaxis interference. Compared to other strategies of generating the focusing multiple VBs, the metasurface zone plate proposed in this work represents a more intuitive route to introduce both the phase for focusing and the phase for controlling the topological charges of the vortex beams.
Results and discussion
Design and fabrication of the metasurface zone plates
According to the HuygensFresnel principle, a typical Fresnel zone plate for focusing light wave consists of concentric rings with radii of \( {r}_n=\sqrt{nf{\lambda}_0+\frac{n^2{\lambda}_0^2}{4}} \), where n is the serial number of rings, Î»_{0} is the wavelength of the incident light and f is the focal length corresponding to Î»_{0} [42]. Under normal incidence, the lights transmitted from two neighbored rings should have a Ï€phase difference at the focal point. In other words, the lights transmitted from all the evennumbered zones or from all the oddnumbered zones have the phase difference of 2qÏ€ at the focal point, q is an arbitrary integer. In addition, the spiral phase zone plate for generating VB with specific OAM value can be obtained by introducing extra spiral phase profiles into the even and oddnumbered zones respectively. Thus, the phase profiles of the spiral phase zone plate can be expressed as:
where Î¸â€‰=â€‰arctan(y/x) represents the azimuth coordinate at any position (x, y) on the zone plate and m is nonzero positive integer.
It should be noted that, the odd and evennumbered zones can also provide a degree of freedom for independently generating two VBs with different OAM values, and therefore can perform the onaxis interference between different VBs. In this case, the spiral phase profiles are defined as:
where l_{1} and l_{2} can be arbitrary integers, representing the topological charges of the VBs generated by the odd and evennumbered zones, respectively.
In this work, the required phase profiles are introduced by using SiN_{x} metaatoms (Figs.Â 1a and b). The phase retardation, which is mainly due to the waveguide effect, can be described by \( {\phi}_{WG}=\frac{2\pi }{\lambda }{n}_{eff}H \), where n_{eff} and H are the effective index and the height of the metaatoms [14]. At the wavelength of 633â€‰nm, the values of H and L are numerically optimized, which are Hâ€‰=â€‰1â€‰Î¼m and Lâ€‰=â€‰400â€‰nm. Then, the value of n_{eff} can be adjusted by varying the radius of the metaatom. Then, the phase retardations of the metaatoms with different radii are calculated by using commercial finite difference time domain (FDTD) solver (Lumerical Inc.). The measured complex refractive index of the SiN_{x} material (Fig. S1) is used in the calculation. As shown in Fig. 1c, the eight phase retardations are equally spaced ranging from zero to 2Ï€. The transmittances of the metaatoms in a periodic lattice are also calculated and all of them are above 90%.
To verify the concept of generating focusing VB with the metasurface zone plate, four metasurface devices with eight phase steps are designed and fabricated. The focal lengths f of all the devices are set to be 2.0â€‰mm at the wavelength of 633â€‰nm. FiguresÂ 2a and b show the phase profiles for generating focusing VBs with topological charges of lâ€‰=â€‰2 and 3, respectively. In comparison, Figs.Â 2c and d correspond to the metasurfaces for generating focusing VBs with topological charges of +/âˆ’ 2 and +/âˆ’ 3, respectively. The scanning electron microscopic (SEM) images of the fabricated samples are shown in Figs. 2el, where all the areas without metaatoms correspond to the phase retardation of zero.
Optical characterization of the fabricated metasurface zone plates
All the four fabricated metasurface zone plates are experimentally characterized by using a homebuild optical setup (Fig. S2). Firstly, the focusing properties of the fabricated metasurface zone plates with topological charges of lâ€‰=â€‰2 and lâ€‰=â€‰3 are measured. According to the geometrical symmetry of the metaatom, we know that these samples are insensitive to the polarization of normally incident light. Without lack of generality, Figs.Â 3ad and il show the measured intensity profiles along the propagating direction with horizontally polarized incident lights at four different wavelengths of 633â€‰nm, 600â€‰nm, 570â€‰nm, and 532â€‰nm. The corresponding focal lengths at the four wavelengths are 2.01â€‰mm, 2.12â€‰mm, 2.23â€‰mm, and 2.37â€‰mm, respectively. This negative dispersion property of the focal length is consistent with the theoretical prediction. According to the diffraction theory, the focal length of a Fresnel zone plate is \( f\left(\lambda \right)=\frac{r_1^2}{\lambda } \) [42], where Î» is the incident wavelength and r_{1} is the radius of the first zone. The calculated relative deviations of the four measured focal lengths from the theoretical values are all less than 1%.
FiguresÂ 3eh and mp show the doughnutshaped intensity profiles of light at the corresponding focal planes at the four wavelengths of the metasurfaces with topological charges of lâ€‰=â€‰2 and 3. The intensity distributions at the focal planes can be analytically calculated by using KirchhoffFresnel diffraction integral formula (Fig. S5), which are consistent with the experimental results. In order to determine the orbital angular momentum of the vortex beams, we calculate the offaxis interference patterns of the vortex beams with a Gaussian beam. As shown in Fig. S6, the fork patterns have two and three dislocated fringes, which indicate that topological charges of the VBs are lÂ =â€‰2 and lÂ =â€‰3, respectively. The intensity profiles in both Figs.Â 3eh and Figs. 3mp gradually deviate from an ideal doughnut shape when the wavelength of light is away from the designed wavelength of 633â€‰nm. This is because that both the phase retardation and the transmission efficiency of every single SiN_{x} metaatom are away from the optimized values. In order to verify the polarization insensitivity of our design, vertically polarized incident light is also used in the experiment. The measured results are same as those using a horizontally polarized incident light (Fig. S3). In addition, the polarization state of the transmitted light is experimentally analyzed (Figs.Â 4a and b). The polarization state of the transmitted light is almost same as that of the incident light.
Under the illumination of horizontally polarized light, the optical efficiencies of the metasurfaces with topological charges of lâ€‰=â€‰2 and lâ€‰=â€‰3 are characterized. As shown in Fig.Â 4c, the focusing efficiencies of the two metasurface devices are above 12% over the wavelength region from 560â€‰nm to 680â€‰nm. For the two metasurface devices, there are some differences in the wavelength dependent diffraction efficiency. This should be due to the different spiral phase profiles encoded into the metasurface zone plates. It seems that the measured optical efficiencies of the metasurfaces deviates far from the calculated ones in Fig. 1b. However, it should be noted that the metaatoms in Fig. 1b are periodically arranged in a square lattice, which is very different from the metasurface zone plate. To estimate the diffraction efficiency of the metasurfaces, we assume the metasurface zone plate has an ideal phase distribution as that of a conventional Fresnel zone plate. The theoretical focusing efficiency of the primary focal point of an ideal phasetype zone plate is about 40.5% (Supplementary Information Section V). Thus, it reasonable to obtain the measured focusing efficiency lower than this value. We expect that the measured focusing efficiencies of the metasurface zone plate can be improved by optimizing the nanofabrication processes.
The metasurface devices with composite topological charges of l_{1}â€‰=â€‰âˆ’l_{2}â€‰=â€‰2 and l_{1}â€‰=â€‰âˆ’l_{2}â€‰=â€‰3 are also experimentally characterized. The intensity distributions of the VBs at the focal planes are shown in Figs.Â 5ad, with working wavelengths of 633â€‰nm, 600â€‰nm, 570â€‰nm, and 532â€‰nm respectively. The petal distributions are produced by the interference of two different VBs. Comparing with the theoretically calculated results in Figs. 5e and j, it is found that the experimental results are consistent with the theoretical expectations. By using similar concepts, onaxis interference between arbitrary two VBs can be realized by encoding the spiral phase profiles into the odd and evennumbered zones of a dielectric metasurface. This proposed device may have important applications in quantum information processing [37,38,39], angular velocity measurement of an object, rotating a tiny particle and so on.
Conclusions
In summary, the designs of polarizationinsensitive metasurface zone plates for generating the focusing VB and the multiple VBs with different OAM values are proposed and experimentally demonstrated. The metasurface zone plate takes the advantages of the intuitive design of the conventional phasetype Fresnel zone plate and the multiple degrees of freedom of the metasurfaces. It should be noted that the numerical aperture of the metasurface zone plate and topological charges of the generated vortex beams will finally be limited by the pixel size of the metaatoms. The proposed strategy in this work may open new avenues for designing optical vortex beams with multiple functionalities.
Methods
Nanofabrication of the metasurfaces
Firstly, a 1000â€‰nm thick SiN_{x} film was deposited on a silica substrate by using plasma enhanced chemical vapor deposition method. Then, a 125â€‰nm thick electron resist (PMMA) layer was spincoated onto the substrate and baked at the temperature 180â€‰Â°C for 3 min. After that, a chargedissipation layer was spincoated on top of the PMMA layer and baked at the temperature of 90â€‰Â°C for 2 min. Subsequently, the patterns of the metasurfaces were written into the PMMA layer by using the electron beam lithography. The chargedissipation layer was removed with DI water, and the PMMA layer was developed with MIBK: IPA solution for two mins. Afterwards, a 20â€‰nm thick Cr layer was deposited on top of the PMMA pattern by using ebeam evaporation and the patterns are transferred to the Cr layer through liftoff processes. The sample with the patterned Cr hard mask layer was etched through the inductivelycoupledplasma etching process. Finally, the metasurface devices were obtained after the removal of the Cr layer in the chromium etchant solution.
Availability of data and materials
The data and the relevant methods are available on request from the corresponding authors.
Abbreviations
 VB:

Vortex beam
 OAM:

Orbital angular momentum
 PB:

PancharatnamBerry
 SiN_{x} :

Silicon nitride
 FDTD:

Finite difference time domain
 SEM:

Scanning electron microscope
References
Allen L, Beijersbergen MW, Spreeuw R, Woerdman JP. Orbital angular momentum of light and the transformation of LaguerreGaussian laser modes. Phys Rev A. 1992;45:8185â€“9.
Simpson NB, Allen L, Padgett MJ. Optical tweezers and optical spanners with Laguerreâ€“Gaussian modes. J Mod Opt. 1996;43:2485â€“91.
Grier DG. A revolution in optical manipulation. Nature. 2003;424:810â€“6.
Gibson G, Courtial J, Padgett MJ, Vasnetsov M, Pasâ€™ko V, Barnett SM, et al. Freespace information transfer using light beams carrying orbital angular momentum. Opt Express. 2004;12:5448â€“56.
Mair A, Vaziri A, Weihs G, Zeilinger A. Entanglement of the orbital angular momentum states of photons. Nature. 2001;412:313â€“6.
Vallone G, D'Ambrosio V, Sponselli A, Slussarenko S, Marrucci L, Sciarrino F, et al. Freespace quantum key distribution by rotationinvariant twisted photons. Phys Rev Lett. 2014;113:060503.
Lavery MP, Speirits FC, Barnett SM, Padgett MJ. Detection of a spinning object using light's orbital angular momentum. Science. 2013;341:537â€“40.
Georgi P, Schlickriede C, Li G, Zhang S, Zentgraf T. Rotational Doppler shift induced by spinorbit coupling of light at spinning metasurfaces. Optica. 2017;4:1000â€“5.
Beijersbergen M, Coerwinkel R, Kristensen M, Woerdman J. Helical wavefront laser beams produced with a spiral phase plate. Opt Commun. 1994;112:321â€“7.
Leach J, Gibson GM, Padgett MJ, Esposito E, McConnell G, Wright AJ, et al. Generation of achromatic Bessel beams using a compensated spatial light modulator. Opt Express. 2006;14:5581â€“7.
Yu N, Genevet P, Kats MA, Aieta F, Tetienne JP, Capasso F, et al. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science. 2011;334:333â€“7.
Khorasaninejad M, Chen WT, Devlin RC, Oh J, Zhu AY, Capasso F. Metalenses at visible wavelengths: diffractionlimited focusing and subwavelength resolution imaging. Science. 2016;352:1190â€“4.
Khorasaninejad M, Capasso F. Metalenses: Versatile multifunctional photonic components. Science. 2017;358:eaam8100.
Khorasaninejad M, Zhu AY, RoquesCarmes C, Chen WT, Oh J, Mishra I, et al. Polarizationinsensitive metalenses at visible wavelengths. Nano Lett. 2016;16:7229â€“34.
Balli F, Sultan M, Lami SK, Hastings JT. A hybrid achromatic metalens. Nat Commun. 2020;11:1â€“8.
Zheng G, MÃ¼uhlenbernd H, Kenney M, Li G, Zentgraf T, Zhang S. Metasurface holograms reaching 80% efficiency. Nat Nanotechnol. 2015;10:308â€“12.
Wang L, Kruk S, Tang H, Li T, Kravchenko I, Neshev DN, et al. Grayscale transparent metasurface holograms. Optica. 2016;3:1504â€“5.
Deng ZL, Li G. Metasurface optical holography. Mater Today Phys. 2017;3:16â€“32.
Mao N, Deng J, Zhang X, Tang Y, Jin M, Li Y, et al. Nonlinear diatomic metasurface for real and Fourier space image encoding. Nano Lett. 2020;20:7463â€“8.
Ding X, Wang Z, Hu G, Liu J, Zhang K, Li H, et al. Metasurface holographic image projection based on mathematical properties of Fourier transform. PhotoniX. 2021;1:16.
Chen WT, Yang KY, Wang CM, Huang YW, Sun G, Chiang ID, et al. Highefficiency broadband metahologram with polarizationcontrolled dual images. Nano Lett. 2014;14:225â€“30.
Wen D, Yue F, Li G, Zheng G, Chan K, Chen S, et al. Helicity multiplexed broadband metasurface hologram. Nat Commun. 2015;6:8241.
Li G, Kang M, Chen S, Zhang S, Pun EYB, Cheah KW, et al. Spinenabled plasmonic metasurfaces for manipulating orbital angular momentum of light. Nano Lett. 2013;13:4148â€“51.
Maguid E, Yulevich I, Veksler D, Kleiner V, Brongersma ML, Hasman E. Photonic spincontrolled multifunctional sharedaperture antenna array. Science. 2016;352:1202â€“6.
Devlin RC, Ambrosio A, Rubin NA, Mueller JB, Capasso F. Arbitrary spintoorbital angular momentum conversion of light. Science. 2017;358:896â€“901.
Yuan Y, Zhang K, Ratni B, Song Q, Ding X, Wu Q, et al. Independent phase modulation for quadruplex polarization channels enabled by chiralityassisted geometricphase metasurfaces. Nat Commun. 2020;11:4186.
Yuan Y, Sun S, Chen Y, Zhang K, Ding X, Ratni B, et al. A fully phasemodulated metasurface as an energycontrollable circular polarization router. Adv Sci. 2020;7:2001437.
Mehmood MQ, Mei S, Hussain S, Huang K, Siew SY, Zhang L, et al. Visiblefrequency metasurface for structuring and spatially multiplexing optical vortices. Adv Mater. 2016;28:2533â€“9.
Ma X, Pu M, Li X, Huang C, Wang Y, Pan W, et al. A planar chiral metasurface for optical vortex generation and focusing. Sci Rep. 2015;5:10365.
Ou K, Li G, Li T, Yang H, Yu F, Chen J, et al. High efficiency focusing vortex generation and detection with polarizationinsensitive dielectric metasurfaces. Nanoscale. 2018;10:19154â€“61.
Bai X, Kong F, Qian J, Song Y, He C, Liang X, et al. Polarizationinsensitive metasurface lens for efficient generation of convergent OAM beams. IEEE Antennas and Wireless Propagation Lett. 2019;18:2696â€“700.
Zhang K, Yuan Y, Zhang D, Ding X, Ratni B, Burokur SN, et al. Phaseengineered metalenses to generate converging and nondiffractive vortex beam carrying orbital angular momentum in microwave region. Opt Express. 2018;26:1351â€“60.
Liu X, Deng J, Jin M, Tang Y, Zhang X, Li KF, et al. Cassegrain metasurface for generation of orbital angular momentum of light. Appl Phys Lett. 2019;115:221102.
Ding F, Chen Y, Bozhevolnyi SI. Focused vortexbeam generation using gapsurface plasmon metasurfaces. Nanophotonics. 2020;9:371â€“8.
Tang S, Ding F. Highefficiency focused optical vortex generation with geometric gapsurface plasmon metalenses. Appl Phys Lett. 2020;117:011103.
Divitt S, Zhu W, Zhang C, Lezec HJ, Agrawal A. Ultrafast optical pulse shaping using dielectric metasurfaces. Science. 2019;364:890â€“4.
Wang K, Titchener JG, Kruk SS, Xu L, Chung HP, Parry M, et al. Quantum metasurface for multiphoton interference and state reconstruction. Science. 2018;361:1104â€“8.
Stav T, Faerman A, Maguid E, Oren D, Kleiner V, Hasman E, et al. Quantum entanglement of the spin and orbital angular momentum of photons using metamaterials. Science. 2018;361:1101â€“4.
Georgi P, Massaro M, Luo KH, Sain B, Montaut N, Herrmann H, et al. Metasurface interferometry toward quantum sensors. Light Sci Appl. 2019;8:70.
Zhu L, Liu X, Sain B, Wang M, Schlickriede C, Tang Y, et al. Dielectric metasurface optical chip for the generation of cold atoms. Sci Adv. 2020;6:eabb6667.
Li L, Liu Z, Ren X, Wang S, Su VC, Chen MK, et al. Metalensarrayâ€“based highdimensional and multiphoton quantum source. Science. 2020;368:1487â€“90.
Attwood D. Soft XRays and Extreme Ultraviolet Radiation: Principles and Applications. Cambridge: Cambridge University Press; 1999.
Born M, Wolf E. Principles of optics. Cambridge: Cambridge University Press; 1980.
Acknowledgements
Not applicable.
Funding
This research was supported by the National Natural Science Foundation of China (91950114, 11774145), China Postdoctoral Science Foundation (No. 2020â€‰M680271), Guangdong Provincial Innovation and Entrepreneurship Project (2017ZT07C071), Natural Science Foundation of Shenzhen Innovation Commission (JCYJ20200109140808088), Shenzhen DRC project [2018]1433, andÂ Beijing Postdoctoral Research Foundation (Q6101013202101).
Author information
Authors and Affiliations
Contributions
Y. H. and X. L. carried out the simulations. M. J. fabricated the metasurfaces. Y. H., X. L., Y. T., X. Z., K. L., and G. L. measured the optical properties of the metasurfaces. J. Z., G. L. and X. L. supervised the project. All authors contributed to the discussion and manuscript writing. The authors read and approved the final manuscript.
Corresponding authors
Ethics declarations
Ethics approval and consent to participate
Not applicable.
Competing interests
The authors declare no competing interests.
Additional information
Publisherâ€™s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Additional file 1.
This supplementary information provides details on refractive index of the SiN_{x} layer, the optical measurements and the calculated intensity distributions of the vortex beams.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Hu, Y., Liu, X., Jin, M. et al. Dielectric metasurface zone plate for the generation of focusing vortex beams. PhotoniX 2, 10 (2021). https://doi.org/10.1186/s4307402100035z
Received:
Accepted:
Published:
DOI: https://doi.org/10.1186/s4307402100035z