## Abstract

Optical vortices, carrying quantized orbital angular momentum (OAM) states, have been widely investigated because of their promising applications in both classical and quantum realms. Among these applications, efficient generation and measurement of OAM beams are critical. Current techniques available for generating OAM beams generally suffer from bulky size, low operation efficiency, or single-function or complicated fabrication processes. Here we propose and experimentally demonstrate an approach to generate arbitrary optical vortices with a chip-scale device based on all-dielectric two-dimensional (2D) polarization-independent metasurface grating. Based on multi-beam interference in principle and nanofabrication techniques for implementation, our device allows efficient and simultaneous on-chip generation of multi-channel beams with different OAM. We further demonstrate that our device can also work reversely in detecting the OAM spectrum of various pure and mixed optical vortices (e.g., fractional OAM orders) with low crosstalk. Our scheme may find potential applications in developing new integrated photonics for OAM-based high-dimensional quantum information processing in future quantum network.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

The study of optical angular momentum could be traced back to 1909 when Poynting first realized that the left- and right-handed circularly polarized light beams can carry a spin angular momentum of $\pm \hslash $ per photon, respectively [1,2]. While in 1992, Allen *et al.* [3] recognized that light beams with an azimuthal phase dependence of $\mathrm{exp}(il\phi )$can carry a well-defined orbital angular momentum (OAM) of $l\hslash $ per photon, where $\phi $ is the azimuthal angle and $l$ is an integer called the topological charge. In the past decades, OAM beams have been extensively studied in a variety of fields, ranging from optical manipulation, optical communications, quantum information processing [4–11], to topological photonics [12,13]. Among these applications, the efficient generation and measurement of OAM are essential and critical. However, traditional methods employing bulky optics, such as spatial light modulators (SLMs), spiral phase plates (SPPs), and Q-plates, suffer from the large device size, relatively low spatial resolution, limited materials or complicated fabrication process.

In recent years, a promising solution to overcome the above problem in bulky devices is to explore optical elements based on a subwavelength-thick thin film with fine structures, i.e. metasurface [14–16]. It enables the control of light’s reflection and diffraction by utilizing subwavelength metallic nanoantennas [17,18] and high refractive index dielectric materials [19–22]. However, the first mentioned method can suffer from low operation efficiency due to the prominent ohmic loss, absorption in the optical frequency and high scattering loss in metallic materials [23,24]. Also, the discrete phase step in both of metallic and high refractive index dielectric materials inevitably leads to the OAM mode crosstalk [25]. Here, we propose, design and fabricate a chip-scale ($0.5\text{mm}\times 0.5\text{mm}$) OAM device of two-dimensional grating based on an all-dielectric metasurface, i.e., a so-called metasurface grating [26,27]. Here the size of each unit is several micrometer and the height is about half wavelength. Based on such device, we demonstrate efficient and simultaneous generation of multiple OAM beams with topological charge from $l=-3$ to $\text{+}3$. We also show that our device can be applied reversely to detect pure OAM states with a crosstalk less than −18 dB. Besides, we measure the OAM spectrum of a non-integer optical vortex, manifesting its potential in developing a multi-function integrated OAM analyzer.

## 2. Design

In 1948, a two-step imaging process discovered by Gabor involves photographing the Fresnel diffraction pattern of an object and using the recorded pattern, called a hologram, to construct an image of the object [28,29]. In recent years, the holographic approach based on multiple beam interference in generating photoresist lattice masks has attracted great attentions [30–33]. Two-dimensional (2D) photonic crystals (PCs) have been widely adopted for various materials to generate various novel optical phenomena. For example, a holographic optical element (HOE), previously obtained by a three-beam interference pattern, has been applied to generate three interference beams and their conjugated light beams simultaneously under the illumination of a single laser beam [34]. In this framework, if the beams used to do the interference carry orbital angular momenta, the generated beams constructed from the hologram will also carry well-defined OAM, with topological charges determined by the original beams. Considering monochromatic incident beams with the electric field of ${\overrightarrow{E}}_{i}(\overrightarrow{r},\phi )={\overrightarrow{E}}_{i}\mathrm{exp}(i{\overrightarrow{k}}_{i}\xb7\overrightarrow{r})\mathrm{exp}(i{l}_{i}\phi )$, the intensity distribution of the interference pattern is given by

_{and $\phi $}are the position vector and the azimuthal coordinate, and ${\overrightarrow{E}}_{i(j)}$, ${\overrightarrow{k}}_{i(j)}$ and ${l}_{i(j)}$ are the complex amplitude, the wave vector, and the topological charge of each incident light beam, respectively. Considering three beams with topological charges of 0, + 1 and + 3 involved in the interference, the interference pattern can be obtained as shown in Fig. 1(a) using numerical simulation, whose period would depend on the interference angle and influence the diffraction angle [35].

It is noted that there are three one-dimensional (1D) forked gratings with different numbers of dislocations localized in three different directions. That is, in the direction of A-A’, there is a 1D forked grating with one dislocation; in the direction of B-B’, the number of dislocation is 3; and in the direction of C-C’, the number is 2. In fact, there exists a generalized formula that can describe the relationship between the number of dislocations and topological charges of these beams used to interfere. Here, denoting ${l}_{1},{l}_{2},{l}_{3}$ as the number of topological charges, and ${m}_{1},{m}_{2},{m}_{3}$ as the number of dislocations, we can have

After binarization of the interference pattern, it is noted that the shape of lattices is similar to a hexagon, so in order to simplify the fabrication requirement, we replace each construction pattern by a uniform hexagon lattice with the same size, which depends on the grating period. The redistributed interference pattern is presented in Fig. 1(b). It is worth mentioning that the distorted interference pattern at the center could be replaced by several well-distributed hexagon lattices without affecting the function of this device [36], because in our design design, the key is the dislocation of the forked grating, rather than the local area at the center. Besides, to ensure a high diffraction efficiency, the relative phase difference within the two-dimensional phase grating should equals $\pi $ corresponding to the maximum phase difference, and thus the height of each lattice should be fixed by

where $d$ is the height of the lattices, $n$ and ${n}_{0}$ being the refractive index of material and air, respectively, and $\lambda $ is the wavelength of incident light in free space. For $\lambda \text{=}632.8\text{nm}$ and $n=2.0024$, the calculated height should be $d=316\text{nm}$, in a sub-wavelength range.We would like to point out that the above design can be further generalized with more beams involved in the interference and reconstruction processes. The number of the generated LG beams denoted as${N}_{LG}$ relates to the number of the interference beams denoted as ${N}_{B}$ through ${N}_{LG}=2{C}_{{N}_{B}}^{2}$, where $C$ represents the number of combinations. For example, in the case of a two-beam interference with ${N}_{B}=2$, there will be two LG beams generated with the forked grating as ${N}_{LG}=2{C}_{2}^{2}\text{=}2$. The topological charges of the generated LG beams also depend on the difference values of any two interference beams which are translated to the numbers of dislocations of the forked gratings. In this way, one can obtain more LG beams with the forked gratings formed through more beam interference in the design, which may be restricted by the spatial resolution of the fabrication techniques in practice though.

## 3. Fabrication

The fabrication process of the designed metasurface-grating device is described in the following. The inductively coupled plasma-chemical vapor deposition (ICP-CVD) process is firstly optimized to deposit a silicon nitride film (316 nm in thickness) on a silica substrate, as depicted in Fig. 1(c). After deposition, a high resolution positive resist ZEP 520A (330 nm in thickness, ZEON Inc) is coated on the substrate, followed by sputtering a ~50-nm aluminum (Al) layer to enhance the electro-conductivity of the substrate. Subsequently the OAM grating patterns are defined in the resist by an electron-beam lithography (EBL) system (Vistec EBPG5000 ES) at 100 KV. After dissolution of Al layer and development of ZEP 520A to obtain the defined structures in the resist, the reactive-ion-etch (RIE) (Oxford Instrument Plasmalab System 100 RIE180) with a mixture of CHF_{3} and O_{2} gases is applied to etch through the silicon nitride layer. The RIE process has been optimized with regard to vertical and smooth sidewalls of hexagon micro- or nano-posts. Finally, O_{2} plasma ash is applied to remove residual resist and hence silicon nitride layer are patterned as the desired OAM metasurface gratings.

## 4. Experiment and results

The experimental characterizations of the device are performed with the optical setup shown in Fig. 2. The light source is a linearly polarized fundamental Gaussian mode emitted from a He-Ne laser (2-mW, 633-nm). After being collimated by a telescope, the light beam shines on a computer-controlled spatial light modulator (SLM, Hamamatsu, X10486-1) that works as a reconfigurable reflective element. The SLM is also used to control the complex amplitude of the reflected beam simultaneously. By loading the holographic grating in the SLM, the reflected beams are used as the source of Gaussian beams and OAM beams. After passing through a 4f system, the reflected light is divided into two beams by BS1, in which the reflected beam serves as the reference beam, while the transmitted one after illuminating the 2D grating are converted into multiple OAM beams with topological charge from $l=-3$ to $\text{+}3$ simultaneously. BS2 is subsequently used to divide the generated beams into two parts. The intensity of the transmitted part is recorded by CCD1 (denoted as part-**A**), while the reflected part interfering with the reference beam is recorded by CCD2. In addition, the part- **A** will be replaced by the part-**B** shown in Fig. 2 to measure the intensity of the generated light by an optical power meter after coupling into a single mode fiber.

Under the illumination of the Gaussian beam, six diffractive beams with different OAM (*l = $\pm 1,\pm 2,\pm 3$*, respectively) are generated simultaneously and recorded by the CCD camera, as shown in Fig. 3(a). At the center of the pattern is the zero-order diffraction with a near-perfect spot. The intensity of each diffractive beam exceeding 70% of that of the zero-order diffracted light, which means up to 82% diffraction efficiency achieved even if higher-order diffracted beams are neglected due to their dimness. Each generated beam features a dark core in the center and a higher value of topological charge $\left|l\right|$ corresponds to a larger radius, which is the typical characteristic of an optical vortex, despite their elliptical shape due to a slight angle between the propagation direction of each diffractive beam and the recorded plane.

In order to verify the topological charge of generated beams, interference patterns of diffractive beams interfering with a reference Gaussian beam are recorded by CCD2 and presented in Figs. 3(b)–3(g). The number of forked dislocations equals to the value of $l$ and the direction of forked dislocation corresponds to its sign. Note that both the values and signs of the topological charge number of the first order diffractive light beam are related to the 1D forked gratings and its direction according to Eq. (2) as expected.

With the principle of reciprocity for a linear system, this device can also be used to detect OAM states of the incident optical vortices. For example, if the topological charge of incident light is $l(l=\text{-}1,\text{-}2,\text{-}3,\text{+}1,\text{+}2,\text{+}3)$, the topological charge of each diffractive beam would increase by $l$ to *l* + *l*_{0}, where *l*_{0} is the original topological charge of diffractive beam. Therefore, in some special conditions, the transformation between Gaussian beam and OAM beam can be reversible, which means it is practically feasible to detect the incident OAM beams. When the condition *l* + *l*_{0} = 0 satisfies, the corresponding diffractive light will be transformed to a Gaussian beam with a central bright spot, while the centers of the other diffractive beams remain dark region with null intensity. The SLM is used to generate different OAM beam (*l* = + 1, + 2, + 3, −1, −2, and −3, respectively), and the corresponding diffractive patterns are obtained, as shown in Figs. 4(a)–4(f), in which white dotted circle denotes the generated Gaussian beam. We can see that the incident beams with different topological charge values are transformed to corresponding Gaussian beams in different directions, suggesting an effective and simple approach to detect the OAM beams.

After replacing part-**A** with part-**B**, the intensity of the Gaussian spot from each diffractive beam is measured quantitatively and the calculated crosstalk matrix of 7 OAM beams ($l=0,\pm 1,\pm 2,\pm 3$) is shown in Fig. 4(g), where the measured data have been normalized [37]. Note that the crosstalk between input and output OAM beams that do not satisfy *l* + *l*_{0} = 0 is measured to be about 1.4% or about −18 dB. It is worth noting that the center of the incident beam needs to be aligned with the center of the device perfectly in the experiment; otherwise, the crosstalk will increase [38]. Moreover, this metasurface-based grating can be used to simultaneously measure the OAM spectrum (from −3 to + 3) of a non-eigenstate fractional optical vortex by recording the power of the Gaussian spot from all diffractive beams. Taking optical vortices with $l=0.5$ and 1.5, respectively, the calculated and measured OAM spectra are shown in Figs. 4(h) and 4(i). We can see that there are two intensity peaks localized by the side of the OAM value of the incident optical vortex, indicating a good agreement with the theoretical results. Therefore, the proposed device opens an efficient and simple way to decode the incident optical vortices flexibly.

## 5. Conclusion

In conclusion, we have proposed a chip-scale metasurface grating based on an all-dielectric silicon nitride thin film with half-wavelength in thickness. This metasurface grating enables the simultaneous generation of six diffractive beams carrying different topological charges with a total conversion efficiency of up to 82%. Beyond the demonstrated three-beam interference design for the generation of six OAM beams, our scheme could be extended to using more-beam interference for generating more OAM beams. Taking advantage of such designed multiple holographic metasurface grating, one can convert both the Gaussian beam and the OAM states of an incident optical vortex to multi-channel OAM states as well. In addition, we have demonstrated that the metasurface grating can be used to detect both the integral and fractional OAM states of the incident light beam with a low crosstalk less than −18 dB. The proposed all-dielectric metasurface grating thus provides a functional integration platform for the generation and the detection of OAM states in the high-capacity optical communication systems.

## Funding.

National Natural Science Foundation of China (91636109, 11774437, 61490715, U1701661); Fundamental Research Funds for the Central Universities at Xiamen University (20720190057); Fundamental Research Funds for Xiamen University (20720182003); Natural Science Foundation of Fujian Province of China for Distinguished Young Scientists (2015J06002); Program for New Century Excellent Talents in University of China (NCET-13-0495); Science and Technology Program of Guangzhou (201707020017, 201804010302), Local Innovative and Research Teams Project of Guangdong Pearl River Talents Program (2017BT01X121), Major Program of Science and Technology of Guangdong Province (2018B010114002).

## References

**1. **J. H. Poynting, “The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light,” Proc. R. Soc. Lond. Ser. A **82**, 560–567 (1909).

**2. **R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. **50**(2), 115–125 (1936). [CrossRef]

**3. **L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A **45**(11), 8185–8189 (1992). [CrossRef] [PubMed]

**4. **Y. S. Kivshar and E. A. Ostrovskaya, “Optical Vortices Folding and Twisting Waves of Light,” Opt. Photonics News **12**, 24–28 (2001). [CrossRef]

**5. **M. Padgett, J. Courtial, and L. Allen, “Light’s orbital angular momentum,” Phys. Today **57**(5), 35–40 (2004). [CrossRef]

**6. **G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted Photons,” Nat. Phys. **3**(5), 305–310 (2007). [CrossRef]

**7. **A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics **3**(2), 161–204 (2011). [CrossRef]

**8. **W. Zhang, D. S. Ding, M. X. Dong, S. Shi, K. Wang, S. L. Liu, Y. Li, Z. Y. Zhou, B. S. Shi, and G. C. Guo, “Experimental realization of entanglement in multiple degrees of freedom between two quantum memories,” Nat. Commun. **7**(1), 13514 (2016). [CrossRef] [PubMed]

**9. **S. Yu, “Potentials and challenges of using orbital angular momentum communications in optical interconnects,” Opt. Express **23**(3), 3075–3087 (2015). [CrossRef] [PubMed]

**10. **A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics **7**(1), 66–106 (2015). [CrossRef]

**11. **J. Wang, “Advances in communications using optical vortices,” Photon. Res. **4**(5), B14–B28 (2016). [CrossRef]

**12. **Y. Li, Z.-Y. Zhou, S.-L. Liu, S.-K. Liu, C. Yang, Z.-H. Xu, Y.-H. Li, G.-C. Guo, and B.-S. Shi, “Topological charge independent frequency conversion of twisted light,” arXiv e-prints arXiv:1810.07846 [physics.optics] (2018).

**13. **X. W. Luo, C. Zhang, G. C. Guo, and Z. W. Zhou, “Topological photonic orbital-Angular-momentum switch,” Phys. Rev. A (Coll. Park) **97**(4), 043841 (2018). [CrossRef]

**14. **H. T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Rep. Prog. Phys. **79**(7), 076401 (2016). [CrossRef] [PubMed]

**15. **F. Ding, A. Pors, and S. I. Bozhevolnyi, “Gradient metasurfaces: a review of fundamentals and applications,” Rep. Prog. Phys. **81**(2), 026401 (2018). [CrossRef] [PubMed]

**16. **S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovski, “Metasurfaces: From microwaves to visible,” Phys. Rep. **634**, 1–72 (2016). [CrossRef]

**17. **J. Sun, X. Wang, T. Xu, Z. A. Kudyshev, A. N. Cartwright, and N. M. Litchinitser, “Spinning light on the nanoscale,” Nano Lett. **14**(5), 2726–2729 (2014). [CrossRef] [PubMed]

**18. **A. Pors, M. G. Nielsen, G. Della Valle, M. Willatzen, O. Albrektsen, and S. I. Bozhevolnyi, “Plasmonic metamaterial wave retarders in reflection by orthogonally oriented detuned electrical dipoles,” Opt. Lett. **36**(9), 1626–1628 (2011). [CrossRef] [PubMed]

**19. **A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, “Strong magnetic response of submicron silicon particles in the infrared,” Opt. Express **19**(6), 4815–4826 (2011). [CrossRef] [PubMed]

**20. **L. Zou, W. Withayachumnankul, C. M. Shah, A. Mitchell, M. Bhaskaran, S. Sriram, and C. Fumeaux, “Dielectric resonator nanoantennas at visible frequencies,” Opt. Express **21**(1), 1344–1352 (2013). [CrossRef] [PubMed]

**21. **J. Du and J. Wang, “Dielectric metasurfaces enabling twisted light generation/detection/(de)multiplexing for data information transfer,” Opt. Express **26**(10), 13183–13194 (2018). [CrossRef] [PubMed]

**22. **J. Olmos-Trigo, C. Sanz-Fernández, F. Sebastián Bergeret, and J. José Sáenz, “Asymmetry and spin-orbit coupling of light scattered from subwavelength particles,” Opt. Lett. **44**(7), 1762–1765 (2019). [CrossRef] [PubMed]

**23. **M. Kim, A. M. H. Wong, and G. V. Eleftheriades, “Optical Huygens metasurfaces with independent control of the magnitude and phase of the local reflection coefficients,” Phys. Rev. X **4**(4), 041042 (2014). [CrossRef]

**24. **Z. Ma, S. M. Hanham, P. Albella, B. Ng, H. T. Lu, Y. Gong, S. A. Maier, and M. Hong, “Terahertz All-Dielectric Magnetic Mirror Metasurfaces,” ACS Photonics **3**(6), 1010–1018 (2016). [CrossRef]

**25. **X. Wang, Z. Nie, Y. Liang, J. Wang, T. Li, and B. Jia, “Recent advances on optical vortex generation,” Nanophotonics **7**(9), 1533–1556 (2018). [CrossRef]

**26. **S. M. Chen, Y. Cai, G. X. Li, S. Zhang, and K. W. Cheah, “Geometric metasurface fork gratings for vortex-beam generation and manipulation,” Laser Photonics Rev. **10**(2), 322–326 (2016). [CrossRef]

**27. **L. Liu, X. Zhang, M. Kenney, X. Su, N. Xu, C. Ouyang, Y. Shi, J. Han, W. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. **26**(29), 5031–5036 (2014). [CrossRef] [PubMed]

**28. **D. Gabor, “A new microscopic principle,” Nature **161**(4098), 777–778 (1948). [CrossRef] [PubMed]

**29. **E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. **52**(10), 1123–1130 (1962). [CrossRef]

**30. **D. H. Kim, C. O. Cho, Y. G. Roh, H. Jeon, Y. S. Park, J. Cho, J. S. Im, C. Sone, Y. Park, W. J. Choi, and Q. H. Park, “Enhanced light extraction from GaN-based light-emitting diodes with holographically generated two-dimensional photonic crystal patterns,” Appl. Phys. Lett. **87**(20), 203508 (2005). [CrossRef]

**31. **M. L. Hsieh and Y. S. Lan, “Controllable fabrication of the micropore shape of two-dimensional photonic crystals using holographic lithography,” J. Vac. Sci. Technol. B **26**(3), 914–917 (2008). [CrossRef]

**32. **L. J. Wu, Y. C. Zhong, C. T. Chan, K. S. Wong, and G. P. Wang, “Fabrication of large area two- and three-dimensional polymer photonic crystals using single refracting prism holographic lithography,” Appl. Phys. Lett. **86**(24), 241102 (2005). [CrossRef]

**33. **V. Berger, O. Gauthier-Lafaye, and E. Costard, “Photonic band gaps and holography,” J. Appl. Phys. **82**(1), 60–64 (1997). [CrossRef]

**34. **X. Zhang, S. Li, S. Liu, H. Lin, X. Chen, and X. Ren, “Fabrication of 2D photonic crystals with micron to sub-micron hexagonal lattices using single-exposure holographic technique,” Proc. SPIE **7358**, 735814 (2009). [CrossRef]

**35. **X. Chen, X. Zhang, S. Liu, and X. Ren, “Extraction of guided waves by diffraction of 2D photonic crystals fabricated on the surface of waveguides,” Proc. SPIE **6837**, 683710 (2008).

**36. **L. Chen, W. Zhang, Q. Lu, and X. Lin, “Making and identifying optical superpositions of high orbital angular momenta,” Phys. Rev. A **88**(5), 053831 (2013). [CrossRef]

**37. **R. Fickler, M. Ginoya, and R. W. Boyd, “Custom-tailored spatial mode sorting by controlled random scattering,” Phys. Rev. B **95**(16), 161108 (2017). [CrossRef]

**38. **A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature **412**(6844), 313–316 (2001). [CrossRef] [PubMed]