Abstract

We propose, design, fabricate and demonstrate nanophotonic all-dielectric metasurfaces enabling the generation, detection and (de)multiplexing of twisted light having helical phase structure and carrying orbital angular momentum (OAM). The designed metasurfaces are based on dielectric elliptical resonators on standard silicon-on-insulator (SOI) platform. One can achieve full-phase control of 0-2π and flexible amplitude adjustment by properly changing the geometric dimensions (long axis, short axis) and orientation of dielectric elliptical resonator based on the Mie resonance effect. Using the designed and fabricated all-dielectric metasurfaces, we demonstrate the generation and detection of OAM beams with topological charge number from l = −4 to 4. The crosstalk matrix of generated OAM beams is also characterized showing −16 dB crosstalk. We further demonstrate the (de)multiplexing of two OAM beams (OAM+1 & OAM+4 or OAM+2 & OAM+3) each carrying a binary image (“A” & “B” or “HUST” & “WNLO”). The obtained results show error-free data information transfer with favorable performance. The presented alternative approach of all-dielectric metasurfaces shows distinct features of easy fabrication process and easy chip-scale integration facilitating ultrathin optical applications. The demonstrations may open a door to find more interesting applications in all-dielectric metasurfaces enabled spatial light manipulation and optical communications and interconnects.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Orbital angular momentum (OAM) is one of the fundamental physical quantities of photons. Extensive researches on the OAM of photons have been carried out since it was recognized by Allen in 1992 [1]. Optical beams carrying OAM, also called “OAM beams”, have helical phase fronts of exp(ilφ), comprising an OAM of l per photon (where φ is the azimuth angle, l corresponds to the topological number, and is Plank’s constant h divided by 2π). OAM beams featuring twisted phase structure are also referred to as “twisted light”. In contrast to spin angular momentum (SAM) manifested as the state of polarization of light with only two possible states, OAM is linked to the spatial phase distribution of light [2–4] with in principle unbounded states. OAM beams with different topological number l are orthogonal with each other. Owing to these attractive features, OAM beams have given rise to many developments in a diversity of fields such as optical manipulation, trapping, tweezers, optical knots, imaging, sensing, quantum information processing and optical communications [5–23]. The generation of OAM beams is of great importance to support these wide OAM-enabled applications.

To generate OAM beams, it is necessary to achieve a full spatial phase control varying from 0 to 2π. Traditional optical elements used to acquire OAM beams such as spiral phase plates (SPPs), Q-plate and spatial light modulators (SLMs) are based on refraction, diffraction or reflection of light [24–26]. Their ability of light shaping relies on propagation through media whose refractive index or thickness can be tailored to control the light path. As a consequence, those conventional optical elements suffer from thick material, large volume, long working distance, incompatibility with chip-scale integration, and relatively low optical manipulation accuracy. For instance, the minimum size of each liquid crystal unit of commercially available SLMs is several micrometer, which may see its limitation to generate complex spatial distribution with fine structure (e.g. OAM beams with superlarge topological charge number). One solution to this issue is using metasurface-based flat optical elements instead of traditional ones. They are able to flexibly shape the spatial structure of light beams by introducing a variety of electric or dielectric dipole resonators replacing conventional propagation effect [27–47]. Some impressive prior art works to realize OAM beams manipulation utilizing metasurfaces have been promoted: 1) obtaining a complete amplitude and phase control of scattering light at mid-infrared band using gold V-shaped antenna array [27]; 2) generating broadband OAM carrying vector beams using two concentric rings consisting of subwavelength rectangular apertures with gradually varied orientation in a gold film [31]; 3) utilizing rectangular dielectric resonators combining metal mirror to generate broadband OAM beams with high-efficiency [45]. However, most of previous works focus on the generation of OAM beams and rare of them pay attention to the detection of OAM beams and their applications in OAM (de)multiplexing communications. In this scenario, a laudable goal would be to use metasurfaces to enable the generation, detection and (de)multiplexing of OAM beams for data information transfer in optical communications and interconnects.

In this paper, a chip-scale all-dielectric metasurface array with a cell of nanoscale dimension is proposed, designed and fabricated. Each cell is based on a kind of dielectric elliptical resonator, which is more favorable to fabrication process compared with rectangular ones. We simulate and experimentally demonstrate the generation and detection of OAM beams with topological charge number from l = −4 to 4 using the designed and fabricated dielectric metasurfaces. The generation and detection of OAM beams using metasurfaces together with OAM (de)multiplexing are applied in optical communications and interconnects. Multiplexing and demultiplexing of two OAM beams (OAM+1 & OAM+4 or OAM+2 & OAM+3) each carrying a binary image are demonstrated for error-free data information transfer in the experiment, showing favorable performance of dielectric metasurfaces enabling twisted light generation, detection and (de)multiplexing for optical communications and interconnects.

2. Concept and principle

Figure 1(a) shows the schematic drawing of the proposed all-dielectric metasurface array which is based on silicon-on-insulator (SOI) platform, consisting of 220-nm-height silicon elliptical resonators, a 3000-nm-height silica layer and a silicon substrate. The inset shows the top-view details and working principle of a dielectric elliptical resonator. The polarization of incident light is along x-axis, which can be decomposed into two perpendicular components correspond to the long and short axis (marked as a and b, respectively) of the elliptical resonator, respectively. The reflection amplitudes of response for a resonator in both components are almost the same while the relative phase retardation is around π, where the linear polarization conversion occurs, resulting in a y polarized reflected light. This working mechanism is verified in Fig. 1(b). Finite-difference time-domain (FDTD) method is used to simulate the amplitude and phase responses of reflected lights polarized along the long and short axis of the elliptical resonator. One can see that for incident lights Ea_inc and Eb_inc, the amplitude responses of their reflected lights Ea_ref and Eb_ref are almost the same, while there exists a relative phase shift of π between Ea_ref and Eb_ref. This can be briefly explained as follows. The linearly polarized incident light can be decomposed into two orthogonal circularly polarized lights. When the orientation of resonator is rotating, the reflected light will induce a phase shift on each component of circularly polarized light. When the rotation angle of resonator is 180°, the orientation of resonator coincides with its initial state and the reflected light has a phase shift of 2π. When the rotation angle of resonator is 90°, the phase shift of reflected light becomes half. Hence, for incident lights Ea_inc and Eb_inc, it is equivalent to an operation that the resonator has a rotation angle of 90° and there exists a relative phase shift of π between Ea_ref and Eb_ref [43, 45, 48–50]. What’s more, the Mie resonance effect is associated with the dimensions and orientation of dielectric elliptical resonator. It is possible to control the amplitude and phase of reflected lights by varying the size and orientation of elliptical resonators, which is considerably important for OAM beams manipulation. Figure 1(c) shows the concept of OAM beams generation through dielectric metasurface array consisting of a series of elliptical resonators covering a full-phase modulation. When a Gaussian beam of vertical polarization is incident to the metasurface, the reflected beam can be transformed into OAM beams of horizontal polarization. In view of cross polarization rotation happened on the metasurface, one can easily separate the incident and reflected lights. Additionally, the transformation between Gaussian beam and OAM beam on the metasurface is a reciprocal process, meaning that using the proposed metasurface to detect OAM beam is theoretically feasible. Those manipulations on OAM beams such as generation and detection can be applied in data information transfer for optical communications and interconnects. Figure 1(d) illustrates the concept of generation, detection and (de)multiplexing of OAM beams for data information transfer using the dielectric metasurfaces. At the multiplexing side (transmitter), each communication channel employs a dielectric metasurface array of li (i = 1, 2, ..., n). The data-carrying input Gaussian beam (topological charge number l = 0) in each channel is converted to an OAM beam of li after reflected by the metasurface array. Utilizing a multiplexer, the generated multiple OAM beams can be combined together and transmitted collinearly. At the demultiplexing side (receiver) after free-space data information transfer, the superimposed OAM beams are divided into multiple parts using beam splitter. Each part is sent to a metasurface array with inverted topological charge number - li that can remove the helical phase front of desired OAM beam of li. After reflected by the metasurface array, the superimposed OAM beams in each path will emerge a bright spot (l = 0) at the beam center, meaning that the desired OAM beam can be separated from other ones having doughnut intensity profiles by spatial filtering and demultiplexing is realized. Shown in Fig. 1(d) are one typical example of (de)multiplexing of two OAM beams. Each OAM beam carries a digital time-varying signal (e.g. “…0101…” and “…0110…”) representing a binary image (e.g. “HUST” and “WNLO”).

 

Fig. 1 (a) Schematic diagram of designed all-dielectric metasurface based on silicon-on-insulator (SOI) platform. (b) Simulated amplitude and phase responses of reflected lights polarized along long and short axis of dielectirc elliptical resonator. Here, b = 50 nm. (c) Concept of OAM beam generation using all-dielectric metasurface array. (d) Concept of generation, detection and (de)multiplexing of data-carrying OAM beams using all-dielectric metasurfaces for data information transfer in optical communications and interconnects.

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To design the dielectric metasurface array, the amplitude and phase responses of the near-field of cross-polarized reflected light are simulated at the wavelength of 632.8 nm using FDTD method, as depicted in Figs. 2(a) and 2(b), respectively. One can see that the simulated response of a resonator can cover a phase varying over 0 to π and wide shifting of amplitude. It is relatively easy to find out a series of resonators covering phase of 0-to-π control while maintaining an approximately constant amplitude. Then four kinds of resonators (marked as 1, 2, 3, and 4, respectively) with different geometric dimensions are chosen to provide an equal-spacing phase shift of π/4 from 0 to π and a nearly constant amplitude, as plotted in Fig. 2(c). By simply rotating the chosen four resonators by 90° (marked as 5, 6, 7, and 8, respectively), the additional phase shift of π can be acquired for realizing full 2π phase coverage. Using the selected eight dielectric resonators, one can conveniently manipulate OAM beams with various topological number by properly assembling those resonators into phase patterns. Figure 2(d) displays the design process of metasurface arrays to generate/detect OAM beams. OAM beams carrying helical phase front can be generated by introducing helical phase modulation of exp(ilφ) to the transverse section of Gaussian beams. Similarly, OAM beams can be detected by using inverse helical phase modulation of exp(-ilφ) on the transverse section of OAM beams. Considering that the designed dielectric elliptical resonators can cover 0-2π full phase control on the reflected light, the helical phase modulation can be achieved by the metasurfaces composed of dielectric elliptical resonators. To design a metasurface array to generate/detect OAM beams, the first step is to convert continuous helical phase pattern into discrete one. For instance, the continuous 0-2π phase varying can be divided into 8 levels. Each phase level is corresponding to a dielectric elliptical resonator. By replacing the discrete phase pattern with dielectric elliptical resonators, the metasurface array structure is formed to generate/detect OAM beams.

 

Fig. 2 (a) Amplitude and (b) phase responses of the cross-polarized reflected light for different resonator geometries. The polarization of incident light is 45° (x-polarization) with respect to the symmetry axis of the resonator. (c) Schematic of eight resonators chosen to provide a phase shift from 0 to 2π and have nearly constant amplitude. The dimensions of resonators 1−4 are chosen as: (1) a = 86 nm, b = 53 nm; (2) a = 106 nm, b = 50 nm; (3) a = 122 nm, b = 53 nm; (4) a = 142 nm, b = 57 nm. Resonators 5−8 are mirror structures by rotating 90 degree the resonators 1−4. (d) Design process of metasurfaces to generate/detect OAM beams.

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3. Results

3.1 Generation and detection of OAM beams using all-dielectric metasurfaces

The designed dielectric metasurface arrays are fabricated through simple steps: standard electron-beam lithography (EBL) to generate patterns followed by a 220-nanometer-depth induced coupled plasma (ICP) silicon etching. Figure 3(a) displays the scanning electron microscope (SEM) images of the fabricated metasurface array to produce OAM beam of l = −1. Considering the fabrication feasibility, ~500-nm lattice period of metasurfaces is chosen. Figure 3(b) shows the experiment setup for the generation and detection of OAM beams using the fabricated metasurface array. A He-Ne laser is used to provide the light source at the wavelength of 632.8 nm. Firstly, the mirror in front of camera 1 is removed and the OAM beams generated by metasurface array on chip 1 are recorded by camera 1. The beam splitter (BS) can interfere the generated OAM beams with a reference Gaussian beam. By adjusting the neutral density filter (NDF), one can control the appearance of the interference. The measured results are depicted in Fig. 4. For metasurfaces with topological charge number from −4 to 4, annular intensity profiles are observed, as shown in Fig. 4(c). One can point out that higher absolute value of topological charge number |l| corresponds to larger radius of intensity distribution, which is in good agreement with simulations plotted in Fig. 4(a). To further verify the topological charge number of generated OAM beams in the experiment, interferograms of OAM beams interfering with a reference Gaussian beam are measured in Fig. 4(d). The number of interference fringe is equal to the value of |l| and the direction of rotation of interference fringe reverses as the topological charge number becomes opposite, which is agreement with the spatial phase distributions plotted in Fig. 4(b).

 

Fig. 3 (a) Measured scanning electron microscope (SEM) images of top view of a fabricated all-dielectric metasurface array of l = −1. (b) Experimental setup for the generation and detection of OAM beams. NDF: neutral density filter; Pol.: polarizer; HWP: half-wave plate; QWP: quarter-wave plate; BS: beam splitter.

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Fig. 4 (a)(b) Simulated intensity and phase distributions of generated OAM beams, respectively. (c) Measured intensity profiles of OAM beams generated by fabricated all-dielectric metasurfaces. (d) Measured interferograms of generated OAM beams interfering with a reference Gaussian beam (l = 0).

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Then the mirror ahead of camera 1 is added to let light beam irradiate on the metasurface array of chip 2, as shown in Fig. 3(b). NDF can be adjusted to absorb the intensity of Gaussian beam to eliminate the interference effect. The OAM beams generated by metasurface chip 1 are detected by metasurface chip 2 which removes the helical phase front of the OAM beams. Figure 5(a) depicts the measured intensity profiles of OAM beams (l = 1, 2, 3 and 4) after detection by metasurface array of l = −1, −2, −3 and −4 on camera 2, respectively. When the absolute value of topological charge number of metasurface array on chip 2 is equal to that of OAM beam, there appears a bright spot at the beam center. Otherwise the beam center remains a dark region with null intensity. It implies that one can detect the topological charge number of OAM beams using metasurface with inverted topologic charge number. As shown in Fig. 5(a), for all diagonal intensity profiles, one can clearly see bright spots at the beam center (yellow circle region). Those are typical intensity profiles after detection of OAM beams when correctly removing the helical phase front. For out of diagonal intensity profiles in Fig. 5(a), despite complex intensity profiles, the beam center still has null intensity since the helical phase front is not correctly removed. Additionally, considering the fabrication error and discrete pattern design (only eight kinds of resonator covering full-phase change), the practically fabricated metasurfaces might not be seen as perfect helical phase patterns. Hence, using metasurfaces to detect OAM beams might suffer from quality degradation, resulting in relatively complex intensity profiles in the out of diagonal intensity profiles. With future improvement, further optimization of fabrication technique might benefit the generation and detection of OAM beams with favorable performance. Figure 5(b) displays the measured topological charge number spectrum of OAM beams (l = 1, 2, 3, and 4) by recording the power at the beam center after detection by metasurfaces and finally captured by camera 2. The power ratios of OAM beam of desired topological charge number (e. g. l = 2) to its neighboring ones (e. g. l = 1, and 3) are approximately 15 dB. The crosstalk matrix of 4 OAM beams (l = 1, 2, 3, and 4) generated by the metasurfaces is also characterized [47], as depicted in Fig. 5(c). One can see that the crosstalk between OAM beams with different topological charge number is measured to be about −16 dB, indicating favorable performance of generated OAM beams. The measured efficiency of reflected OAM beams is about 3.2%.

 

Fig. 5 (a) Measured intensity profiles of OAM beams after detection by all-dielectric metasurface arrays from l = −1 to −4. (b) Measured topological charge number spectrum of OAM beams generated by all-dielectric metasurface arrays. (c) Measured crosstalk matrix of 4 OAM beams.

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3.2 (De)multiplexing of OAM beams for data information transfer

Furthermore, we demonstrate the generation, detection and (de)multiplexing of OAM beams for data information transfer applications in optical communications and interconnects. Figure 6(a) shows the experiment setup for (de)multiplexing of OAM beams. Utilizing the metasurface arrays on chip 1 and chip 2, one can generate two data-carrying (e.g. “…1010…”, “…0100…”) OAM beams with different topological charge number at the same time. The BS can multiplex the two OAM beams to transmit collinearly. The metasurface arrays on chip 3 having inverted topological charge number can filter the desired OAM beam. Figures 6(b) and 6(c) respectively show the measured intensity profiles of (de)multiplexing of OAM beams with l = 1, 4 and l = 2, 3. One can see that multiplexed OAM beams still have dark center. When the absolute value of topological charge number of metasurface array at the demultiplexing side is equal to that of multiplexed OAM beams (e. g. l = −1, 4 in Fig. 6(b) or l = −2, −3 in Fig. 6(c)), bright spot emerges at the beam center. Otherwise the beam center is still dark. The topological charge number spectra of multiplexed OAM beams are also recorded, as plotted in Figs. 7(a) and 7(c). The measured power radio of multiplexed OAM beams of desired topological charge number to undesired ones is above 8 dB approximately.

 

Fig. 6 (a) Experimental setup for (de)multiplexing of OAM beams. M: modulator. (b) Measured intensity profiles of OAM beams of l = 1, 4 after multiplexing and demultiplexing. (c) Measured intensity profiles of OAM beams of l = 2, 3 after multiplexing and demultiplexing.

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Fig. 7 (a) Measured topological charge number spectrum of multiplexed OAM beams with l = 1 and 4. (b) Binary images before (Tx) and after (Rx) OAM (de)multiplexing system with l = 1 carrying “A” and l = 4 carrying “B”. (c) Measured topological charge number spectrum of multiplexed OAM beams with l = 2 and 3. (d) Binary images before (Tx) and after (Rx) OAM (de)multiplexing system with l = 2 carrying “HUST” and l = 3 carrying “WNLO”.

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Then two intensity modulators are added in front of chip 1 and chip 2 to modulate data information onto two OAM beams for the proof-of-concept demonstration of generation, detection and (de)multiplexing of OAM beams for data information transfer using metasurfaces, as shown in Fig. 6(a). In the experiment, two different binary images (“A” and “B” or “HUST” and “WNLO”) are transformed into two time-varying binary sequences and modulated on two OAM beams of different topological charge number simultaneously at the transmitter side. At the receiver side, the camera can play the role of photo-detector and the received binary sequences are recovered into binary images. Figures 7(b) and 7(d) display the binary images at the transmitter and receiver after passing through the OAM (de)multiplexing system assisted by metasurfaces. The obtained results indicate error-free data information transfer.

4. Discussion

There have been prior art works on metasurfaces, showing impressive operation performance, such as dolphin-shaped cell metasurface, silicon nanoblock cell metasurface, rectangular cell metasurface on TiO2 material platform, amorphous silicon posts on hexagonal unit cells, etc [40–44]. In contrast, we propose, design, simulate, fabricate and experimentally demonstrate an alternative metasurface approach in managing OAM beams by exploiting dielectric elliptical resonator array on standard SOI platform. Managing OAM beams is enabled by appropriately adjusting the geometric dimensions (short axis, long axis) and orientation of dielectric elliptical resonator. The dielectric metasurface structure is based on the widely used 220-nm SOI wafer. Only standard EBL followed by just one-step ICP etching is required to form the metasurface structure on SOI platform. From the design and fabrication aspects, our approach shows distinct features of easy fabrication process and easy chip-scale integration facilitating ultrathin optical applications. From the application aspect, most of previous works focused more on the beam generation. Our approach demonstrates not only OAM beam generation but also OAM beam detection, (de)multiplexing and extended applications in data information transfer for optical communications and interconnects.

Remarkably, the main purpose of the work is the demonstration of generation, detection and (de)multiplexing of OAM beams and their applications in data information transfer assisted my all-dielectric metasurfaces. In the proof-of-concept experiment, low-speed switching on/off modulation (several hertz) at 632.8 nm is considered to modulate data information on the multiplexed OAM beams based on the currently available lab conditions. Digital binary images (“A”, “B”, “HUST”, “WNLO”) represented by time-varying binary sequences are considered for data information transfer. The transmitted image is completely reproduced in the received image without observing data information transfer error (i.e. error-free data information transfer). In spite of the low-speed data information transfer demonstration, the presented approach, in principle, is not limited by the transmission data rate. That is, high-speed data information transfer (e.g. tens of Gbit/s) is also applicable.

Moreover, this work considers the situation of ± 45-degree orientation angle of dielectric resonators to realize the 90-degree polarization shift between incident and reflected light, which is convenient to separate reflected light from incident light. If the orientation angle of dielectric resonators can be adjusted, the polarization state of reflected light can be controlled, which might bring some interesting applications in vector beam generation [31], polarization filter [48], wave-plates [43], spin-to-orbital angular momentum converters [51], etc.

With future improvement, the approach can be further extended to data information transfer for a set of images with a larger dynamic range. More OAM beams can be employed to take full advantage of OAM degree of freedom with unbounded states. Additionally, we may also consider all-dielectric metasurfaces working in the 1550 nm wavelength range, providing added opportunities to capacity scalable fiber-optic communications.

5. Conclusion

An all-dielectric metasurface is proposed, designed and fabricated for generating, detecting and (de)multiplexing OAM beams. The presented metasurface is based on dielectric elliptical resonators with variant geometric dimensions (long axis, short axis) and orientation, which can achieve full-phase control and flexible amplitude adjustment. The size of each resonator in the metasurface is only nano-scaled and the total area of metasurface array is about 0.5 × 0.5 mm2 containing 1000 × 1000 cells, which is much smaller than that of traditional bulky optical elements. This nano-scaled all-dielectric metasurface is able to provide a choice to be compatible with compact optical systems. Using the designed and fabricated dielectric elliptical resonator metasurfaces on SOI platform, we demonstrate the generation and detection of OAM beams with topological charge number from l = −4 to 4. We further demonstrate the (de)multiplexing of two OAM beams (OAM+1 & OAM+4 or OAM+2 & OAM+3) each carrying a binary image (“A” & “B” or “HUST” & “WNLO”) for error-free data information transfer. The demonstrations with favorable performance indicate the successful implementation of generation, detection and (de)multiplexing of OAM beams using all-dielectric metasurfaces, which may open a door to facilitate more metasurface-enabled spatial light manipulation and optical communications applications.

Funding

National Natural Science Foundation of China (NSFC) (11574001, 61761130082, 11774116, 11274131); National Basic Research Program of China (973 Program) (2014CB340004); Royal Society-Newton Advanced Fellowship; National Program for Support of Top-notch Young Professionals; Program for HUST Academic Frontier Youth Team.

Acknowledgments

The authors thank Shuhui Li, Jun Liu, Shi Chen, Yifan Zhao, Nan Zhou, Shuang Zheng, and Long Zhu for their technical supports and helpful discussions. The authors thank the Center of Micro-Fabrication and Characterization (CMFC) of Wuhan National Laboratory for Optoelectronics (WNLO) for the support in the manufacturing process on silicon photonics platform. The authors also thank the facility support of the Center for Nanoscale Characterization and Devices of WNLO.

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33. S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. Condens. Matter 14(15), 4035–4044 (2002).

34. L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett. 98(15), 157403 (2007). [PubMed]  

35. B. I. Popa and S. A. Cummer, “Compact dielectric particles as a building block for low-loss magnetic metamaterials,” Phys. Rev. Lett. 100(20), 207401 (2008). [PubMed]  

36. Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12(12), 60–69 (2009).

37. J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012). [PubMed]  

38. J. Du and J. Wang, “Design of on-chip N-fold orbital angular momentum multicasting using V-shaped antenna array,” Sci. Rep. 5, 9662 (2015). [PubMed]  

39. J. Du and J. Wang, “Chip-scale optical vortex lattice generator on a silicon platform,” Opt. Lett. 42(23), 5054–5057 (2017). [PubMed]  

40. Z. Yang, D. F. Kuang, and F. Cheng, “Vector vortex beam generation with dolphin-shaped cell meta-surface,” Opt. Express 25(19), 22780–22788 (2017). [PubMed]  

41. H. Yang and Y. Deng, “Broadband and high efficiency all-dielectric metasurfaces for wavefront steering with easily obtained phase shift,” Opt. Commun. 405, 39–42 (2017).

42. R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin-to-orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017). [PubMed]  

43. A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015). [PubMed]  

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

45. Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014). [PubMed]  

46. Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, and T. F. Krauss, “Efficient silicon metasurfaces for visible light,” ACS Photonics 4(3), 544–551 (2017).

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

48. Y. Ke, Y. Liu, J. Zhou, Y. Liu, H. Luo, and S. Wen, “Photonic spin filter with dielectric metasurfaces,” Opt. Express 23(26), 33079–33086 (2015). [PubMed]  

49. D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014). [PubMed]  

50. L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12(11), 5750–5755 (2012). [PubMed]  

51. R. C. Devlin, A. Ambrosio, D. Wintz, S. L. Oscurato, A. Y. Zhu, M. Khorasaninejad, J. Oh, P. Maddalena, and F. Capasso, “Spin-to-orbital angular momentum conversion in dielectric metasurfaces,” Opt. Express 25(1), 377–393 (2017). [PubMed]  

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  33. S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. Condens. Matter 14(15), 4035–4044 (2002).
  34. L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett. 98(15), 157403 (2007).
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  47. R. Fickler, M. Ginoya, and R. W. Boyd, “Custom-tailored spatial mode sorting by controlled random scattering,” Phys. Rev. B 95(16), 161108 (2017).
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    [PubMed]
  49. D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
    [PubMed]
  50. L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12(11), 5750–5755 (2012).
    [PubMed]
  51. R. C. Devlin, A. Ambrosio, D. Wintz, S. L. Oscurato, A. Y. Zhu, M. Khorasaninejad, J. Oh, P. Maddalena, and F. Capasso, “Spin-to-orbital angular momentum conversion in dielectric metasurfaces,” Opt. Express 25(1), 377–393 (2017).
    [PubMed]

2018 (1)

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

2017 (10)

R. C. Devlin, A. Ambrosio, D. Wintz, S. L. Oscurato, A. Y. Zhu, M. Khorasaninejad, J. Oh, P. Maddalena, and F. Capasso, “Spin-to-orbital angular momentum conversion in dielectric metasurfaces,” Opt. Express 25(1), 377–393 (2017).
[PubMed]

J. Du and J. Wang, “Chip-scale optical vortex lattice generator on a silicon platform,” Opt. Lett. 42(23), 5054–5057 (2017).
[PubMed]

Z. Yang, D. F. Kuang, and F. Cheng, “Vector vortex beam generation with dolphin-shaped cell meta-surface,” Opt. Express 25(19), 22780–22788 (2017).
[PubMed]

H. Yang and Y. Deng, “Broadband and high efficiency all-dielectric metasurfaces for wavefront steering with easily obtained phase shift,” Opt. Commun. 405, 39–42 (2017).

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin-to-orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017).
[PubMed]

Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, and T. F. Krauss, “Efficient silicon metasurfaces for visible light,” ACS Photonics 4(3), 544–551 (2017).

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

L. Fang, M. J. Padgett, and J. Wang, “Sharing a common origin between the rotational and linear Doppler effects,” Laser Photonics Rev. 11(6), 1700183 (2017).

J. Wang, “Data information transfer using complex optical fields: a review and perspective,” Chin. Opt. Lett. 15(3), 030005 (2017).

L. Zhu, A. Wang, S. Chen, J. Liu, Q. Mo, C. Du, and J. Wang, “Orbital angular momentum mode groups multiplexing transmission over 2.6-km conventional multi-mode fiber,” Opt. Express 25(21), 25637–25645 (2017).
[PubMed]

2016 (3)

2015 (6)

J. Du and J. Wang, “High-dimensional structured light coding/decoding for free-space optical communications free of obstructions,” Opt. Lett. 40(21), 4827–4830 (2015).
[PubMed]

A. Wang, L. Zhu, J. Liu, C. Du, Q. Mo, and J. Wang, “Demonstration of hybrid orbital angular momentum multiplexing and time-division multiplexing passive optical network,” Opt. Express 23(23), 29457–29466 (2015).
[PubMed]

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, 66–106 (2015).

Y. Ke, Y. Liu, J. Zhou, Y. Liu, H. Luo, and S. Wen, “Photonic spin filter with dielectric metasurfaces,” Opt. Express 23(26), 33079–33086 (2015).
[PubMed]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[PubMed]

J. Du and J. Wang, “Design of on-chip N-fold orbital angular momentum multicasting using V-shaped antenna array,” Sci. Rep. 5, 9662 (2015).
[PubMed]

2014 (3)

Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
[PubMed]

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[PubMed]

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).

2013 (4)

M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12(1), 20–24 (2013).
[PubMed]

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013).
[PubMed]

Z. Zhao, J. Wang, S. Li, and A. E. Willner, “Metamaterials-based broadband generation of orbital angular momentum carrying vector beams,” Opt. Lett. 38(6), 932–934 (2013).
[PubMed]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[PubMed]

2012 (4)

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54(2), 10–35 (2012).

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[PubMed]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12(11), 5750–5755 (2012).
[PubMed]

2011 (5)

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).

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

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13(6), 064001 (2011).

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[PubMed]

2010 (1)

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[PubMed]

2009 (1)

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12(12), 60–69 (2009).

2008 (2)

B. I. Popa and S. A. Cummer, “Compact dielectric particles as a building block for low-loss magnetic metamaterials,” Phys. Rev. Lett. 100(20), 207401 (2008).
[PubMed]

S. Franke‐Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).

2007 (2)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett. 98(15), 157403 (2007).
[PubMed]

2006 (1)

2004 (1)

2002 (2)

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002).
[PubMed]

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. Condens. Matter 14(15), 4035–4044 (2002).

1994 (1)

M. W. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).

1992 (1)

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).
[PubMed]

Ahmed, N.

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, 66–106 (2015).

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).

Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[PubMed]

Allen, L.

S. Franke‐Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).

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).
[PubMed]

Ambrosio, A.

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin-to-orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017).
[PubMed]

R. C. Devlin, A. Ambrosio, D. Wintz, S. L. Oscurato, A. Y. Zhu, M. Khorasaninejad, J. Oh, P. Maddalena, and F. Capasso, “Spin-to-orbital angular momentum conversion in dielectric metasurfaces,” Opt. Express 25(1), 377–393 (2017).
[PubMed]

Arbabi, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[PubMed]

Arlt, J.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002).
[PubMed]

Ashrafi, N.

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, 66–106 (2015).

Ashrafi, S.

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, 66–106 (2015).

Bagheri, M.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[PubMed]

Bai, B.

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12(11), 5750–5755 (2012).
[PubMed]

Bao, C.

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, 66–106 (2015).

Barnett, S.

Barnett, S. M.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[PubMed]

Basilio, L. I.

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[PubMed]

Beijersbergen, M. W.

M. W. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).

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).
[PubMed]

Bernet, S.

Blanchard, R.

M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12(1), 20–24 (2013).
[PubMed]

Boltasseva, A.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013).
[PubMed]

Booth, J.

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54(2), 10–35 (2012).

Bowman, R.

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).

Boyd, R. W.

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

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[PubMed]

Bozhevolnyi, S. I.

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

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[PubMed]

Brener, I.

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[PubMed]

Briggs, D. P.

Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
[PubMed]

Brongersma, M. L.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[PubMed]

Cao, Y.

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, 66–106 (2015).

Capasso, F.

R. C. Devlin, A. Ambrosio, D. Wintz, S. L. Oscurato, A. Y. Zhu, M. Khorasaninejad, J. Oh, P. Maddalena, and F. Capasso, “Spin-to-orbital angular momentum conversion in dielectric metasurfaces,” Opt. Express 25(1), 377–393 (2017).
[PubMed]

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin-to-orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017).
[PubMed]

M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12(1), 20–24 (2013).
[PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[PubMed]

Chen, H.

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett. 98(15), 157403 (2007).
[PubMed]

Chen, S.

Chen, X.

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12(11), 5750–5755 (2012).
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Cheng, F.

Cižmár, T.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).

Clem, P. G.

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[PubMed]

Coerwinkel, R.

M. W. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).

Courtial, J.

Cummer, S. A.

B. I. Popa and S. A. Cummer, “Compact dielectric particles as a building block for low-loss magnetic metamaterials,” Phys. Rev. Lett. 100(20), 207401 (2008).
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De Leon, I.

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).

Deng, Y.

H. Yang and Y. Deng, “Broadband and high efficiency all-dielectric metasurfaces for wavefront steering with easily obtained phase shift,” Opt. Commun. 405, 39–42 (2017).

Devlin, R. C.

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin-to-orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017).
[PubMed]

R. C. Devlin, A. Ambrosio, D. Wintz, S. L. Oscurato, A. Y. Zhu, M. Khorasaninejad, J. Oh, P. Maddalena, and F. Capasso, “Spin-to-orbital angular momentum conversion in dielectric metasurfaces,” Opt. Express 25(1), 377–393 (2017).
[PubMed]

Dholakia, K.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002).
[PubMed]

Ding, F.

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

Dolinar, S.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).

Du, C.

Du, J.

Dudley, A.

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).

Fan, P.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[PubMed]

Fang, H.

Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, and T. F. Krauss, “Efficient silicon metasurfaces for visible light,” ACS Photonics 4(3), 544–551 (2017).

Fang, L.

L. Fang, M. J. Padgett, and J. Wang, “Sharing a common origin between the rotational and linear Doppler effects,” Laser Photonics Rev. 11(6), 1700183 (2017).

Faraon, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[PubMed]

Fazal, I. M.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).

Fickler, R.

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

Forbes, A.

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).

Franke-Arnold, S.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[PubMed]

S. Franke‐Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
[PubMed]

Fürhapter, S.

Gaburro, Z.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[PubMed]

Genevet, P.

M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12(1), 20–24 (2013).
[PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[PubMed]

Gibson, G.

Ginn, J. C.

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[PubMed]

Ginoya, M.

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

Gordon, J. A.

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54(2), 10–35 (2012).

Grzegorczyk, T. M.

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett. 98(15), 157403 (2007).
[PubMed]

Hasman, E.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[PubMed]

Hines, P. F.

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[PubMed]

Holloway, C. L.

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54(2), 10–35 (2012).

Horie, Y.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[PubMed]

Huang, H.

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, 66–106 (2015).

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[PubMed]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).

Huang, L.

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12(11), 5750–5755 (2012).
[PubMed]

Ihlefeld, J. F.

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[PubMed]

Ireland, D. G.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[PubMed]

Jack, B.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[PubMed]

Jesacher, A.

Jha, A. K.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[PubMed]

Jin, G.

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12(11), 5750–5755 (2012).
[PubMed]

Karimi, E.

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13(6), 064001 (2011).

Kats, M. A.

M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12(1), 20–24 (2013).
[PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[PubMed]

Ke, Y.

Khorasaninejad, M.

Kildishev, A. V.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013).
[PubMed]

Kong, J. A.

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett. 98(15), 157403 (2007).
[PubMed]

Krauss, T. F.

Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, and T. F. Krauss, “Efficient silicon metasurfaces for visible light,” ACS Photonics 4(3), 544–551 (2017).

Kravchenko, I. I.

Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
[PubMed]

Kristensen, M.

M. W. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[PubMed]

Kuang, D. F.

Kuester, E. F.

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54(2), 10–35 (2012).

Lavery, M. P. J.

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, 66–106 (2015).

Leach, J.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[PubMed]

Li, G.

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12(11), 5750–5755 (2012).
[PubMed]

Li, J.

Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, and T. F. Krauss, “Efficient silicon metasurfaces for visible light,” ACS Photonics 4(3), 544–551 (2017).

Li, K.

Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, and T. F. Krauss, “Efficient silicon metasurfaces for visible light,” ACS Photonics 4(3), 544–551 (2017).

Li, L.

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, 66–106 (2015).

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Figures (7)

Fig. 1
Fig. 1 (a) Schematic diagram of designed all-dielectric metasurface based on silicon-on-insulator (SOI) platform. (b) Simulated amplitude and phase responses of reflected lights polarized along long and short axis of dielectirc elliptical resonator. Here, b = 50 nm. (c) Concept of OAM beam generation using all-dielectric metasurface array. (d) Concept of generation, detection and (de)multiplexing of data-carrying OAM beams using all-dielectric metasurfaces for data information transfer in optical communications and interconnects.
Fig. 2
Fig. 2 (a) Amplitude and (b) phase responses of the cross-polarized reflected light for different resonator geometries. The polarization of incident light is 45° (x-polarization) with respect to the symmetry axis of the resonator. (c) Schematic of eight resonators chosen to provide a phase shift from 0 to 2π and have nearly constant amplitude. The dimensions of resonators 1−4 are chosen as: (1) a = 86 nm, b = 53 nm; (2) a = 106 nm, b = 50 nm; (3) a = 122 nm, b = 53 nm; (4) a = 142 nm, b = 57 nm. Resonators 5−8 are mirror structures by rotating 90 degree the resonators 1−4. (d) Design process of metasurfaces to generate/detect OAM beams.
Fig. 3
Fig. 3 (a) Measured scanning electron microscope (SEM) images of top view of a fabricated all-dielectric metasurface array of l = −1. (b) Experimental setup for the generation and detection of OAM beams. NDF: neutral density filter; Pol.: polarizer; HWP: half-wave plate; QWP: quarter-wave plate; BS: beam splitter.
Fig. 4
Fig. 4 (a)(b) Simulated intensity and phase distributions of generated OAM beams, respectively. (c) Measured intensity profiles of OAM beams generated by fabricated all-dielectric metasurfaces. (d) Measured interferograms of generated OAM beams interfering with a reference Gaussian beam (l = 0).
Fig. 5
Fig. 5 (a) Measured intensity profiles of OAM beams after detection by all-dielectric metasurface arrays from l = −1 to −4. (b) Measured topological charge number spectrum of OAM beams generated by all-dielectric metasurface arrays. (c) Measured crosstalk matrix of 4 OAM beams.
Fig. 6
Fig. 6 (a) Experimental setup for (de)multiplexing of OAM beams. M: modulator. (b) Measured intensity profiles of OAM beams of l = 1, 4 after multiplexing and demultiplexing. (c) Measured intensity profiles of OAM beams of l = 2, 3 after multiplexing and demultiplexing.
Fig. 7
Fig. 7 (a) Measured topological charge number spectrum of multiplexed OAM beams with l = 1 and 4. (b) Binary images before (Tx) and after (Rx) OAM (de)multiplexing system with l = 1 carrying “A” and l = 4 carrying “B”. (c) Measured topological charge number spectrum of multiplexed OAM beams with l = 2 and 3. (d) Binary images before (Tx) and after (Rx) OAM (de)multiplexing system with l = 2 carrying “HUST” and l = 3 carrying “WNLO”.

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