Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Dielectric multi-momentum meta-transformer in the visible

Abstract

Metasurfaces as artificially nanostructured interfaces hold significant potential for multi-functionality, which may play a pivotal role in the next-generation compact nano-devices. The majority of multi-tasked metasurfaces encode or encrypt multi-information either into the carefully tailored metasurfaces or in pre-set complex incident beam arrays. Here, we propose and demonstrate a multi-momentum transformation metasurface (i.e., meta-transformer), by fully synergizing intrinsic properties of light, e.g., orbital angular momentum (OAM) and linear momentum (LM), with a fixed phase profile imparted by a metasurface. The OAM meta-transformer reconstructs different topologically charged beams into on-axis distinct patterns in the same plane. The LM meta-transformer converts red, green and blue illuminations to the on-axis images of “R”, “G” and “B” as well as vivid color holograms, respectively. Thanks to the infinite states of light-metasurface phase combinations, such ultra-compact meta-transformer has potential in information storage, nanophotonics, optical integration and optical encryption.

Introduction

Metasurfaces composed of tailored nanostructures arranged two-dimensionally hold great capabilities to locally control light’s phase, amplitude and polarization states at the subwavelength scale1,2,3,4,5,6,7. Due to this control capability, metasurfaces can provide specific transmission (T) and reflection (R) functions to work as planar photonic components carrying customized information. Such information can be unlocked via a distinguished field distribution reconstructed at the observed region. When an incident light Uinc(x0, y0) impinges upon a metasurface \({\mathbf{U}}_{{\mathbf{meta}}}^{{\mathbf{T}}/{\mathbf{R}}}\left( {x_0,y_0} \right)\), the field distribution can be expressed by the convolution of \({\mathbf{U}}_{{\mathbf{meta}}}^{{\mathbf{T}}/{\mathbf{R}}}\left( {x_0,y_0} \right){\mathbf{U}}_{{\mathbf{inc}}}\left( {x_0,y_0} \right)\) and an impulse response h(x, y, z) that relates the fields at the metasurface. Therefore, the field distribution on the observation plane can be expressed as (more detail are shown in Supplementary Note 1):

$${\mathbf{U}}\left( {x,y,z} \right) = \iint\limits^{\! + \infty }_{\!\!\!-\infty } {{\mathbf{U}}_{{\mathbf{meta}}}^{{\mathbf{T}}/{\mathbf{R}}}} \left( {x_0,y_0} \right){\mathbf{U}}_{{\mathbf{inc}}}\left( {x_0,y_0} \right)h\left( {x - x_0,y - y_0,z} \right)dx_0dy_0$$
(1)

The diversity of metasurfaces’ function \({\mathbf{U}}_{{\mathbf{meta}}}^{{\mathbf{T}}/{\mathbf{R}}}\left( {x_0,y_0} \right)\) serves as the base for realizing lenses8,9,10, color11,12,13,14, polarization filters15,16 and holograms17,18,19,20.

Multi-tasked metasurface is preferably desired for more compact nanophotonic devices, which could reconstruct multiple distinguished field distributions U(n) at observed regions. Based on Eq. 1, previously reported multi-tasked metasurfaces can be divided into three categories (shown in Fig. 1a–c). The first approach takes advantage of spatial separation as shown in Fig. 1a. By separating the observed regions (S(n))21,22 or interleaving subarrays \(\left( {S_0^{(n)}} \right)\)23,24,25,26,27,28,29 specifically designed for each functionality on the metasurface, the spatial multiplexed metasurface can reconstruct different field distributions (U(n)), but its efficiency is limited. The second approach resorts to adjusting functions \({\mathbf{U}}_{{\mathbf{meta}}}^{\left( {\boldsymbol{n}} \right)}\) of the metasurface by changing polarizations30,31,32,33,34,35,36, incident angles37 or wavelengths38 of beams as shown in Fig. 1b. By tailoring meta-atoms, the structurally multiplexed metasurface carries polarization-, angle- or wavelength-dependent responses \({\mathbf{U}}_{{\mathbf{meta}}}^{\left( {\boldsymbol{n}} \right)}\) to reconstruct different field distributions (U(n)). This method can achieve higher efficiency than the previous one, but the efficiency is still limited by the coverage of the required phases that meta-atoms need to achieve. Another approach, as shown in Fig. 1c, is based on OAM multiplexing chip to read out the pre-set incident light (Ainc)39, which pre-generate various information-carrying multifocal beams arrays with corresponding OAM states. Each ring groove of the chip can out-couple a determined OAM order40,41, which equivalently provides a “key” array to read out the distributions U(n) locked in the preset beams by the spatial light modulator (SLM)39. However, the outcoupling efficiency of slits is much smaller than that in the previous two methods and it needs the beam array to illuminate each meta-atom. So far, a majority of reported multi-tasked metasurface are resorting to the spatial freedom, structure complexity or pre-modulation with decoupler, and there is a lack of a convenient way to realize multi-tasked functionality by intrinsic properties of light.

Fig. 1
figure1

Comparative elaborations of multi-tasked metasurfaces (ac) and our multi-momentum meta-transformer (dh). a Schematic illustration of a spatially multiplexed metasurface21,22,23,24,25,26,27,28,29. The spatial multiplexed metasurface reconstructed several distinguished field distribution \({\mathbf{{U}}}^{({\boldsymbol{n}})}\) based on the spatial separations of metasurface \(\left( {S_0^{(n)}} \right)\) or observed region (S(n)). The x0 and y0 (x, y, and z) are the coordinated variables of the metasurface plane S0 (observation region S). b Illustration of a structurally multiplexed metasurface30,31,32,33,34,37,38. The structurally multiplexed metasurface reconstructed several distinguished field distribution \({\mathbf{{U}}}^{({\boldsymbol{n}})}\) based on the metasurface function \({\mathbf{U}}_{{\mathbf{meta}}}^{({\boldsymbol{n}})}\). c Schematic illustration of a multi-beam meta-opener39. The multi-beam meta-opener is formed by several kinds of “key arrays”, which is used to read out the distributions \({\mathbf{{U}}}^{({\boldsymbol{n}})}\) carried by the preset incident beams. d Illustration of transmission-type multi-momentum meta-transformer. The multi-momentum meta-transformer decoder phase profile is implemented with TiO2 nano-fin array with in-plane orientations on a quartz substrate. It controls multi-beams with different momenta (l(nand \(k_0^{\left( n \right)}\)) to reconstruct corresponding field distributions \({\mathbf{{U}}}^{({\boldsymbol{n}})}\) Schematic of the OAM meta-transformer. Under the illumination of vortex beams with right circular polarization (RCP), the decoder can generate distinct images at the same plane with left circular polarization (LCP). f Schematic of the LM meta-transformer. Under the illumination of different LM beams with RCP, the meta-transformer can generate distinct LM-dependent field distributions at the same region on optical axis. g Top-view scanning electron microscopy (SEM) images of a partial region of the fabricated TiO2 nano-fins arrays. Scale bar: 2 μm. h Oblique-view SEM image. Scale bar: 2 μm. Each TiO2 nano-fin represents a phase pixel as defined in the meta-transformer

In this paper, we report a transmission-type multi-momentum meta-transformer, which transforms the intrinsic phases of OAM () and LM (k0ħ) of the incidence light, into various distinct patterns in the same plane (Fig. 1d). The meta-transformer is made of the minimalist TiO2 nano-fin array (Fig. 1g, h) and provides a phase profile \(\psi _{{\mathrm{meta}}}\left( {x_0,y_0} \right) = 2\varphi \left( {x_0,y_0} \right)\) for the right circularly polarized beam with spin angular momentum (SAM). The phase is based on geometric phase and φ(x0, y0) is the orientation angle of nano-fins as a function of position. For a given fabricated metasurface, incident beams Uinc(x0, y0) carrying OAM or LM are able to impart extra phase profiles ψOAM(x0, y0) or affect impulse response h(k0) to the transmitted light to realize distinct patterns in the same plane right on axis. A multi-OAM phase retrieval algorithm is developed to design the OAM meta-transformer, which can “read out” the order of the incident vortex beam. To be more specific, an image which tells the order of the incident vortex beam will be reconstructed at a given plane under illumination of vortex beam with certain orders as shown in Fig. 1e. In addition a multi-LM phase retrieval algorithm is proposed to design a LM meta-transformer, that can reconstruct patterns “R”, “G” and “B” in the same plane by illuminating it with red \(\left( {k_0^{\left( {\mathrm{R}} \right)}} \right)\), green \(\left( {k_0^{\left( {\mathrm{G}} \right)}} \right)\), and blue \(\left( {k_0^{\left( {\mathrm{B}} \right)}} \right)\) beams, respectively (Fig. 1f). This is due to the impulse response in Eq. 1 which is k0-dependent. Moreover, such LM meta-transformer has demonstrated the capability to display vivid colorful images, thanks to the high-efficiency of the dielectric metasurface and the on-axis imaging feature for all wavelengths.

Results

Principle of multi-momentum meta-transformer

The metasurface consists of a set of amorphous TiO2 nano-fins arranged in square pixels on a quartz substrate (Fig. 2a). The pixel size is 325 × 325 nm2 and the TiO2 nano-fin is 80-nm-wide, 250-nm-long and 600-nm-high, which rotates in plane with an orientation angle φ. When a circularly polarized beam is normally incident on the metasurface from the side of quartz, the transmitted light converts to the opposite circular polarization (CP) and acquires a phase delay of ±2φ (Supplementary Note 2). Lumerical FDTD solution is employed to optimize the geometrical parameters of nano-fins, such that the conversion from one CP to the opposite CP is efficient for the operation in broadband visible range (as shown in Fig. 2b).

Fig. 2
figure2

Principle and demonstration of multi-momentum meta-transformer. a Geometry of the designed unit cell structure representing one pixel in the meta-transformer, with the periodicity of 325 nm. The TiO2 nano-fin parameters are w = 80 nm, l = 250 nm, and h = 600 nm. The in-plane rotating angle φ of nano-fin will introduce the geometric phase of 2φ for the incident beam with RCP. b Measured conversion efficiency of the meta-transformer. The conversion efficiency is defined as the optical power of the transmitted light with opposite CP divided by the incident optical power. c Design principle of OAM meta-transformer. Under the illumination of vortex beam 1 (l(1) = −5) with RCP, the transmitted beam with opposite CP carries the total phase profile \(\psi _{{\mathrm{OAM}} = - 5}\left( {x_0,y_0} \right) + \psi _{{\mathrm{meta}}}\left( {x_0,y_0} \right)\) and reconstructs “apple” pattern in the observation plane. When using vortex beam 2 (l(2) = 5) with RCP, the total phase profile of the transmitted beam is \(\psi _{{\mathrm{OAM}} = 5}\left( {x_0,y_0} \right) + \psi _{{\mathrm{meta}}}\left( {x_0,y_0} \right)\), which causes the reconstructed pattern change to a spider-shaped pattern. d Simulated (top) and measured (bottom) reconstructed patterns by vortex beam 1 (l(1) = −5) (left) and vortex beam 2 (l(2) = 5) (right). Scale bar: 20 μm. e Design principle of LM meta-transformer. Under the illumination of right circularly polarized beam with \({\mathrm{LM}} = k_0^{\left( {\mathrm{R}} \right)}\hbar\), the transmitted beam with opposite CP carry the dispersionless phase profile of metasurface ψmeta (x0, y0). Due to the convolution of \({\mathbf{U}}_{{\mathbf{inc}}}\left( {x_0,y_0} \right)exp\left( {i\psi _{{\mathrm{meta}}}\left( {x_0,y_0} \right)} \right)\) and impulse response \(h\left( {x,y,z,k_0^{\left( {\mathrm{R}} \right)}} \right)\), the transmitted beam reconstructs patterns at the observation plane. Because the impulse response is k0-dependent, by changing LM of incidence, the reconstructed images “R”, “G” and “B” components can be shifted to one identical plane (z = Z0). f Simulated (top) and experimental (bottom) reconstruction of three-primary color holograms at the imaging plane. Scale bar: 20 μm. The original “spider” image was obtained from PNG image website

Figure 2c presents the schematic of OAM meta-transformer. A collimated vortex beam with native phase profile ψOAM (x0, y0) illuminates the metasurface with its own as-fabricated phase ψmeta(x0, y0) from the quartz substrate, and the transmitted beam carries the total phase profile \(\psi _{\mathrm{T}}\left( {x_0,y_0} \right) = \psi _{{\mathrm{OAM}}}\left( {x_0,y_0} \right) + \psi _{{\mathrm{meta}}}\left( {x_0,y_0} \right)\) on illuminating area (Supplementary Note 3). The metasurface’s phase function ψmeta(x0, y0), which is fixed after the fabrication, is defined by the in-plane orientation of nano-fin array. The extra phase profile ψOAM(x0, y0) from the incident vortex beam is dynamically changeable. As a degree of freedom of light, by feeding different spiral phases to the single-phase metasurface, one meta-transformer can, therefore, provide multiple different phase profiles, resulting in different patterns on the same plane.

The phase function ψmeta(x0, y0) of OAM meta-transformer is designed by the multi-OAM phase retrieval algorithm (Supplementary Note 4). The orientation angle of each nano-fin is determined by the retrieval phase ψmeta(x0, y0). The schematic diagram of the experimental setup is shown in Supplementary Fig. 3a and its specification can be found in Supplementary Note 6. As shown in Fig. 2d, at the given observation plane (z = 60 μm), a judiciously designed metasurface reconstructs an “apple” pattern under illumination with a collimated Laguerre Gaussian beam with l(1) = −5, while it shows a “spider” pattern instead when the OAM of the incident beam is changed to l(2) = 5. The reconstructed images restore the features of the designed pattern and the crosstalk is suppressed.

Figure 2e presents the physical principle of LM meta-transformer. The phase function ψmeta(x0, y0) of a metasurface is defined by the in-plane orientation of nano-fin array, which means that the designed metasurface is able to provide the dispersionless phase profile. In the Fresnel region, the impulse response h of Eq. 1 is

$$h\left( {x,y,z} \right) = \frac{{e^{ik_0z}}}{{i\lambda z}}e^{i\frac{{k_0}}{{2z}}\left[ {x^2 + y^2} \right]}$$
(2)

Therefore, when collimated monochromatic beams illuminate the metasurface, this dispersionless phase profile ψmeta(x0, y0) can control the monochromatic beams with different LMs to achieve different E-field distribution in a given plane (shown in Fig. 2e).

To realize the LM meta-transformer, the key idea is to reconstruct LM-dependent patterns in the same plane. In the visible region, the monochromatic beams with different LMs represent different colors. So three-primary colors (red 633 nm, green 532 nm, and blue 488 nm) are chosen in this work. Based on the k0-dependent impulse response, the multi-LM phase retrieval algorithm (Supplementary Note 5) is deployed here to calculate the phase distribution ψmeta(x0, y0). Hence, the wavelength-dependent patterns are reconstructed in the same plane (at Z0) and the unwanted patterns are moved out of the observed plane. In this design, based on the retrieval phase profile ψmeta(x0, y0), the nano-fins (600 × 600) with rotation angles are fabricated on a total area of 192 × 192 μm2. The schematic diagram of the experiment setup of color meta-hologram is shown in Supplementary Fig. 3b and the specification of the experiment setup can be found in Supplementary Note 6. The image is captured by a CCD camera. Figure 2f shows the holographic images of letter patterns “R”,”G”,”B” at a certain distance (z =195 μm), corresponding to the RGB color incident beams (633 nm, 532 nm, and 488 nm). The images corresponding to the RGB color incident beams are independent from each other, and the cross-talk among different LMs is eliminated, due to k0-dependent impulse response.

Discussion

The OAM meta-transformer can now work as an OAM displayer, as demonstrated in Fig. 3a. This meta-transformer is formed by 300 × 300 nano-fins on the total area 97.5 × 97.5 μm2. As shown in Fig. 3b, the designed OAM meta-transformer reconstructs the patterns “0”, “3” and “6” with the incident 0th-, 3rd- and 6th-order vortex beams, respectively. Compared with Fig. 2d, the OAM meta-transformer in Fig. 3b has lower phase difference among the incident vortex beams and encodes more OAM states, which may reduce the performance. Nevertheless, the reconstructions in Fig. 3b are clearly recognizable. The reconstructed patterns present the incident beam’s topological charge values, which suggests a potential application of OAM topological charge displayer (OAM detection by direct reading) with such OAM meta-transformer.

Fig. 3
figure3

OAM meta-transformer for the read-out of three OAM states. a Schematic of OAM meta-transformer designed on three OAM states. This meta-transformer is designed to reconstructed “0”, “3” and “6” patterns at l(n) = 0, 3, and 6, respectively. b Simulated (top) and measured (bottom) reconstructed patterns. Scale bar: 20 μm

Based on k0-dependent impulse response, the LM meta-transformer generates LM-dependent patterns on the identical position (Fig. 2e, f). Under illumination of red, green and blue beams simultaneously, these generated patterns overlapping each other enable the realization of colorful holographic images (Supplementary Note 7). The colorful holographic images contain not only three-primary colors (RGB) but also their secondary colors (cyan, magenta, yellow, as well as white). Moreover, the LM meta-transformer can also support complex patterns with gradient color (in Fig. 4a, b). Figure 4b reports the simulation and experimental results for each color and their superposition. These results indicate the accurate spatial control of the reconstructed images, and the crosstalk among different LMs is eliminated. The key feature for such gradient color image is that the color gamut spans the whole color triangle. Therefore, the LM meta-transform has the capability to display vivid colorful image.

Fig. 4
figure4

Reconstruction of color images. a Schematic illustration of reconstruction of gradient color image. b Intensity profiles corresponding to red, green, and blue beams and the graded color holographic image. Scale bar: 30 μm. The original “merlion” image was obtained from Vecteezy.com

The capability is a critical issue for the multi-tasked metasurface. Based on the multi-momentum phase retrieval algorithm provided in this work, a single meta-transformer is able to support 5 OAM states ranging from −8 to 8 or 6 LM states in the visible region (Supplementary Note 8). With the help of the polarization-dependent response21,42,43 of TiO2 nano-fins, the number of patterns encoded in a meta-transformer can increase to 9 for OAM or 11 for LM. Furthermore, the capability of a meta-transformer can also be improved by increasing the number of units25, and widening the multi-momentum state region. Besides, by considering the donut shapes of vortex beams, introducing random phase mask44, and combining the LM and OAM simultaneously in the phase retrieval algorithm, the multi-momentum meta-transformer has the potential to remarkably increase the carried information states.

In summary, we report a synergetic strategy of engaging OAM and LM of the incident beam with a single-phase metasurface, which significantly enriches the output of reconstructed patterns. OAM introduces the additional phase information from the incident beam, while the LM affects the phase information of impulse response. These two momentum degrees of freedom, in principle lead to infinite combined states, which enables metasurface with a large number of functions and may lead to new opportunities in 3D imaging, anti-counterfeiting, optical communication, and real-time detection.

Methods

Numerical simulation

The amorphous TiO2 nano-fins were optimized by Lumerical FDTD Solution (a commercial software). In this simulation, TiO2 nano-fins with measured refractive index were placed on quartz substrate. Two sources polarized along x- and y-axes with a 90° phase shift was used to form the right circularly polarized incident beam, and this beam illuminated TiO2 nano-fins from the substrate side. The periodic boundary condition was used along x- and y-directions, and the perfect matched layer (PML) was chosen along z-direction.

Data availability

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

Code availability

The codes that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

References

  1. 1.

    Yu, N. et al. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science 334, 333–337 (2011).

    ADS  CAS  PubMed  Article  Google Scholar 

  2. 2.

    Huang, L. et al. Dispersionless phase discontinuities for controlling light propagation. Nano. Lett. 12, 5750–5755 (2012).

    ADS  CAS  PubMed  Article  Google Scholar 

  3. 3.

    Kildishev, A. V., Boltasseva, A. & Shalaev, V. M. Planar photonics with metasurfaces. Science 339, 1232009 (2013).

    PubMed  Article  CAS  Google Scholar 

  4. 4.

    Yu, N. & Capasso, F. Flat optics with designer metasurfaces. Nat. Mater. 13, 139–150 (2014).

    ADS  CAS  PubMed  Article  Google Scholar 

  5. 5.

    Zhu, A. Y., Kuznetsov, A. I., Luk’yanchuk, B., Engheta, N. & Genevet, P. Traditional and emerging materials for optical metasurfaces. Nanophotonics 6, 452–471 (2017).

    CAS  Article  Google Scholar 

  6. 6.

    Li, Z. et al. Full-space cloud of random points with a scrambling metasurface. Light Sci. Appl 7, 63 (2018).

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  7. 7.

    Huang, K. et al. Spiniform phase-encoded metagratings entangling arbitrary rational-order orbital angular momentum. Light Sci. Appl 7, 17156 (2018).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  8. 8.

    Paniagua-Dominguez, R. et al. A metalens with a near-unity numerical aperture. Nano. Lett. 18, 2124–2132 (2018).

    ADS  CAS  PubMed  Article  Google Scholar 

  9. 9.

    Lalanne, P. & Chavel, P. Metalenses at visible wavelengths: past, present, perspectives. Laser Photonics Rev. 11, 1600295 (2017).

    ADS  Article  CAS  Google Scholar 

  10. 10.

    Lin, D., Fan, P., Hasman, E. & Brongersma, M. L. Dielectric gradient metasurface optical elements. Science 345, 298–302 (2014).

    ADS  CAS  PubMed  Article  Google Scholar 

  11. 11.

    Kristensen, A. et al. Plasmonic colour generation. Nat. Rev. Mater. 2, 16088 (2017).

    ADS  CAS  Article  Google Scholar 

  12. 12.

    Dong, Z. et al. Printing beyond sRGB Color gamut by mimicking silicon nanostructures in free-space. Nano. Lett. 17, 7620–7628 (2017).

    ADS  CAS  PubMed  Article  Google Scholar 

  13. 13.

    Gu, Y., Zhang, L., Yang, J. K., Yeo, S. P. & Qiu, C. W. Color generation via subwavelength plasmonic nanostructures. Nanoscale 7, 6409–6419 (2015).

    ADS  CAS  PubMed  PubMed Central  Article  Google Scholar 

  14. 14.

    Yan, C., Yang, K.-Y. & Martin, O. J. F. Fano-resonance-assisted metasurface for color routing. Light Sci. Appl. 6, e17017 (2017).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  15. 15.

    Wu, P. C. et al. Versatile polarization generation with an aluminum plasmonic metasurface. Nano. Lett. 17, 445–452 (2017).

    ADS  CAS  PubMed  Article  Google Scholar 

  16. 16.

    Zhu, A. Y. et al. Giant intrinsic chiro-optical activity in planar dielectric nanostructures. Light Sci. Appl 7, 17158 (2018).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  17. 17.

    Huang, K. et al. Ultrahigh-capacity non-periodic photon sieves operating in visible light. Nat. Commun. 6, 7059 (2015).

    ADS  CAS  PubMed  Article  Google Scholar 

  18. 18.

    Li, X. et al. Athermally photoreduced graphene oxides for three-dimensional holographic images. Nat. Commun. 6, 6984 (2015).

    ADS  PubMed  PubMed Central  Article  Google Scholar 

  19. 19.

    Ni, X., Kildishev, A. V. & Shalaev, V. M. Metasurface holograms for visible light. Nat. Commun. 4, 2807 (2013).

    ADS  Article  CAS  Google Scholar 

  20. 20.

    Wang, L. et al. Grayscale transparent metasurface holograms. Optica 3, 1504–1505 (2016).

    ADS  Article  Google Scholar 

  21. 21.

    Huang, K. et al. Silicon multi‐meta‐holograms for the broadband visible light. Laser Photonics Rev. 10, 500–509 (2016).

    ADS  CAS  Article  Google Scholar 

  22. 22.

    Huang, L. et al. Broadband hybrid holographic multiplexing with geometric metasurfaces. Adv. Mater. 27, 6444–6449 (2015).

    CAS  PubMed  Article  Google Scholar 

  23. 23.

    Avayu, O., Almeida, E., Prior, Y. & Ellenbogen, T. Composite functional metasurfaces for multispectral achromatic optics. Nat. Commun. 8, 14992 (2017).

    ADS  CAS  PubMed  PubMed Central  Article  Google Scholar 

  24. 24.

    Maguid, E. et al. Photonic spin-controlled multifunctional shared-aperture antenna array. Science 352, aaf3417 (2016).

    ADS  Article  CAS  Google Scholar 

  25. 25.

    Maguid, E. et al. Multifunctional interleaved geometric-phase dielectric metasurfaces. Light Sci. Appl. 6, e17027 (2017).

    PubMed  PubMed Central  Article  Google Scholar 

  26. 26.

    Mehmood, M. Q. et al. Visible-Frequency Metasurface for Structuring and Spatially Multiplexing Optical Vortices. Adv. Mater. 28, 2533–2539 (2016).

    CAS  PubMed  Article  Google Scholar 

  27. 27.

    Mei, S. et al. Flat helical nanosieves. Adv. Funct. Mater. 26, 5255–5262 (2016).

    CAS  Article  Google Scholar 

  28. 28.

    Montelongo, Y., Tenorio-Pearl, J. O., Milne, W. I. & Wilkinson, T. D. Polarization switchable diffraction based on subwavelength plasmonic nanoantennas. Nano. Lett. 14, 294–298 (2014).

    ADS  CAS  PubMed  Article  Google Scholar 

  29. 29.

    Wang, B. et al. Visible-frequency dielectric metasurfaces for multiwavelength achromatic and highly dispersive holograms. Nano. Lett. 16, 5235–5240 (2016).

    ADS  CAS  PubMed  Article  Google Scholar 

  30. 30.

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

    ADS  CAS  PubMed  Article  Google Scholar 

  31. 31.

    Balthasar Mueller, J. P., Rubin, N. A., Devlin, R. C., Groever, B. & Capasso, F. Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization. Phys. Rev. Lett. 118, 113901 (2017).

    ADS  CAS  PubMed  Article  Google Scholar 

  32. 32.

    Chen, W. T. et al. High-efficiency broadband meta-hologram with polarization-controlled dual images. Nano. Lett. 14, 225–230 (2014).

    ADS  PubMed  Article  CAS  Google Scholar 

  33. 33.

    Goh, X. M. et al. Three-dimensional plasmonic stereoscopic prints in full colour. Nat. Commun. 5, 5361 (2014).

    ADS  CAS  PubMed  PubMed Central  Article  Google Scholar 

  34. 34.

    Khorasaninejad, M. et al. Multispectral chiral imaging with a metalens. Nano. Lett. 16, 4595–4600 (2016).

    ADS  CAS  PubMed  Article  Google Scholar 

  35. 35.

    Xu, H.-X. et al. Interference-assisted kaleidoscopic meta-plexer for arbitrary spin-wavefront manipulation. Light Sci. Appl 8, 3 (2019).

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  36. 36.

    Huang, L. et al. Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity. Light Sci. Appl. 2, e70 (2013).

    Article  CAS  Google Scholar 

  37. 37.

    Kamali, S. M. et al. Angle-multiplexed metasurfaces: encoding independent wavefronts in a single metasurface under different illumination angles. Phys. Rev. X 7, 041056 (2017).

    Google Scholar 

  38. 38.

    Shi, Z. et al. Single-layer metasurface with controllable multiwavelength functions. Nano. Lett. 18, 2420–2427 (2018).

    ADS  CAS  PubMed  Article  Google Scholar 

  39. 39.

    Ren, H., Li, X., Zhang, Q. & Gu, M. On-chip noninterference angular momentum multiplexing of broadband light. Science 352, 805–809 (2016).

    ADS  CAS  PubMed  Article  Google Scholar 

  40. 40.

    Mei, S. et al. On-chip discrimination of orbital angular momentum of light with plasmonic nanoslits. Nanoscale 8, 2227–2233 (2016).

    ADS  CAS  PubMed  Article  Google Scholar 

  41. 41.

    Yue, Z., Ren, H., Wei, S., Lin, J. & Gu, M. Angular-momentum nanometrology in an ultrathin plasmonic topological insulator film. Nat. Commun. 9, 4413 (2018).

    ADS  PubMed  PubMed Central  Article  CAS  Google Scholar 

  42. 42.

    Jin, L. et al. Noninterleaved Metasurface for (26-1) Spin- and Wavelength-Encoded Holograms. Nano. Lett. 18, 8016–8024 (2018).

    ADS  CAS  PubMed  Article  Google Scholar 

  43. 43.

    Wen, D. et al. Helicity multiplexed broadband metasurface holograms. Nat. Commun. 6, 8241 (2015).

    ADS  PubMed  PubMed Central  Article  Google Scholar 

  44. 44.

    Makey, G. et al. Breaking crosstalk limits to dynamic holography using orthogonality of high-dimensional random vectors. Nat. Photon 13, 251–256 (2019).

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

This work was supported from the National Research Foundation, Prime Minister’s Office, Singapore under its Competitive Research Program (CRP award NRF CRP15-2015-03). X.L. acknowledges the support from National Natural Science Foundation of China (NSFC) (Grant 61522504), Guangdong Provincial Innovation and Entrepreneurship Project (Grant 2016ZT06D081). F.C., Y.W.H., and W.T.C. acknowledge the financial support in part by the Air Force Office of Scientific Research (Grant Nos. MURI FA9550-14-1-0389 and FA9550-16-1-0156) and King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) (Award No. OSR-2016-CRG5-2995).

Author information

Affiliations

Authors

Contributions

L.J. and C.W.Q. conceived the idea. L.J., Z.J., S.M., M.J., and C.W.Q. designed the nanostructures and did the optical characterization of the hologram. Y.W.H. and R.C.D did the nanofabrication of nanostructures. Z.W. provided the expertise knowledge on the phase retrieval algorithm. Z.D., W.T.C., H.L., J.T., A.D., X.L., S.X., S.Z., C.Y., and J. K.W.Y. participated in the discussions and contributed with valuable suggestions for the multi-momentum meta-transformer. The paper was written by L.J. with inputs from Y.W.H, Z.J., S.M., F.C., and C.W.Q. C.W.Q. supervised the project. All authors analyzed the data, read and corrected the paper before paper submission.

Corresponding authors

Correspondence to Federico Capasso or Cheng-Wei Qiu.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Communications thanks Xianzhong Chen and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

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 license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license 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 license, visit http://creativecommons.org/licenses/by/4.0/.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Jin, L., Huang, YW., Jin, Z. et al. Dielectric multi-momentum meta-transformer in the visible. Nat Commun 10, 4789 (2019). https://doi.org/10.1038/s41467-019-12637-0

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing