Surfaces covered by ultrathin plasmonic structures—so-called metasurfaces1,2,3,4—have recently been shown to be capable of completely controlling the phase of light, representing a new paradigm for the design of innovative optical elements such as ultrathin flat lenses5,6,7, directional couplers for surface plasmon polaritons4,8,9,10 and wave plate vortex beam generation1,11. Among the various types of metasurfaces, geometric metasurfaces, which consist of an array of plasmonic nanorods with spatially varying orientations, have shown superior phase control due to the geometric nature of their phase profile12,13. Metasurfaces have recently been used to make computer-generated holograms14,15,16,17,18,19, but the hologram efficiency remained too low at visible wavelengths for practical purposes. Here, we report the design and realization of a geometric metasurface hologram reaching diffraction efficiencies of 80% at 825 nm and a broad bandwidth between 630 nm and 1,050 nm. The 16-level-phase computer-generated hologram demonstrated here combines the advantages of a geometric metasurface for the superior control of the phase profile and of reflectarrays for achieving high polarization conversion efficiency. Specifically, the design of the hologram integrates a ground metal plane with a geometric metasurface that enhances the conversion efficiency between the two circular polarization states, leading to high diffraction efficiency without complicating the fabrication process. Because of these advantages, our strategy could be viable for various practical holographic applications.
In traditional phase-only computer-generated hologram (CGH) designs, the phase profile is controlled by etching different depths into a transparent substrate. Because of their ease of fabrication, two-level binary CGHs have widely been used. Such CGHs have a theoretical diffraction efficiency of only 40.5% and the issue of twin-image generation cannot be avoided. Multi-level-phase CGHs can alleviate the problem of low efficiency and twin-image generation, but fabricating such CGHs requires expensive and complicated greyscale lithography, variable-dose or multi-step lithography20. Furthermore, the unavoidable etching error, resolution error and alignment error can dramatically degrade the performance of CGHs, leading to a low signal-to-noise ratio, poor uniformity and strong zero-order intensity. To obtain higher efficiency and less manufacturing complexity, an effective medium approach has been proposed20, where two-level-depth subwavelength structures with variable cell dimensions can function as an effective medium with geometry-controlled effective refractive index, and consequently act as a multi-level CGH. However, such a design involves extremely small feature sizes with high aspect ratios, limiting the observed efficiency of a three-level CGH to less than 30%, which is significantly lower than the theoretical value of 48%.
Geometric metasurfaces (GEMS) provide an alternative approach to achieving high-efficiency holograms without complicated fabrication procedures. GEMS rely on inversion of the absolute rotation direction of the electric field of the radiation (in transmission or reflection) with respect to that of the incident circularly polarized one21,22. This is equivalent to flipping the circular polarization in transmission or maintaining the same circular polarization in reflection. A geometric phase, or Pancharatnam–Berry phase, is acquired through inversion of the electric field rotation, leading to an antenna-orientation-controlled phase that does not depend on the specific antenna design or wavelength, thus making its performance broadband and highly robust against fabrication latitude and variation in the material properties. However, GEMS operating at visible and near-infrared wavelengths have been limited so far by the low efficiency of conversion between the two circular polarization states.
To increase the efficiency of GEMS, a multilayer design is used to achieve high polarization conversion23,24,25,26. The reflective metasurface hologram consists of three layers: a ground metal plane, a dielectric spacer layer and a top layer of antennas (Fig. 1). It is well known that a half wave plate can fully convert a circularly polarized beam into the oppositely polarized one in transmission as the result of a phase delay of π between the fast and slow axes. Hence, to achieve high conversion between the two circular polarization states, it is desirable that the phase difference between the reflection with polarization along the long axis (rl) and the short axis (rs) of the nanorod antenna equals π. The simulated results in Fig. 1d,e show that, with an optimized configuration, the phase difference between the reflection coefficients rl and rs approaches π within a wide wavelength range of 600–1,000 nm. At the same time, the configuration maintains very large reflection amplitudes over 0.8 for both linear polarizations. Therefore, regardless of the orientation of the antennas, it is expected that the circularly polarized incident light almost completely flips the absolute rotation direction of the electric field upon reflection, thus preserving its circular polarization state (given that the wavevector is also reversed). This forms the basis of the high-efficiency GEMS. A detailed discussion and a simplified model to explain the high efficiency and broadband responses of the nanorod metasurface are provided in Supplementary Figs 1–7.
The high efficiency of maintaining the same circular polarization state upon reflection is verified by numerical simulations for a uniform metasurface with all nanorod antennas aligned along the same direction (Fig. 1f). The reflected wave in general consists of both circular polarization states: one has the same handedness as the incident circularly polarized light but with an additional phase delay 2ϕ (ϕ is the orientation angle of the nanorod antenna), and the other has the opposite handedness without the additional phase delay. For the specific geometry configuration shown in Fig. 1a, with normal light incidence the numerical simulation shows that the reflectivity of light with the same circular polarization state is over 80% in a broad wavelength range between 550 nm and 1,000 nm, covering nearly a full optical octave. This efficiency is surprisingly high considering the ohmic loss of metal at visible and near-infrared frequencies. Interestingly, the ohmic loss in our configuration is very close to that of light transmitted through a single metasurface layer (without the ground metal plane) around the resonance wavelength (800–850 nm) of the antenna (Supplementary Fig. 8). On the other hand, the efficiency of the unwanted opposite polarization is extremely low (<3%) over a broad wavelength range.
To confirm the high efficiency of our numerical simulations we designed a GEMS-based CGH, as shown in Fig. 2. The CGH was designed for circularly polarized light at normal incidence. A design where the holographic image appears off-axis was used to avoid overlapping of the holographic image and the zero-order spot. The CGH was designed to create a wide image angle of 60° × 30°. A 2 × 2 periodic array of the hologram pattern was used (Fig. 2b; more details of the advantages of the 2 × 2 periodic arrangement over a single hologram are provided in Supplementary Fig. 9). To create a holographic image with a pixel array measuring m × n within the angular range αx × αy in the far field, the period of the CGH in the x and y directions can be calculated according to dx = mλ/(2tan(αx/2)) and dy = nλ/(2tan(αy/2)), respectively. The number of pixels of the CGH is determined by M = dx/Δp and N = dy/Δp, where Δp is the pixel size of the CGH in both x and y directions.
With the above structural parameters, a phase-only CGH with pixel dimensions of 300 nm × 300 nm and periods of 333.3 μm × 333.3 μm was designed according to the classical Gerchberg–Saxton algorithm27. Note that the pixel size along each direction is less than half the wavelength, ensuring that the hologram pattern is sampled at least at twice the maximum spatial frequency in either direction, thereby satisfying the Shannon–Nyquist sampling theorem. The phase distribution obtained for the hologram is shown in Fig. 2b. In the design of the CGH, the conversion efficiency, signal-to-noise ratio and uniformity were taken as merit functions for optimization. Because the phase delay is determined solely by the orientation of the nanorod antennas, 16 phase levels (Fig. 1c) were used to obtain the high performance from the CGH. Simulation shows that in our optimized design with an ideal hologram neglecting optical losses, the window efficiency, which is defined as the ratio between the optical power projected into the image region and the input power, reaches 94%.
The metasurface CGH was fabricated on top of a silicon substrate following the design described above (Fig. 3a). The simulated and measured holographic images, including both the zoomed-in views of the face and the letter ‘M’, show good agreement with one another. This demonstrates the extremely high fidelity of the metasurface hologram. To determine the conversion efficiency, the linear polarization state of light from a supercontinuum light source (Fianium Supercontinuum) was converted to circular polarization using a linear polarizer and a quarter wave plate. The reflected holographic image was collected by two condenser lenses with high numerical aperture, and the hologram image was measured in the range from 600 nm to 1,100 nm in steps of 25 nm. The optical efficiency (holographic window efficiency) was finally determined by subtracting the zeroth-order beam signal from the image intensity (Fig. 3b). We found a relatively broad spectral range from 630 nm to 1,050 nm with a high window efficiency larger than 50%, which reaches a maximum of 80% at a wavelength of 825 nm. At the same time the unwanted zeroth-order efficiency is only ∼2.4%. More importantly, we did not observe the twin image effect from which traditional binary holograms usually suffer.
Theoretically, the metasurface hologram has an even broader spectral response (Fig. 1f) when compared to the measured efficiency. The lower bandwidth probably arises from the fact that the calculated conversion efficiency is obtained on a metasurface under normal incidence. In the present experiment the holographic image from the metasurface hologram was projected into a broad angular range. We expected this broad-angle scattering to induce a narrower bandwidth and lower peak reflection than the calculated results shown in Fig. 1f. A detailed discussion of the diffraction efficiency of a metasurface consisting of nanoantennas with non-uniform orientations is provided in Supplementary Figs 10 and 11. In addition, a weak near-field coupling effect among neighbouring nanorod antennas introduces a small phase deviation when compared to the design (Supplementary Fig. 12).
In summary, we have presented a reflective-phase-only hologram based on GEMS that has a diffraction efficiency as high as 80%, an extremely low zeroth-order efficiency, and a broadband spectral response in the visible/near-infrared range. Our metasurface has an ultrathin and uniform thickness of 30 nm and is compatible with scalar diffraction theory, even with subwavelength pixel sizes28, thus simplifying the design of holograms. Given its simple and robust phase control, its good tolerance to wavelength variations and fabrication errors, our geometric phase-based CGH design could overcome the current limitations of traditional depth-controlled CGH and find applications in fields such as laser holographic keyboards, random spot generators for body motion, optical anti-counterfeiting and laser beam-shaping. Moreover, our approach can be readily extended from phase-only to amplitude-controlled holograms, simply by changing the size of the nanorods. Because we exploit a phase effect resulting from a polarization state change, the only restriction of our technique arises from the fact that the polarization state of the light cannot be controlled; that is, the incident light has to be circularly polarized. Finally, we note that such nanorod metasurfaces could be fabricated on a large scale and at much lower costs by nano-imprinting, thus making them promising candidates for large-scale holographic technology.
Simulation of conversion efficiency
The nanorod cell was designed and simulated by CST (www.CST.com) microwave studio software. In the simulation, a linearly polarized plane wave was normally incident onto a single nanorod with periodic boundary conditions. The spectra of reflection coefficients rxx, rxy, ryy, ryx were obtained from the simulation. From the reflection of linear polarized light we could retrieve the reflection coefficients for circularly polarized light as rrr = (rxx + ryy – (rxy – ryx)·i)/2 and rlr = (rxx – ryy – (ryx + rxy)·i)/2. The performance of the nanorods was optimized by sweeping the geometric parameters of the nanorod (including the cell size, spacer and gold thickness).
Design of the metasurface hologram
A complex digital image containing Einstein's portrait (550 × 300 pixels and 256 greyscale levels) was chosen as a holographic target image. Because of the large angular range, the Rayleigh–Sommerfeld diffraction method was used to simulate the holographic image29. The hologram was pre-compensated to avoid pattern distortion. To avoid the formation of laser speckles in the holographic image, the concept of Dammann gratings30 was used for the hologram design.
Fabrication and experimental set-up
The samples were fabricated on a gold and MgF2-coated silicon substrate with standard electron-beam lithography, subsequent deposition of 30 nm gold, and lift-off processes. For the imaging experiment we used a red laser (He-Ne laser, wavelength of 632.8 nm) and a near-infrared diode laser (780 nm). The circularly polarized laser source was incident onto the metasurface hologram, and the reflected holographic image was projected onto a white screen 300 mm away from the surface of the hologram. We captured the red and near-infrared holographic image using commercial digital cameras (Nikon D3200 and ELOP-Contour CMOS IR digital camera). Details of the experimental set-up, efficiency calculation and incident angle scanning for optical efficiency measurements are provided in Supplementary Figs 13–15.
This research was partly supported by the Engineering and Physical Sciences Research Council (EP/J018473/1). The authors thank L. Zhu and W. He for discussions. H.M. and T.Z. acknowledge financial support from the Deutsche Forschungsgemeinschaft Research Training Group GRK1464. S.Z. and T.Z. acknowledge support from the European Commission under the Marie Curie Career Integration Program. S.Z. acknowledges financial support from the National Natural Science Foundation of China (grant no. 61328503).