Open Access
Add to BibSonomy
Abstract
Metasurfaces have shown unusual abilities to modulate the phase, amplitude and polarization of an incident lightwave with spatial resolution at the subwavelength scale. Here, we experimentally demonstrate a dielectric metasurface enabled with both geometric phase and magnetic resonance that scatters an incident light beam filling the full reflective 2π-space with high-uniformity. Specifically, by delicately reconfiguring the orientations of dielectric nanobricks acting as nano-half-waveplates in a metasurface, the optical power of phase-modulated output light is almost equally allocated to all diffraction orders filling the full reflection space. The measured beam non-uniformity in the full hemispheric space, defined as the relative standard deviation (RSD) of all scattered optical power, is only around 0.25. More interestingly, since the target intensity distribution in a uniform design is rotationally centrosymmetric, the diffraction results are identical under arbitrary polarization states, e.g., circularly polarized, linearly polarized or even unpolarized light, which brings great convenience in practical applications. The proposed uniform-backscattering metasurface enjoys the advantages including polarization insensitivity, high-integration-density and high-stability, which has great potential in sensing, lighting, laser ranging, free-space optical communication and so on.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In the fields such as sensing, lighting, laser ranging, machine vision measuring system and free-space optical communication, a uniform angular distribution from light source can significantly improve the performance of optical measuring systems for many purposes. However, conventional light sources such as light emitting diode (LED) and laser usually have a non-uniform angular distribution. Conventional beam shaping technique with diffractive optical elements (DOEs) [1–2] can be employed to reconfigure the angular distribution of light source. However, limited by the multi-step phase modulation and low pixel resolution (micrometer level), the diffractive light can hardly cover the whole space with precise phase modulation. Although the secondary-optics [3–5] can help to reconfigure the angular distribution of LED light radiation in the whole transmitted space, the bulky secondary-optical lens would hinder the integration and compactness of a light source, which is highly eager in many electronic and optical products towards being lightweight, thin and flexible.
Metasurfaces, a kind of artificially ultrathin planar optical nanostructures, have recently been employed to control the polarization [6–14], phase [15–23] and amplitude [24–26] of incident light at the subwavelength scale. Among them, Pancharatnam-Berry phase or so-called geometric phase has drawn great interest because geometric metasurfaces (GEMSs) can modulate the phase of incident light accurately while remain the amplitude unchanged. GEMSs have been employed to reconfigure the spatial distribution of incident light and applied in imaging [27–31] and holography [32–42]. Since an arbitrary light intensity field can be generated by GEMSs, uniform-backscattering is included in principle.
By using coding metasurfaces, uniform-backscattering has been realized at the microwave frequencies [43–45]. In this paper, we design a 2π-space uniform-backscattering metasurface in visible light, which is realized by assigning a single layer of silicon nanobrick arrays with identical geometric sizes but different orientations on a planar dielectric substrate. Since each nanobrick acts as a half-wave plate and produce a geometric phase which is exact twice of the nanobrick orientation, a continuous phase modulation of the incident light can be achieved with the nanobricks. Thus, by reconfiguring the orientation distribution of the nanobricks with an optimization algorithm, the energy of diffractive light can be uniformly allocated to each diffraction orders that filling the whole reflective space, and 2π-space uniform-backscattering can be acquired. We experimentally demonstrate the 2π-space uniform-backscattering metasurface in a test platform and the high-uniformity of the backscattering light is verified. Our proposed uniform-scattering metasurfaces have promising applications in lighting, light fidelity (LIFI), optical measurement, free-space optical communication and many other related fields.
2. Unit cell design
A general concept of the 2π-space uniform-backscattering metasurface is illustrated in Fig. 1(a). To realize the functionality of uniform-backscattering, the nanostructure should to be carefully designed to precisely modulate the phase of incident light. Figure 1(b) shows the unit-cell structure of a uniform-scattering metasurface consisting of silicon-on-insulator (SOI) material. The SOI structure has three layers: the top-layer composed of crystalline silicon used for nanobricks fabrication, the mid-layer composed of silica and the ground substrate composed of crystalline silicon. All the nanobricks have equal dimensions (cell size C, height H, length L, width W) but different orientation angles α, defined as the long-axis of nanobricks and x-axis. According to the working principle of geometric phase [46–48], when circularly polarized (CP) incident light illuminates a metasurface, the reflected light has two sub-beam parts: one part, called co-polarized light, has the same handedness with the incident light and there is no phase delay; the other part called cross-polarized light carries a phase delay of 2α and has an opposite handedness. Therefore, with incident CP light, the Jones matrix of reflected light can be expressed as
Fig. 1. Illustration and simulation of the 2π-space uniform-backscattering metasurface based on SOI material. (a) Schematic diagram of the uniform-backscattering metasurfaces. The normally incident light is scattered into all directions of the reflective hemi-sphere at an operating wavelength of 633 nm. (b) Illustration of a single nanobrick based on SOI material. All nanobricks in a metasurface have equal dimensions but different orientation angle α. The thickness of silica is 2 µm. (c) The simulated reflectivities versus wavelength shown in the left side under normally incident LP light with polarization direction along the short (green) and long (red) axes, respectively. Right side is the phase difference (blue) of the reflected light between the short and long axes. (d) Simulated efficiencies of the cross-polarized (green) and the co-polarized (red) light versus wavelength.
Owing to the different parameters of L and W which form unequable electromagnetic responses in two orthogonal directions, each nanobrick can be treated as a birefringent nano-element. There are two unequal reflection coefficients (rl and rs) when linearly polarized (LP) light illuminates the nanobrick along the long and the short axes of the nanobricks, respectively. At the same time, a phase difference (δr) exists between the two orthogonal directions of the reflective LP light. Therefore, the optical efficiency related to rl, rs and δr can be written as [34]
As we can see from Eq. (2), the co-polarized light (Rco) which contributes to the unwanted zero-th order light without phase delay should be suppressed as low as possible, implying that rl = rs and δr = π. In the meantime, the cross-polarized light (Rcross) which contributes to the useful light with phase delay should be optimized to the maximum, implying that rl or rs should be as high as possible.
Here, the commercial software CST Studio Suite was used for the design and numerical simulations (more details are provided in Sec. 6 Methods). With the geometric parameters of the nanobrick shown in Fig. 1(b), the optimized nanobrick is designed with C of 300 nm, L of 200 nm, W of 100 nm and H of 220 nm. As shown in Fig. 1(c), the reflective coefficients with the polarization directions along the long and short axes can be nearly equal (∼ 90%) and the phase difference can reach nearly π, at an operating wavelength of 633 nm. The unusual high-reflectivity can be interpreted by magnetic resonance [49], occurring in a dielectric nanostructure. The magnetic resonance originates from the excitation of cyclic displacement current in the silicon nanobricks, which localizes the enhanced magnetic field in the center of the nanobricks. As a result, the reflective cross-polarized efficiency (Rcross) reaches 83% and the co-polarized efficiency (Rco) is suppressed to below 3%, as shown in Fig. 1(d). Therefore, the incident CP light can be converted into that with opposite-handedness with high-efficiency after passing through the designed nanobricks, with a phase delay of 2α.
3. Design of metasurface for uniform-scattering in a reflective hemi-sphere
Since each nanobrick can independently modulate the phase of incident light, we design a uniform-backscattering metasurface based on the optimized nanobricks at an operating wavelength of 633 nm. If a metasurface has pixel numbers of Nx × Ny, the numbers of diffractive orders in the reflection space will be the same as the pixel numbers. However, since the diffractive light fills in the whole reflective hemispherical space, some diffraction orders might be evanescent waves and cannot reach to the far field. Therefore, we need to determine the useful diffractive orders forming the target image before we can conduct a phase optimization. Here, we introduce the spatial frequency to distinguish an evanescent wave order and propagation wave order. The spatial frequency can be defined as
As a result, the diffraction angles in the far field can be expressed as
As an example, we design a metasurface with dimensions of 300 × 300 µm2. Since each unit-cell has dimensions of 300 × 300 nm2, there are 1000 × 1000 nanobrick arrays and corresponding diffraction orders. According to Eqs. (3) and (4), the numbers of propagation waves are around 724k, occupying 72.4% of the total diffraction orders. Interestingly, since the target intensity distribution in the far field is rotationally centrosymmetric, i.e., I(x, y)=I(-x, -y), the diffraction results are identical under arbitrary polarized light such as LCP, RCP and LP. Therefore, our proposed metasurface has a unique characteristic of polarization insensitivity, which can bring convenience for practical purposes.
With above design, we fill the amplitude matrix A0 of the target image with “1” in propagation modes and “0” in evanescent modes, as shown in Fig. 2(a). Since the diffractive characteristics of a metasurface obey the same rules of a conventional DOE, we can design the phase distribution of a uniform-scattering metasurface by the same algorithm. Therefore, we take A0 as an input amplitude matrix and put it into the Gerchbreg-Saxton (G-S) algorithm [50–51] with an initial random phase matrix φ0 to determine the first phase matrix φ1 of the uniform-scattering metasurface.
Fig. 2. Design flowchart of the 2π-space uniform-backscattering metasurface. (a) Initial design intensity distribution versus diffraction orders. (b) Relation of the diffraction angles and the diffraction orders. (c) Intensity distribution of the far field with the calculation results φ1 after the first loop computation by the G-S algorithm. (d) A compensated target intensity distribution by comparing the initial design intensity and the first diffraction results. (e) Phase distribution φ2 after the secondary loop computation. (f) Intensity distribution of the far field with the calculation results φ2. φ0 is a random phase matrix which is only used for the initial calculation.
As shown in Fig. 2(b), the relation between the diffraction angles and orders is nonlinear. As a result, the angle intervals between adjacent orders are varied. However, the Fourier transformation used in G-S algorithm is a linear transformation, which is suitable only for small diffraction angles, i.e., sin(θ)≈θ. Therefore, if we employ the conventional algorithm for phase optimization, an inhomogeneous beam density would occur in the hemispheric space. As shown in Fig. 2(c), with the first phase matrix φ1, the intensity distribution in the far field simulated by the Rayleigh-Sommerfeld (R-S) diffraction is sparse in the edge but dense in the center, which is obviously non-uniform. Therefore, the next step to realize 2π-space uniform-backscattering is to conduct intensity pre-compensation. We should rearrange the target intensity distribution with compensation based on the difference between the target uniform-backscattering and the initial-design non-uniform-backscattering. The new target intensity distribution, as shown in Fig. 2(d), is taken as the input target intensity distribution for G-S algorithm optimization. With the same operation shown above, the final phase distribution φ2 shown in Fig. 2(e) is acquired and its diffraction results in the far field are shown in Fig. 2(f), which agree quite well with the design goal to realize 2π-space uniform-backscattering.
4. Experiments and discussion
By using standard electron-beam lithography (EBL), we fabricate the 2π-space uniform-backscattering metasurface aforementioned. More details about the fabrication of SOI based metasurface is provided in the Methods. The fabricated sample is shown in the insets of Fig. 3(a) with a photo taken by a commercial camera (Nikon 5100) and scanning electron microscopy (SEM) images in partial view, respectively.
Fig. 3. Experimental setup and results of the uniform-scattering metasurface. (a) The experimental setup is used to measure the intensities of the reflective light in all directions of the reflective hemi-sphere space. A LP light beam generated by a He-Ne laser source (633 nm) is incident perpendicular to the sample. The optical power of reflective light is measured by an optic power meter. The insets show the sample and the SEM images. (b) 3D normalized optical power of output light in reflective hemi-sphere. φ and θ are the pitching angle and azimuthal angle, respectively. (c) The cross-sections of (b) with detailed optical power at θ = 15°, 45°, 75°, -15°, -45° and -75°, respectively. The ratios of the mean and maximum values of the measured optical power in each cross-section are 0.767, 0.780, 0.738, 0.763, 0.748 and 0.776, respectively. The shadow areas are unmeasured due to the blocking of the optic power meter in a reflective optical path.
To characterize the fabricated metasurface sample, we use a He-Ne laser source (CVI Melles Griot 25-LHP-991-230) to illuminate the sample without any polarization device since our designed metasurface is insensitive to the polarization state of incident light. In the experiment, we can observe the scattered light in any direction of the hemispheric space, which proves that the scattering light can fill in the whole reflective space. Next, to measure the uniformity of the scattering light, we employ an experimental setup shown in Fig. 3(a). The metasurface sample is placed in the center of a 360° continuous-rotating breadboard (Thorlabs RBB12A) and illuminated by the above He-Ne laser source in a normal incidence. After that, we use an optical power meter (Thorlabs PM100D) to measure the optical power of the output light. Figure 3(b) shows the three-dimensional (3D) measured results of the diffractive optical power after normalization, and the cross-section of 3D results reveal the detailed optical power values at six different azimuthal angles (θ = 15°, 45°, 75°, -15°, -45°, -75°), as shown in Fig. 3(c). Here, the radial components indicate the optical power values in these polar diagrams. The profiles of measurements at six azimuthal angles seem to be identical and hence the light intensity with the same pitching angle is uniform.
In order to evaluate the uniformity of the reflected optical power, we choose the relative standard deviation (RSD) as the evaluation function [52]:
Table 1. RSD of the optical power vs azimuthal angle θ (pitching angle Φ from 0° to 180°).
As it is known, the smaller RSD is, the closer the intensity distribution of the reflected light is to a uniform intensity distribution. Hence, these experimental results around 0.25, which is acceptable [52], confirm that the uniform-scattering metasurface works well as our design.
Besides, as shown in Fig. 3(c), the fluctuation of optical power in the range from 15° to 165° keeps stable and the sharp reduction of optical power happens only at the edges (with diffraction angles of nearly 0° and 180°). Table 2 shows the RSD of output optical power at six different azimuthal angles with pitching angle from 15° to 165°, which is about only a third of the RSD shown in Table 1. The reason for the deteriorated uniformity at the edge regions is caused by the fabrication errors and the non-uniformity of the angular distribution. That is, the angular distribution in the edge regions is sparse and more sensitive to fabrication errors, so the same fabrication error can cause different light intensity fluctuation in the edge and middle regions. A promising solution is increasing the pixel numbers of the metasurfaces to reduce the angular intervals (Δθ ≈ λ/D=λ/(C·Nx)), at the cost of mass-area nanofabrication.
Table 2. RSD of the optical power vs azimuthal angle θ (pitching angle Φ from 15° to 165°).
5. Conclusions
We propose a 2π-space uniform-backscattering metasurface with SOI material by combining geometric phase modulation with magnetic resonance. By reconfiguring the orientations of the SOI nanobrick arrays, the output light carries different phase delays cell-by-cell, which are delicately designed by the modified G-S algorithm. As a result, the reflective light beams fill in the whole reflective hemispheric space and have almost equal intensity density in every diffraction direction in the far field. With the advantages of polarization insensitivity, high-integration-density and high-stability, the compatibility and simplicity of SOI material, the proposed uniform-scattering GEMSs possess a great potential in optical imaging, information encryption, LIFI, optical communication, optical measurement and so on.
6. Methods
6.1 Unit-cell simulation
We used the CST Studio Suite for electromagnetic simulation and optimized the geometric parameters (cell size C, height H, length L, width W) of the unit cell shown in Fig. 1(b). Our optimization goal is not only to make rl = rs and δr = π but also make rl as large as possible. By delicately adjusting the parameters, we can investigate the electromagnetic performance with different lengths and widths. We used the periodic boundary condition along the direction of the x and y axes to simulate and sweep W and L from 50 nm to 250 nm in a step of 10 nm at C = 300 nm and H = 220 nm with the operating wavelength varying from 550 nm to 750 nm. Then we fixed an operating wavelength (633 nm) with optimized nonstructural parameters (length L = 200 nm, width W = 100 nm) and the corresponding simulation results have been shown in Fig. 1(c) with normally incident LP light. In Fig. 1(d), we changed the polarization of the normally incident light from LP to CP with the same simulation conditions, the co-polarized and the cross-polarized light was collected by different ports.
6.2 Sample fabrication
We fabricated the sample with a standard EBL process based on SOI substrate which has a mid-layer silica of 2 µm and a top-layer crystalline silicon of 220 nm. Firstly, a mask of polymethyl methacrylate (PMMA) was patterned on SOI substrate by the EBL process. Secondly, the thermal evaporator was used for the depositing a 30 nm Cr film on the sample, and Cr played the role of etch mask here. After that, the sample was cleaned by ultrasonic waves via immersing it into hot acetone at 75 °C. Subsequently, a solution mixed with 250 sccm (standard-state cubic centimeter per minute) SF6, 95 sccm O2 (at 200 WRF power), 300 sccm CHF3 was used for removing the part without Cr by reactive ion etching. Finally, by removing Cr with the Cr etchant, only silicon nanobricks remained on the substrate.
Appendix 1. Dispersion curves of silica and crystalline silicon
The refractive indexes of silica and crystalline silicon versus wavelength (550 nm ∼ 750 nm) are shown in Fig. 4. Red and green curves in Fig. 4(b) are the real and imaginary parts of crystalline silicon’s refractive index, respectively.
Fig. 4. Dispersion curves of (a) silica and (b) crystalline silicon versus wavelength (550 nm∼750 nm).
Appendix 2. RSD convergence degree versus iteration times in G-S algorithm
We used fast Fourier transform to iterate in the Gerhberg-Saxton algorithm. The change of RSD convergence degree with the number of iterations is shown in Fig. 5. We iterated over 10,000 times in total, and the computing time was about 40 minutes (CPU Intel i7-8550U, RAM 16 GB).
Funding
National Natural Science Foundation of China (91950110, 11774273, 11904267, 61805184); Postdoctoral Innovation Talent Support Program of China (BX20180221); China Postdoctoral Science Foundation (2019M652688).
Disclosures
The authors declare no conflicts of interest.
References
1. F. M. Dickey, Laser beam shaping: theory and techniques, (CRC Press, 2018).
2. W. Freese, T. Kämpfe, E. Kley, and A. Tünnermann, “Design of binary subwavelength multiphase level computer generated holograms,” Opt. Lett. 35(5), 676–678 (2010). [CrossRef]
3. C. Tsuei, J. Pen, and W. Sun, “Simulating the illuminance and the efficiency of the LED and fluorescent lights used in indoor lighting design,” Opt. Express 16(23), 18692–18701 (2008). [CrossRef]
4. H. Lee and B. Lin, “Improvement of illumination uniformity for LED flat panel light by using micro-secondary lens array,” Opt. Express 20(106), A788–A798 (2012). [CrossRef]
5. H. Chen, J. Lin, and H. Chiu, “Rectangular illumination using a secondary optics with cylindrical lens for LED street light,” Opt. Express 21(3), 3201–3212 (2013). [CrossRef]
6. S. Wu, Z. Zhang, Y. Zhang, K. Zhang, L. Zhou, X. Zhang, and Y. Zhu, “Enhanced rotation of the polarization of a light beam transmitted through a silver film with an array of perforated S-shaped holes,” Phys. Rev. Lett. 110(20), 207401 (2013). [CrossRef]
7. P. Yu, S. Chen, J. Li, H. Cheng, Z. Li, W. Liu, B. Xie, Z. Liu, and J. Tian, “Generation of vector beams with arbitrary spatial variation of phase and linear polarization using plasmonic metasurfaces,” Opt. Lett. 40(14), 3229–3232 (2015). [CrossRef]
8. J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13(9), 4269–4274 (2013). [CrossRef]
9. W. Liu, S. Chen, Z. Li, H. Cheng, P. Yu, J. Li, and J. Tian, “Realization of broadband cross-polarization conversion in transmission mode in the terahertz region using a single-layer metasurface,” Opt. Lett. 40(13), 3185–3188 (2015). [CrossRef]
10. Z. Li, W. Liu, H. Cheng, S. Chen, and J. Tian, “Realizing broadband and invertible linear-to-circular polarization converter with ultrathin single-layer metasurface,” Sci. Rep. 5(1), 18106 (2016). [CrossRef]
11. Y. Bao, J. Ni, and C. W. Qiu, “A minimalist single-layer metasurface for arbitrary and full control of vector vortex beams,” Adv. Mater. 32(6), 1905659 (2020). [CrossRef]
12. Q. Dai, L. Deng, J. Deng, J. Tao, Y. Yang, M. Chen, Z. Li, Z. Li, and G. Zheng, “Ultracompact, high-resolution and continuous grayscale image display based on resonant dielectric metasurfaces,” Opt. Express 27(20), 27927–27935 (2019). [CrossRef]
13. J. Deng, L. Deng, Z. Guan, J. Tao, G. Li, Z. Li, Z. Li, S. Yu, and G. Zheng, “Multiplexed anticounterfeiting meta-image displays with single-sized nanostructures,” Nano Lett. 20(3), 1830–1838 (2020). [CrossRef]
14. Y. Zhang, L. Shi, D. Hu, S. Chen, S. Xie, Y. Lu, Y. Cao, Z. Zhu, L. Jin, B. Guan, S. Rogge, and X. Li, “Full-visible multifunctional aluminium metasurfaces by in situ anisotropic thermoplasmonic laser printing,” Nanoscale Horiz. 4(3), 601–609 (2019). [CrossRef]
15. 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). [CrossRef]
16. C. Min, J. Liu, T. Lei, G. Si, Z. Xie, J. Lin, L. Du, and X. Yuan, “Plasmonic nano-slits assisted polarization selective detour phase meta-hologram,” Laser Photonics Rev. 10(6), 978–985 (2016). [CrossRef]
17. Z. Deng, S. Zhang, and G. P. Wang, “Wide-angled off-axis achromatic metasurfaces for visible light,” Opt. Express 24(20), 23118–23128 (2016). [CrossRef]
18. Z. Deng, S. Zhang, and G. P. Wang, “A facile grating approach towards broadband, wide-angle and high-efficiency holographic metasurfaces,” Nanoscale 8(3), 1588–1594 (2016). [CrossRef]
19. W. Liu, Z. Li, H. Cheng, C. Tang, J. Li, S. Zhang, S. Chen, and J. Tian, “Metasurface enabled wide-angle Fourier lens,” Adv. Mater. 30(23), 1706368 (2018). [CrossRef]
20. Z. Li, G. Zheng, P. A. He, S. Li, Q. Deng, J. Zhao, and Y. Ai, “All-silicon nanorod-based Dammann gratings,” Opt. Lett. 40(18), 4285–4288 (2015). [CrossRef]
21. Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5(1), 5753 (2014). [CrossRef]
22. X. Fang, H. Ren, and M. Gu, “Orbital angular momentum holography for high-security encryption,” Nat. Photonics 14(2), 102–108 (2020). [CrossRef]
23. Y. Hu, L. Li, Y. Wang, M. Meng, L. Jin, X. Luo, Y. Chen, X. Li, S. Xiao, and H. Wang, “Trichromatic and tri-polarization-channel holography with non-interleaved dielectric metasurface,” Nano Lett. 20(2), 994–1002 (2020). [CrossRef]
24. K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’Yanchuk, J. Teng, and C. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6(1), 7059 (2015). [CrossRef]
25. Z. Xu, L. Huang, X. Li, C. Tang, Q. Wei, and Y. Wang, “Quantitatively correlated amplitude holography based on photon sieves,” Adv. Opt. Mater. 8(2), 1901169 (2020). [CrossRef]
26. K. Huang, H. Liu, G. Si, Q. Wang, J. Lin, and J. Teng, “Photon-nanosieve for ultrabroadband and large-angle-of-view holograms,” Laser Photonics Rev. 11(3), 1700025 (2017). [CrossRef]
27. M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016). [CrossRef]
28. M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano Lett. 15(8), 5358–5362 (2015). [CrossRef]
29. M. Khorasaninejad, W. Chen, J. Oh, and F. Capasso, “Super-dispersive off-axis meta-lenses for compact high-resolution spectroscopy,” Nano Lett. 16(6), 3732–3737 (2016). [CrossRef]
30. R. Fu, Z. Li, G. Zheng, M. Chen, Y. Yang, J. Tao, L. Wu, and Q. Deng, “Reconfigurable step-zoom metalens without optical and mechanical compensations,” Opt. Express 27(9), 12221–12230 (2019). [CrossRef]
31. G. Zheng, W. Wu, Z. Li, S. Zhang, M. Q. Mehmood, P. A. He, and S. Li, “Dual field-of-view step-zoom metalens,” Opt. Lett. 42(7), 1261–1264 (2017). [CrossRef]
32. X. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4(1), 2807 (2013). [CrossRef]
33. J. Deng, Z. Li, G. Zheng, J. Tao, Q. Dai, L. Deng, P. A. He, Q. Deng, and Q. Mao, “Depth perception based 3D holograms enabled with polarization-independent metasurfaces,” Opt. Express 26(9), 11843–11849 (2018). [CrossRef]
34. Z. Li, Q. Dai, M. Q. Mehmood, G. Hu, B. Luk Yanchuk, J. Tao, C. Hao, I. Kim, H. Jeong, and G. Zheng, “Full-space cloud of random points with a scrambling metasurface,” Light: Sci. Appl. 7(1), 63 (2018). [CrossRef]
35. G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015). [CrossRef]
36. J. Deng, Y. Yang, J. Tao, L. Deng, D. Liu, Z. Guan, G. Li, Z. Li, S. Yu, and G. Zheng, “Spatial frequency multiplexed meta-holography and meta-nanoprinting,” ACS Nano 13(8), 9237–9246 (2019). [CrossRef]
37. L. Li, T. J. Cui, W. Ji, S. Liu, J. Ding, X. Wan, Y. B. Li, M. Jiang, C. Qiu, and S. Zhang, “Electromagnetic reprogrammable coding-metasurface holograms,” Nat. Commun. 8(1), 197 (2017). [CrossRef]
38. D. Wen, F. Yue, G. Li, G. Zheng, K. Chan, S. Chen, M. Chen, K. F. Li, P. W. H. Wong, and K. W. Cheah, “Helicity multiplexed broadband metasurface holograms,” Nat. Commun. 6(1), 8241 (2015). [CrossRef]
39. L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, and C. Qiu, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(1), 2808 (2013). [CrossRef]
40. Y. Hu, X. Luo, Y. Chen, Q. Liu, X. Li, Y. Wang, N. Liu, and H. Duan, “3D-Integrated metasurfaces for full-colour holography,” Light: Sci. Appl. 8(1), 86 (2019). [CrossRef]
41. X. Luo, Y. Hu, X. Li, Y. Jiang, Y. Wang, P. Dai, Q. Liu, Z. Shu, and H. Duan, “Integrated Metasurfaces with Microprints and Helicity-Multiplexed Holograms for Real-Time Optical Encryption,” Adv. Opt. Mater., 1902020 (2020).
42. Y. Bao, Y. Yu, H. Xu, C. Guo, J. Li, S. Sun, Z. Zhou, C. Qiu, and X. Wang, “Full-colour nanoprint-hologram synchronous metasurface with arbitrary hue-saturation-brightness control,” Light: Sci. Appl. 8(1), 1–10 (2019). [CrossRef]
43. M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017). [CrossRef]
44. K. Chen, Y. Feng, Z. Yang, L. Cui, J. Zhao, B. Zhu, and T. Jiang, “Geometric phase coded metasurface: from polarization dependent directive electromagnetic wave scattering to diffusion-like scattering,” Sci. Rep. 6(1), 35968 (2016). [CrossRef]
45. L. Zhang, X. Q. Chen, S. Liu, Q. Zhang, J. Zhao, J. Y. Dai, G. D. Bai, X. Wan, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Space-time-coding digital metasurfaces,” Nat. Commun. 9(1), 4334 (2018). [CrossRef]
46. M. Xiao, G. Ma, Z. Yang, P. Sheng, Z. Q. Zhang, and C. T. Chan, “Geometric phase and band inversion in periodic acoustic systems,” Nat. Phys. 11(3), 240–244 (2015). [CrossRef]
47. J. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118(11), 113901 (2017). [CrossRef]
48. E. Maguid, I. Yulevich, M. Yannai, V. Kleiner, M. L. Brongersma, and E. Hasman, “Multifunctional interleaved geometric-phase dielectric metasurfaces,” Light: Sci. Appl. 6(8), e17027 (2017). [CrossRef]
49. Z. Li, I. Kim, L. Zhang, M. Q. Mehmood, M. S. Anwar, M. Saleem, D. Lee, K. T. Nam, S. Zhang, and B. Luk Yanchuk, “Dielectric meta-holograms enabled with dual magnetic resonances in visible light,” ACS Nano 11(9), 9382–9389 (2017). [CrossRef]
50. H. Hwang, H. T. Chang, and W. Lie, “Multiple-image encryption and multiplexing using a modified Gerchberg-Saxton algorithm and phase modulation in Fresnel-transform domain,” Opt. Lett. 34(24), 3917–3919 (2009). [CrossRef]
51. Z. Zalevsky, D. Mendlovic, and R. G. Dorsch, “Gerchberg-Saxton algorithm applied in the fractional Fourier or the Fresnel domain,” Opt. Lett. 21(12), 842–844 (1996). [CrossRef]
52. X. Mao, H. Li, Y. Han, and Y. Luo, “Polar-grids based source-target mapping construction method for designing freeform illumination system for a lighting target with arbitrary shape,” Opt. Express 23(4), 4313–4328 (2015). [CrossRef]
