Abstract

We demonstrate the realization of a continuous control over the phase change from zero to 2π for second harmonic generation (SHG) from the complementary split-ring resonators (CSRRs) by adjusting their geometrical parameters and reversing their orientations. We verify this concept by designing and fabricating nonlinear metasurfaces consisting of CSRRs with desired nonlinear phase profiles, which can bend and focus the SHG signals. The ability to provide a continuous and subwavelength phase control of the local second-order nonlinearities makes the CSRRs good candidates for applications, such as nonlinear holograms and integrated nonlinear nanophotonic elements that combine the coherent generation and manipulation of harmonic waves.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Metasurfaces are ultrathin planar metamaterials made of periodic subwavelength metallic or dielectric nanostructures, also called meta-atoms [1,2]. The most intriguing feature of metasurfaces is that one can select the geometry and chemical composition of meta-atoms to control the phase, amplitude or the polarization state of light waves propagating through, reflected or scattered from them [3–13]. Unlike conventional optical components, such as lenses, wave-plates and prisms, which rely on gradual phase changes accumulated along the optical path to control and manipulate light, metasurfaces diminish the dependence on the propagation effect by introducing spatial inhomogeneity in optical properties over the thin interface. Thus, metamaterials provide a new degree of freedom of controlling the wavefront of light [1,2]. So far, metasurfaces with abrupt and controllable phase changes have been utilized to realize beam steering [3,4], vortex beams [3,5], ultrathin focusing lenses [6,7], flat waveplates [8,9], optical spin-orbit interactions [10,11], and photonic spin Hall effect [12,13].

Recently, the concept of phased metasurfaces has been extended to the nonlinear regime to enable both coherent generation and manipulation [14–21]. For example, a π phase shift can be imposed on the local second harmonic generation (SHG) nonlinearity by simply inverting the orientation of the metallic split ring resonator (SRR) or complementary SRR (CSRR) [14,15]. Based on this mechanism, binary nonlinear metasurfaces consisting of SRRs or CSRRs have been designed to implement the engineered diffraction, intense focusing, polarization control, and the generation of Airy and vortex beams of the output SHG signals [14–17]. For more complex beam manipulation in nonlinear processes, a continuous and spatially varying phase manipulation is highly desirable. The recent realization of the geometric Berry phase in nonlinear metasurfaces enabled a continuous control over the nonlinear phase change from 0 to 2π by simply rotating the meta-atoms with respect to the laboratory frame [18]. Although the concept of the nonlinear Berry phase provides a simple route for better manipulation of the beam profile of the nonlinear radiation and realization of nonlinear holography [19], it requires circularly polarized fundamental wave (FW) and only generates circularly polarized harmonic generation. More recently, it was demonstrated that under linearly polarized illumination, a full-range nonlinear phase of four-wave mixing (FWM) and third harmonic generation (THG) signals could be obtained in the metasurfaces made of rectangular nanoapertures and V-shaped nanoantennas, respectively, by changing the size and shape of the meta-atoms [20,21]. So far, however, literature addressing the continuous phase engineering of the SHG radiation from the nonlinear metasurfaces illuminated by linearly polarized light is rather limited.

In this study, we demonstrate that by finely adjusting the structural parameters of the meta-atoms made of the CSRRs, the resultant spectral shift between the resonances in the CSRRs and the fundamental wave can introduce a local nonlinear phase with continuous tuning range exceeding π into the SHG processes for linearly polarized excitation. The nonlinear phase tuning range can be further extended to cover the entire 2π range by reversing the orientation of the CSRRs, and consequently imposing an additional π phase shift on the SHG signals [15]. The complete phase control over the nonlinear emission enables us to design flat nonlinear optical components that combine the coherent generation and manipulation of harmonic waves. As a demonstration of this concept, we show that the CSRRs-based metasurfaces with properly designed phase gradient can be utilized to bend and tightly focus the SHG signals.

2. Results and discussions

Figure 1(a) schematically depicts the gold CSRR element serving as the building block of the nonlinear metasurface, in which the local nonlinear effect originates mainly from a microscopic symmetry break at the surface of the CSRR [22]. In this work, CSRRs are chosen because they not only exhibit high quadratic nonlinearities that arise from the coupling of the exciting field and the generated nonlinear surface currents to bright radiating plasmonic modes of the CSRRs [22,23], but also have transmittance maxima at both the excitation and SHG wavelengths [15,22]. Each CSRR element is characterized by a set of structural parameters l (the arm length), w (the arm width), g (the width of the central metal patch) and t (the thickness of the gold film), where g and t are fixed to 50 nm and 20 nm, respectively, while l and w are allowed to be varied. The linear optical properties of the regular arrays of CSRRs sitting on a fused silica (amorphous SiO2) substrate are first investigated using a commercial finite-element method (FEM) software package COMSOL Multiphysics. In the calculations, periodic boundary conditions are employed to mimic periodicities (a = 400 nm) along the x- and y-directions. All the sharp corners are rounded with a radius of curvature of 5 nm to avoid possible numerical artifacts. The refractive index of the fused silica substrate is assumed to be 1.46, and the permittivity of gold is taken from the experimental data of Johnson and Christy [24]. Figure 1(b) shows the transmission spectra of the metasurfaces illuminated by the y-polarized plane-wave propagating along the z-direction (normal incidence) for a fixed arm width (w = 75 nm) while different arm lengths (l). As expected, the transmittance through the CSRRs are interchanged with the reflectance of the corresponding SRRs [23], which ensures transmittance maxima at the fundamental resonance for the CSRRs rather than transmittance minima for the SRRs. It is also seen that the plasmonic resonances of the CSRRs can be spectrally tuned by changing the arm length. For example, as the arm length varies from l = 160 nm to l = 100 nm, the fundamental resonance peak blue-shifts drastically from λ ≈1400 nm to λ ≈1100 nm.

 figure: Fig. 1

Fig. 1 (a) Schematic of a uniform CSRR array with a periodicity of a = 400 nm. The height of the CSRR is t = 20 nm. The width of the central metal patch is g = 50 nm. Normally incident light propagates along the z-axis and is polarized along the y-axis. (b) Calculated linear transmission spectra of the CSRR arrays with a fixed arm width of w = 75 nm but different arm lengths. For clarity, each curve is shifted vertically by a constant of 0.7 relative to the previous one. The red and blue dashed lines indicate the fundamental and SHG wavelengths, respectively. (c) The normalized SHG conversion efficiency from the CSRRs with w = 75 nm and l = 160 nm. (d) The nonlinear phase shift and amplitude in the array of CSRRs with w = 75 nm but different arm lengths. (e) and (f) Calculated SH phase-shift and amplitude for CSRRs with different l and w.

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In addition, the nonlinear phase shift and efficiency of the SHG from the CSRRs can also be calculated using FEM numerical simulation based on a hydrodynamic model of the free electron dynamics [22,25], which has been used previously to handle SHG process in metallic structures such as SRRs, CSRRs, and T-shaped nanoparticles [22,25]. Figure 1(c) shows the normalized SHG conversion efficiency from the CSRRs with an arm width of w = 75 nm and an arm length of l = 160 nm. The maximum efficiency is found to occur at λ ≈1400 nm [Fig. 1(c)], which corresponds to the fundamental resonance of the CSRRs [Fig. 1(b)]. Figure 1(d) shows the calculated SH phase shift and amplitude (red line) at λSH = 700 nm (λFW = 1400 nm) for the CSRRs with a fixed arm width (w = 75 nm) and different arm lengths. It is found that although the SH phase shift exhibits a wide (~300-degree) phase coverage by solely varying the arm length from l = 185 nm to l = 105 nm [blue line in Fig. 1(d)], the SH amplitude is drastically varied from 0 to 1 [red line in Fig. 1(d)]. In order to obtain a complete phase control over the SHG and simultaneously large SH amplitudes, both the arm length and arm width of the CSRRs need to be varied in the calculations. Figures 1(e) and 1(f) show the maps of the calculated phase shift and amplitude of the SHG at a given FW wavelength λFW = 1400 nm, respectively, as functions of the arm length and width, which actually provide guidance for choosing the CSRRs with appropriate structural parameters to create a metasurface with a given phase gradient. For example, to obtain a π/4 phase gradient, the phase shift contours −45°, 0°, 45°, and 90° are first determined and outlined by dashed lines in Fig. 1(e). Then, the contour lines are superimposed to the colour map of the SHG amplitude in Fig. 1(f). Along each contour line, the phase shift of the SHG could remain the same, while its amplitude can be changed by selecting the CSRRs with different combinations of the arm length and width. Two typical sets of four CSRRs are chosen along the path-1 and path-2, as indicated by solid circles and squares in Fig. 1(f), respectively. There are only small differences between the SHG amplitudes of the four CSRRs in the path-1, while SHG amplitude differences between the four CSRRs in the path-2 are relatively large. By simply mirroring the CSRR with respect to its base, one creates an inverted CSRR whose locally generated SHG radiation has an additional π phase shift [10], which equivalently extends the nonlinear phase coverage shown in Fig. 1(e) by π.

As schematically shown in Figs. 2(a) and 2(b), two eight-resonator unit cells with the same incremental phase shift of Δφ = π/4 (along the + x direction) are thus created from the initial four CSRRs located in the path-1 or path-2 and the corresponding four inverted-CSRRs. The far-field SHG emission of the metasurfaces constructed from the above two super-cells excited by a normally incident fundamental wave (λFW = 1400 nm) polarized along the y-direction are calculated and shown in Figs. 2(c) and 2(d). Although the SHG amplitude ratio of the CSRRs along the path-1 (1.1:1.3:1.2:1) and path-2 (1.1:1.5:1.4:1) is different, the SHG radiation patterns of the metasurfaces constructed from these two sets of CSRRs are found to be almost the same. In each case, the SHG could be radiated into the backward hemisphere (90° < θ < 270°, corresponding to the substrate side) and the forward hemisphere (0° < θ < 90° and 270° < θ < 360°, corresponding to the air side) at the emission angles of 192.4° and 347.4° (or equivalently −12.6°), respectively. Since the origins of the two strong side lobes are the same, we only focus on the transmitted SHG signals.

 figure: Fig. 2

Fig. 2 (a) and (b): Schematic view of eight-resonator super-unit cells with a phase gradient of π/4. One super-unit is created from the CSRRs in the path-1, the other is from the CSRRs in the path-2. (c) and (d) Far-field SHG intensity from the metasurfaces consisting of the super-unit cells presented in (a) and (b).

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The radiation at a specified emission angle of θ from the phased array can be analytically expressed as

I=A2|l=1Nei(l1)β[s=18ei(s1)αei(s1)Δφ]|2,=A2sin2[4(α+Δφ)]sin2[(α+Δφ)/2]sin2(Nβ/2)sin2(β/2)
where A is the amplitude of the radiation emitted by the dipole, α = kasinθ with k = 2π/λ being the wavevector is the phase step between neighboring dipoles, Δφ = π/4 is the phase gradient, N is the total number of the eight-dipole super-unit cells, β = kpsinθ is the phase step between neighboring super-unit cells. The last multiplier in Eq. (1) will achieve the maximum value of N2, when β/2 is equal to , which corresponds to the occurrence of mth-order diffraction. In our design, since all the dipoles are equally spaced (p = 8a), we have β = 8α. The radiation intensity into the mth diffraction order is then given by
I=N2A2sin2[(m+1)π]sin2[(m+1)π/8].
For a wavelength of λ = 700 nm and a periodicity of p = 3200 nm, the available propagating diffraction orders are |m| = 0, 1, 2, 3 and 4. According to Eq. (2), only the intensity into the m = −1 diffraction order is non-zero, which is the origin of the side-lobe observed in Figs. 2(c) and 2(d). At normal incidence, the −1-order diffraction angle could be determined by θ-1 = −sin−1(λ/p) = −12.6°, which is found to correspond well to the direction of the strong side lobe in the calculated SHG radiation pattern.

In the following, we experimentally demonstrate that the CSRRs-based metasurfaces with properly designed nonlinear phase gradient can be utilized to bend the SHG beam. As schematically shown in Fig. 3(a), femtosecond pulses with a duration of 100 fs and a repetition rate of 1kHz are derived from an optical parametric amplifier. The FW is polarized along the CSRR arm and focused to a ~30 μm-diameter spot onto the samples from the substrate side under normal incidence. The average power of the FW is ~0.2 mW. The transmitted optical signals pass through a short pass filter to block the pump light and then are collected by an objective (50 × , 0.7 N. A.). With tube lenses L1 and L2, the back focal plane of the objective, which is a Fourier image of the radiation from the sample, is imaged onto a cooled back-illuminated electron multiplying charged coupled device (EMCCD) camera. Figures 3(b)-3(d) show the scanning electron microscopy (SEM) images of the nonlinear metasurfaces consisting of one-CSRR unit cell (uniform array with a phase gradient of Δφ = 0), eight-CSRR super-unit cell with Δφ = π/4, and six-CSRR super-unit cell with Δφ = π/3, respectively. All the CSRR arrays with a footprint of 50 μm × 50 μm are fabricated by focused ion beam milling in a 20-nm-thick gold film supported on a fused silica substrate. Figure 3(e) shows the k-space image of SHG emission from the uniform CSRR array pumped by λFW = 1400 nm. Due to the periodicity of a = 400 nm is smaller than the wavelength of the SHG beam (λSHG = 700 nm), only a zeroth-order SHG diffraction is observed at an emission angle of θ = 0° [Fig. 3(e)]. The k-space images of SHG emission from the nonlinear metasurfaces consisting of eight-CSRR and six-SRR super-unit cells are shown in Figs. 3(f) and 3(g), respectively. In each case, only one spot appears at a negative diffraction angle, which agrees well with the calculated result shown in Fig. 2(c). The measured emission angles are also found to be dependent both on the periodicity (p) and the FW wavelength (λFW) [Figs. 3(f) and 3(g)]. Furthermore, all these measured angles are consistent with the first negative order SHG diffraction angles calculated according to θ-1 = −sin−1(λ/p), which confirm that the CSRRs-based metasurfaces with the proper choice of the phase gradient allow us to control the beam steering of the SHG emission.

 figure: Fig. 3

Fig. 3 (a) Schematic illustration of the experimental setup, where the CDD-camera records either Fourier images or real images of the CSRR-based samples. (b)-(d) SEM images of the nonlinear metasurfaces consisting of one-CSRR unit cell with Δφ = 0, eight-CSRR super-unit cell with Δφ = π/4, and six-CSRR super-unit cell with Δφ = π/3, respectively. Scale bars represent 500 nm. (e)-(g) Measured k-space images of SHG from the samples shown in (b)-(d), respectively. The uniform array in (e) is pumped by FW with a wavelength of 1400 nm. The phase-modulated arrays in (f) and (g) are pumped by FWs with three different wavelengths of 1300nm, 1400 nm, and 1500 nm.

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To further illustrate the flexibility of the continuous phase control over the local second-order nonlinearity, we designed a CSRR-based metasurface that is able to focus SHG beam. In the design of a nonlinear metalens with a desired focal length f, the arm length and width of the CSRRs located in a concentric ring with a given radius of r are chosen from Figs. 1(e) and 1(f) to impose a particular phase shift φ(r)=2πf2+r2/λSHG onto the SHG signals. Figure 4(a) shows the SEM image of the fabricated nonlinear metalens with f = 40 μm. The simulation based on a beam propagation technique [15] for the metalens upon illumination by normally incident FW (λFW = 1400 nm) with its polarization along the CSRR arm is shown in Fig. 4(b). In order to experimentally characterize the focusing effect of the fabricated nonlinear metalens, the EMCCD-camera is placed around the focal plane of the tube lens L1, where the real image of the sample appears, as schematically shown in Fig. 3(a). The measured result is shown in Fig. 4(c) and found to be well consistent with the simulation, presenting the intense focusing of the SHG at the desired focus length. In addition, as indicated by dashed lines in Fig. 4(c), the cross-sectional images of the normalized SHG are recorded at distances z = 5 μm and 40 μm away from the surface of the metalens, and shown in Figs. 4(d) and 4(e), respectively. It is clearly seen that the diameter of the SHG is ~14 μm at the z = 5 μm plane [Fig. 4(d)], and narrows to ~8 μm at the z = 40 μm plane [Fig. 4(e)].

 figure: Fig. 4

Fig. 4 (a) SEM image of a CSRR-based metasurface acting as a nonlinear metalens with a desired focal length f = 40 μm. The scale bar is 5 μm. Dashed line represents a concentric ring with a radius of r on which all the CSRRs have the same phase shift. (b) and (c) Calculated and measured SHG focusing effect of the metalens upon illumination by normally incident FW (λFW = 1400 nm) with its polarization along the CSRR arm, respectively. (d) and (e) Images of the normalized SHG (λSHG = 700 nm) recorded at z = 5 μm and z = 40 μm cross-section planes, respectively.

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3. Conclusions

In summary, we demonstrate that the adjustment of the geometrical parameters, such as the arm length and width, coupled with the mirror inversion of the CSRRs enable a continuous control over the phase change from zero to 2π for the locally generated SHG upon illumination by linearly polarized FW. By designing a nonlinear metasurface consisting of eight-CSRR supercells with a phase gradient of Δφ = π/4, SHG beam bending behavior is experimentally demonstrated and agrees well with the theoretical predictions. We show that the bending angle of the SHG beam can be tailored by varying either the wavelength of FW or the phase gradient. Furthermore, we show that concentrically arranged CSRRs that possess a particular phase shift on each concentric ring can act as a flat nonlinear metalens to focus SHG beam. We hope the complete phase control over the nonlinear emission presented here can be extended to construct three-dimensional nonlinear phase-gradient metamaterials due to the relatively high transmittance through the CSRRs at both fundamental and SHG wavelengths, and can be exploited in the applications, such as nonlinear holograms, data storages, and the coherent generation and manipulation of nonlinear signals in integrated nonlinear photonic circuits.

Funding

National Key R&D Program of China (Grant No. 2017YFA0303700), National Nature Science Foundation of China (NSFC) (11674168, 11474215 and 11621091), Nanjing University Innovation and Creative Program for PhD candidate (2016015).

References and links

1. N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014). [PubMed]  

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

3. 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]  

4. S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012). [PubMed]  

5. 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]  

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

7. F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012). [PubMed]  

8. N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012). [PubMed]  

9. J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013). [PubMed]  

10. Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101(4), 043903 (2008). [PubMed]  

11. 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]  

12. X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013). [PubMed]  

13. N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011). [PubMed]  

14. N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9, 180–184 (2015).

15. X. Yang, C. Zhang, M. Wan, Z. Chen, and Z. Wang, “Engineered second-harmonic diffraction from highly transmissive metasurfaces composed of complementary split-ring resonators,” Opt. Lett. 41(13), 2938–2941 (2016). [PubMed]  

16. S. Keren-Zur, O. Avayu, L. Michaeli, and T. Ellenbogen, “Nonlinear beam shaping with plasmonic metasurfaces,” ACS Photonics 3, 117–123 (2016).

17. O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015). [PubMed]  

18. G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14(6), 607–612 (2015). [PubMed]  

19. W. Ye, F. Zeuner, X. Li, B. Reineke, S. He, C. W. Qiu, J. Liu, Y. Wang, S. Zhang, and T. Zentgraf, “Spin and wavelength multiplexed nonlinear metasurface holography,” Nat. Commun. 7, 11930 (2016). [PubMed]  

20. E. Almeida, G. Shalem, and Y. Prior, “Subwavelength nonlinear phase control and anomalous phase matching in plasmonic metasurfaces,” Nat. Commun. 7, 10367 (2016). [PubMed]  

21. E. Almeida, O. Bitton, and Y. Prior, “Nonlinear metamaterials for holography,” Nat. Commun. 7, 12533 (2016). [PubMed]  

22. C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Second-harmonic generation in metallic nanoparticles: Clarification of the role of the surface,” Phys. Rev. B 86, 115451 (2012).

23. N. Feth, S. Linden, M. W. Klein, M. Decker, F. B. P. Niesler, Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, J. V. Moloney, and M. Wegener, “Second-harmonic generation from complementary split-ring resonators,” Opt. Lett. 33(17), 1975–1977 (2008). [PubMed]  

24. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370 (1972).

25. C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85, 201403 (2012).

References

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  1. N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
    [PubMed]
  2. A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013).
    [PubMed]
  3. 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]
  4. S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
    [PubMed]
  5. 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]
  6. D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
    [PubMed]
  7. F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
    [PubMed]
  8. N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
    [PubMed]
  9. J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
    [PubMed]
  10. Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
    [PubMed]
  11. 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]
  12. X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
    [PubMed]
  13. N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011).
    [PubMed]
  14. N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9, 180–184 (2015).
  15. X. Yang, C. Zhang, M. Wan, Z. Chen, and Z. Wang, “Engineered second-harmonic diffraction from highly transmissive metasurfaces composed of complementary split-ring resonators,” Opt. Lett. 41(13), 2938–2941 (2016).
    [PubMed]
  16. S. Keren-Zur, O. Avayu, L. Michaeli, and T. Ellenbogen, “Nonlinear beam shaping with plasmonic metasurfaces,” ACS Photonics 3, 117–123 (2016).
  17. O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
    [PubMed]
  18. G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14(6), 607–612 (2015).
    [PubMed]
  19. W. Ye, F. Zeuner, X. Li, B. Reineke, S. He, C. W. Qiu, J. Liu, Y. Wang, S. Zhang, and T. Zentgraf, “Spin and wavelength multiplexed nonlinear metasurface holography,” Nat. Commun. 7, 11930 (2016).
    [PubMed]
  20. E. Almeida, G. Shalem, and Y. Prior, “Subwavelength nonlinear phase control and anomalous phase matching in plasmonic metasurfaces,” Nat. Commun. 7, 10367 (2016).
    [PubMed]
  21. E. Almeida, O. Bitton, and Y. Prior, “Nonlinear metamaterials for holography,” Nat. Commun. 7, 12533 (2016).
    [PubMed]
  22. C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Second-harmonic generation in metallic nanoparticles: Clarification of the role of the surface,” Phys. Rev. B 86, 115451 (2012).
  23. N. Feth, S. Linden, M. W. Klein, M. Decker, F. B. P. Niesler, Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, J. V. Moloney, and M. Wegener, “Second-harmonic generation from complementary split-ring resonators,” Opt. Lett. 33(17), 1975–1977 (2008).
    [PubMed]
  24. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370 (1972).
  25. C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85, 201403 (2012).

2016 (5)

X. Yang, C. Zhang, M. Wan, Z. Chen, and Z. Wang, “Engineered second-harmonic diffraction from highly transmissive metasurfaces composed of complementary split-ring resonators,” Opt. Lett. 41(13), 2938–2941 (2016).
[PubMed]

S. Keren-Zur, O. Avayu, L. Michaeli, and T. Ellenbogen, “Nonlinear beam shaping with plasmonic metasurfaces,” ACS Photonics 3, 117–123 (2016).

W. Ye, F. Zeuner, X. Li, B. Reineke, S. He, C. W. Qiu, J. Liu, Y. Wang, S. Zhang, and T. Zentgraf, “Spin and wavelength multiplexed nonlinear metasurface holography,” Nat. Commun. 7, 11930 (2016).
[PubMed]

E. Almeida, G. Shalem, and Y. Prior, “Subwavelength nonlinear phase control and anomalous phase matching in plasmonic metasurfaces,” Nat. Commun. 7, 10367 (2016).
[PubMed]

E. Almeida, O. Bitton, and Y. Prior, “Nonlinear metamaterials for holography,” Nat. Commun. 7, 12533 (2016).
[PubMed]

2015 (3)

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9, 180–184 (2015).

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[PubMed]

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14(6), 607–612 (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]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[PubMed]

2013 (3)

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

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
[PubMed]

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[PubMed]

2012 (6)

S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[PubMed]

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]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[PubMed]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[PubMed]

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85, 201403 (2012).

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Second-harmonic generation in metallic nanoparticles: Clarification of the role of the surface,” Phys. Rev. B 86, 115451 (2012).

2011 (2)

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]

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011).
[PubMed]

2008 (2)

1972 (1)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370 (1972).

Aieta, F.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[PubMed]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[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]

Almeida, E.

E. Almeida, G. Shalem, and Y. Prior, “Subwavelength nonlinear phase control and anomalous phase matching in plasmonic metasurfaces,” Nat. Commun. 7, 10367 (2016).
[PubMed]

E. Almeida, O. Bitton, and Y. Prior, “Nonlinear metamaterials for holography,” Nat. Commun. 7, 12533 (2016).
[PubMed]

Antoniou, N.

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
[PubMed]

Avayu, O.

S. Keren-Zur, O. Avayu, L. Michaeli, and T. Ellenbogen, “Nonlinear beam shaping with plasmonic metasurfaces,” ACS Photonics 3, 117–123 (2016).

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]

Benz, A.

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[PubMed]

Bitton, O.

E. Almeida, O. Bitton, and Y. Prior, “Nonlinear metamaterials for holography,” Nat. Commun. 7, 12533 (2016).
[PubMed]

Blanchard, R.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[PubMed]

Boltasseva, A.

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

Brener, I.

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[PubMed]

Bretner, I.

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011).
[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]

Campione, S.

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[PubMed]

Capasso, F.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[PubMed]

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
[PubMed]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[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]

Cheah, K. W.

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14(6), 607–612 (2015).
[PubMed]

Chen, S.

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14(6), 607–612 (2015).
[PubMed]

Chen, W. T.

S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[PubMed]

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).
[PubMed]

Chen, Z.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370 (1972).

Ciracì, C.

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85, 201403 (2012).

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Second-harmonic generation in metallic nanoparticles: Clarification of the role of the surface,” Phys. Rev. B 86, 115451 (2012).

Decker, M.

Ellenbogen, T.

S. Keren-Zur, O. Avayu, L. Michaeli, and T. Ellenbogen, “Nonlinear beam shaping with plasmonic metasurfaces,” ACS Photonics 3, 117–123 (2016).

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9, 180–184 (2015).

Fan, P.

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

Feth, N.

Gaburro, Z.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[PubMed]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[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]

Genevet, P.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[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]

Gorodetski, Y.

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011).
[PubMed]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
[PubMed]

Guo, G. Y.

S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[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]

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011).
[PubMed]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
[PubMed]

He, Q.

S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[PubMed]

He, S.

W. Ye, F. Zeuner, X. Li, B. Reineke, S. He, C. W. Qiu, J. Liu, Y. Wang, S. Zhang, and T. Zentgraf, “Spin and wavelength multiplexed nonlinear metasurface holography,” Nat. Commun. 7, 11930 (2016).
[PubMed]

Hendler, N.

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9, 180–184 (2015).

Hoyer, W.

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]

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]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370 (1972).

Juan, T. K.

S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[PubMed]

Kadlec, E. A.

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[PubMed]

Kats, M. A.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[PubMed]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[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]

Keren-Zur, S.

S. Keren-Zur, O. Avayu, L. Michaeli, and T. Ellenbogen, “Nonlinear beam shaping with plasmonic metasurfaces,” ACS Photonics 3, 117–123 (2016).

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9, 180–184 (2015).

Kildishev, A. V.

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

Klein, M. W.

Kleiner, V.

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011).
[PubMed]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
[PubMed]

Klem, J. F.

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[PubMed]

Koch, S. W.

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]

Kung, W. T.

S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[PubMed]

Li, G.

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14(6), 607–612 (2015).
[PubMed]

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, X.

W. Ye, F. Zeuner, X. Li, B. Reineke, S. He, C. W. Qiu, J. Liu, Y. Wang, S. Zhang, and T. Zentgraf, “Spin and wavelength multiplexed nonlinear metasurface holography,” Nat. Commun. 7, 11930 (2016).
[PubMed]

Liao, C. Y.

S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[PubMed]

Lin, D.

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

Lin, J.

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
[PubMed]

Linden, S.

Liu, J.

W. Ye, F. Zeuner, X. Li, B. Reineke, S. He, C. W. Qiu, J. Liu, Y. Wang, S. Zhang, and T. Zentgraf, “Spin and wavelength multiplexed nonlinear metasurface holography,” Nat. Commun. 7, 11930 (2016).
[PubMed]

N. Feth, S. Linden, M. W. Klein, M. Decker, F. B. P. Niesler, Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, J. V. Moloney, and M. Wegener, “Second-harmonic generation from complementary split-ring resonators,” Opt. Lett. 33(17), 1975–1977 (2008).
[PubMed]

Liu, S.

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[PubMed]

Luk, T. S.

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[PubMed]

Michaeli, L.

S. Keren-Zur, O. Avayu, L. Michaeli, and T. Ellenbogen, “Nonlinear beam shaping with plasmonic metasurfaces,” ACS Photonics 3, 117–123 (2016).

Moitra, 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]

Moloney, J. V.

Mueller, J. P. B.

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
[PubMed]

Mühlenbernd, H.

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]

Niesler, F. B. P.

Niv, A.

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
[PubMed]

Pholchai, N.

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14(6), 607–612 (2015).
[PubMed]

Poutrina, E.

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Second-harmonic generation in metallic nanoparticles: Clarification of the role of the surface,” Phys. Rev. B 86, 115451 (2012).

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85, 201403 (2012).

Prior, Y.

E. Almeida, O. Bitton, and Y. Prior, “Nonlinear metamaterials for holography,” Nat. Commun. 7, 12533 (2016).
[PubMed]

E. Almeida, G. Shalem, and Y. Prior, “Subwavelength nonlinear phase control and anomalous phase matching in plasmonic metasurfaces,” Nat. Commun. 7, 10367 (2016).
[PubMed]

Pun, E. Y. B.

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14(6), 607–612 (2015).
[PubMed]

Qiu, C. W.

W. Ye, F. Zeuner, X. Li, B. Reineke, S. He, C. W. Qiu, J. Liu, Y. Wang, S. Zhang, and T. Zentgraf, “Spin and wavelength multiplexed nonlinear metasurface holography,” Nat. Commun. 7, 11930 (2016).
[PubMed]

Ravikumar, A. P.

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[PubMed]

Reineke, B.

W. Ye, F. Zeuner, X. Li, B. Reineke, S. He, C. W. Qiu, J. Liu, Y. Wang, S. Zhang, and T. Zentgraf, “Spin and wavelength multiplexed nonlinear metasurface holography,” Nat. Commun. 7, 11930 (2016).
[PubMed]

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14(6), 607–612 (2015).
[PubMed]

Rho, J.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[PubMed]

Scalora, M.

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Second-harmonic generation in metallic nanoparticles: Clarification of the role of the surface,” Phys. Rev. B 86, 115451 (2012).

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85, 201403 (2012).

Segal, N.

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9, 180–184 (2015).

Shalaev, V. M.

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

Shalem, G.

E. Almeida, G. Shalem, and Y. Prior, “Subwavelength nonlinear phase control and anomalous phase matching in plasmonic metasurfaces,” Nat. Commun. 7, 10367 (2016).
[PubMed]

Shaner, E. A.

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[PubMed]

Shitrit, N.

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011).
[PubMed]

Sinclair, M. B.

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[PubMed]

Smith, D. R.

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Second-harmonic generation in metallic nanoparticles: Clarification of the role of the surface,” Phys. Rev. B 86, 115451 (2012).

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85, 201403 (2012).

Sun, S.

S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[PubMed]

Tan, Q.

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]

Tetienne, J. P.

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]

Tsai, D. P.

S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[PubMed]

Valentine, J.

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]

Wan, M.

Wang, C. M.

S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[PubMed]

Wang, Q.

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
[PubMed]

Wang, W.

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]

Wang, Y.

W. Ye, F. Zeuner, X. Li, B. Reineke, S. He, C. W. Qiu, J. Liu, Y. Wang, S. Zhang, and T. Zentgraf, “Spin and wavelength multiplexed nonlinear metasurface holography,” Nat. Commun. 7, 11930 (2016).
[PubMed]

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[PubMed]

Wang, Z.

Wegener, M.

Wolf, O.

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[PubMed]

Wong, P. W. H.

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14(6), 607–612 (2015).
[PubMed]

Xiao, S.

S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[PubMed]

Yang, K. Y.

S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[PubMed]

Yang, X.

Yang, Y.

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]

Ye, W.

W. Ye, F. Zeuner, X. Li, B. Reineke, S. He, C. W. Qiu, J. Liu, Y. Wang, S. Zhang, and T. Zentgraf, “Spin and wavelength multiplexed nonlinear metasurface holography,” Nat. Commun. 7, 11930 (2016).
[PubMed]

Ye, Z.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[PubMed]

Yin, X.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[PubMed]

Yu, N.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[PubMed]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[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]

Yuan, G.

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
[PubMed]

Yuan, X. C.

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
[PubMed]

Zeng, Y.

Zentgraf, T.

W. Ye, F. Zeuner, X. Li, B. Reineke, S. He, C. W. Qiu, J. Liu, Y. Wang, S. Zhang, and T. Zentgraf, “Spin and wavelength multiplexed nonlinear metasurface holography,” Nat. Commun. 7, 11930 (2016).
[PubMed]

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14(6), 607–612 (2015).
[PubMed]

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]

Zeuner, F.

W. Ye, F. Zeuner, X. Li, B. Reineke, S. He, C. W. Qiu, J. Liu, Y. Wang, S. Zhang, and T. Zentgraf, “Spin and wavelength multiplexed nonlinear metasurface holography,” Nat. Commun. 7, 11930 (2016).
[PubMed]

Zhang, C.

Zhang, S.

W. Ye, F. Zeuner, X. Li, B. Reineke, S. He, C. W. Qiu, J. Liu, Y. Wang, S. Zhang, and T. Zentgraf, “Spin and wavelength multiplexed nonlinear metasurface holography,” Nat. Commun. 7, 11930 (2016).
[PubMed]

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14(6), 607–612 (2015).
[PubMed]

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]

Zhang, X.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[PubMed]

Zhou, L.

S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[PubMed]

ACS Photonics (1)

S. Keren-Zur, O. Avayu, L. Michaeli, and T. Ellenbogen, “Nonlinear beam shaping with plasmonic metasurfaces,” ACS Photonics 3, 117–123 (2016).

Nano Lett. (6)

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011).
[PubMed]

S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[PubMed]

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]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[PubMed]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[PubMed]

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]

Nat. Commun. (4)

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[PubMed]

W. Ye, F. Zeuner, X. Li, B. Reineke, S. He, C. W. Qiu, J. Liu, Y. Wang, S. Zhang, and T. Zentgraf, “Spin and wavelength multiplexed nonlinear metasurface holography,” Nat. Commun. 7, 11930 (2016).
[PubMed]

E. Almeida, G. Shalem, and Y. Prior, “Subwavelength nonlinear phase control and anomalous phase matching in plasmonic metasurfaces,” Nat. Commun. 7, 10367 (2016).
[PubMed]

E. Almeida, O. Bitton, and Y. Prior, “Nonlinear metamaterials for holography,” Nat. Commun. 7, 12533 (2016).
[PubMed]

Nat. Mater. (2)

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14(6), 607–612 (2015).
[PubMed]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[PubMed]

Nat. Photonics (1)

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9, 180–184 (2015).

Opt. Lett. (2)

Phys. Rev. B (3)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370 (1972).

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85, 201403 (2012).

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Second-harmonic generation in metallic nanoparticles: Clarification of the role of the surface,” Phys. Rev. B 86, 115451 (2012).

Phys. Rev. Lett. (1)

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
[PubMed]

Science (5)

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

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

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[PubMed]

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
[PubMed]

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Figures (4)

Fig. 1
Fig. 1 (a) Schematic of a uniform CSRR array with a periodicity of a = 400 nm. The height of the CSRR is t = 20 nm. The width of the central metal patch is g = 50 nm. Normally incident light propagates along the z-axis and is polarized along the y-axis. (b) Calculated linear transmission spectra of the CSRR arrays with a fixed arm width of w = 75 nm but different arm lengths. For clarity, each curve is shifted vertically by a constant of 0.7 relative to the previous one. The red and blue dashed lines indicate the fundamental and SHG wavelengths, respectively. (c) The normalized SHG conversion efficiency from the CSRRs with w = 75 nm and l = 160 nm. (d) The nonlinear phase shift and amplitude in the array of CSRRs with w = 75 nm but different arm lengths. (e) and (f) Calculated SH phase-shift and amplitude for CSRRs with different l and w.
Fig. 2
Fig. 2 (a) and (b): Schematic view of eight-resonator super-unit cells with a phase gradient of π/4. One super-unit is created from the CSRRs in the path-1, the other is from the CSRRs in the path-2. (c) and (d) Far-field SHG intensity from the metasurfaces consisting of the super-unit cells presented in (a) and (b).
Fig. 3
Fig. 3 (a) Schematic illustration of the experimental setup, where the CDD-camera records either Fourier images or real images of the CSRR-based samples. (b)-(d) SEM images of the nonlinear metasurfaces consisting of one-CSRR unit cell with Δφ = 0, eight-CSRR super-unit cell with Δφ = π/4, and six-CSRR super-unit cell with Δφ = π/3, respectively. Scale bars represent 500 nm. (e)-(g) Measured k-space images of SHG from the samples shown in (b)-(d), respectively. The uniform array in (e) is pumped by FW with a wavelength of 1400 nm. The phase-modulated arrays in (f) and (g) are pumped by FWs with three different wavelengths of 1300nm, 1400 nm, and 1500 nm.
Fig. 4
Fig. 4 (a) SEM image of a CSRR-based metasurface acting as a nonlinear metalens with a desired focal length f = 40 μm. The scale bar is 5 μm. Dashed line represents a concentric ring with a radius of r on which all the CSRRs have the same phase shift. (b) and (c) Calculated and measured SHG focusing effect of the metalens upon illumination by normally incident FW (λFW = 1400 nm) with its polarization along the CSRR arm, respectively. (d) and (e) Images of the normalized SHG (λSHG = 700 nm) recorded at z = 5 μm and z = 40 μm cross-section planes, respectively.

Equations (2)

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I = A 2 | l = 1 N e i ( l 1 ) β [ s = 1 8 e i ( s 1 ) α e i ( s 1 ) Δ φ ] | 2 , = A 2 sin 2 [ 4 ( α + Δ φ ) ] sin 2 [ ( α + Δ φ ) / 2 ] sin 2 ( N β / 2 ) sin 2 ( β / 2 )
I = N 2 A 2 sin 2 [ ( m + 1 ) π ] sin 2 [ ( m + 1 ) π / 8 ] .

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