Abstract

Electro-optic switching of refraction is experimentally demonstrated in a phase-discontinuity complementary metasurface twisted nematic cell. The phase-discontinuity complementary metasurface is fabricated by focused-ion-beam milling, and a twisted nematic cell is constructed with complementary V-shape slot antenna metasurface. By application of an external voltage, switching is achieved between ordinary refraction and extraordinary refraction satisfying the generalized Snell’s law. It has a strong implication for applications in spatial light modulation and wavelength division multiplexer/demultiplexer in a near-IR spectral range.

© 2014 Optical Society of America

1. Introduction

By employing V-shape antennas in a metasurface, it has been shown that an extraordinary refraction takes place satisfying the generalized Snell’s law, where a gradient of optical phase residing at the V-shape antenna metasurface (VMS) has to be taken into account [13]. The metasurface is a linear array of eight V-shape antennas possessing different folding angles with the symmetry axis along 45° with respect to the array direction. According to the analysis of dipolar scattering at V-shape antennas in terms of symmetric and anti-symmetric induced currents, the extraordinary refraction of a linearly polarized light with polarization angle ϕent undergoes a polarization rotation of 90° − ϕent while no polarization rotation takes place for the ordinary refraction [4, 5].

On the other hand, by adopting a twisted nematic liquid crystal (TNLC) cell structure with metasurface as one of windows of TNLC cell, optical and electric controls of transmission or reflection resonances of metamaterial have been demonstrated for a normally incident light [68]. Considering that VMS incurs both polarization rotation and extraordinary refraction while TNLC allows for an electro-optic control of polarization rotation, an optical device can be envisioned where the refraction can be electrically controlled by combining VMS and TNLC cell structure, namely, by constructing a VMS-TNLC cell. Differently from the TNLC-metamaterials structures introduced in [68], VMS-TNLC cell permits a refraction control which has potential applications to broadband spatial light modulation and wavelength division multiplexer/demultiplexer.

For a given nano-sized pattern of metasurface, either positive or negative metasurface can be prepared [9]. Metallic nanoantennas patterned on dielectric substrate are examples of positive metasurface, while Babinet-inverted complementary antennas or slot antennas patterned on thin metallic film are examples of negative metasurface. Importantly, in case of VMS, both positive and negative metasurfaces give rise to the same extraordinary refraction, simply because the angular distribution of radiation of a slot antenna is identical to that of a dipole antenna [10,11].

We point out two important advantages of complementary V-shape antenna metasurface (cVMS) over VMS in an electro-optic application. First, a large area of metal surface in the cVMS can serve as an electrode keeping each V-shape slot antenna spatially separated from others. The spatial separation of V-shape antenna is a key feature in achieving a phase discontinuity by metasurface, which cannot be configured in VMS positive metasurface when an electro-optic application is sought in VMS meta-structure [7,12]. Second, a large area of metal surface in the cVMS blocks unscattered incident light enhancing beam deflection efficiency significantly when compared with VMS [13].

In this work, we demonstrate an electro-optic control of refraction by employing a complementary V-shape antenna metasurface twisted nematic liquid crystal (cVMS-TNLC) cell. Section 2 presents cVMS fabrication by focused ion beam milling and finite-difference time-domain (FDTD) simulation and measurements of optical characteristics. In Sec.3, we address efficiencies of beam deflection and polarization conversion in cVMS versus VMS from FDTD simulation results. Section 4 describes a twisted nematic cell construction with cVMS as one of cell windows. Polarization states of ordinary and extraordinary refracted beams are experimentally examined and theoretically analyzed. Lastly, in sec.5 we demonstrate an electro-optic switching of refraction in cVMS-TNLC cell.

2. cVMS fabrication and its optical characteristics

We adopt the design of V-shape antenna pattern introduced in [1]. A linear array of eight V-shape apertures is repeated with the lattice constant Γ of 2400nm. Focused ion beam milling is utilized to fabricate cVMS on e-beam evaporated 30nm-thick Au film on top of fused silica substrate with adhesion layer of 3nm thick titanium. Figure 1(a) shows SEM image of cVMS fabricated by focused ion beam milling. The cVMS is designed to provide a phase discontinuity of dΦdx=2πΓ=2.618rad/μm at the metasurface.

 figure: Fig. 1

Fig. 1 (a) SEM image of cVMS fabricated by focused ion beam milling. (b) A row of cVMS is shown with the superlattice periodicity of Γ = 2400nm. Schematics of ordinary/extraordinary reflection and refraction with the reflection angle θr and refraction angle θt are shown in (c) the normal incidence and (d) an incidence angle θi for s-polarized incident beam. In both (c) and (d), θr = θt. See text.

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It has been reported that the extraordinary refraction can be described in terms of both phase discontinuity incorporating the generalized Snell’s law and a blazed grating diffraction [14]. In V-shape antenna structure, however, the extraordinary refraction always incurs polarization conversion, which can be achieved by a subwavelength-scale design of each V-shape antenna separated by Γ/8. Therefore, it is necessary to have a full consideration of each V-shape antenna for the polarization conversion analysis in scattered fields from VMS, and a description of VMS structure in terms of the blazed grating of superlattices with periodicity Γ does not provide a proper analysis framework.

In Figs. 1(c) and 1(d), the angles of reflection θr and refraction θt are related to the incidence angle θi by the generalized Snell’s law, sinθi+1k0dΦdx=sinθt=sinθr [1]. We note that θt = θr for any incidence angle θi. For a given incidence angle, there occurs extraordinary refraction from dΦdx and an additional refraction takes place in passing through the interface of metasurface and fused quartz substrate. At the interface of fused quartz and air at the bottom of the sample, another refraction takes place simply shifting the lateral position of the extraordinary refraction. As a result, the extraordinary reflection angle θr is equal to the extraordinary refraction angle θt, both being determined by dΦdx at the metasurface.

FDTD numerical simulation calculation was carried out to identify the spectral region where amplitude and phase of scattered light in cross-polarization from each V-shape slot antenna of cVMS behave such as to provide a prescribed phase discontinuity of dΦdx=2πΓ, which is plotted in Fig. 2.

 figure: Fig. 2

Fig. 2 2-dimensional plot of (a) normalized amplitude and (b) phase of scattered light in cross-polarization is shown as a function of wavelength and x-position. For a series of wavelengths, (c) normalized amplitude and (d) phase of scattered light in cross-polarization are plotted for each V-shape slot antenna from number 1 to number 8.

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We employed the commercial software FDTD solution Lumerical [15]. One superlattice of V shape slot antennas array of Au was adopted as a unit cell in the simulation region, which was positioned horizontally in −0.5Γ ≤ x ≤ +0.5Γ and vertically in −30nmz ≤ 0nm. A minimum mesh step size of 0.25nm was defined, and the periodic boundary conditions are adopted in the x- and y-directions and perfectly matched layers boundary conditions are adopted in the z-direction.

A far-field characteristics of transmitted light from cVMS is obtained from 2D Z-normal frequency domain power monitor located above z = +3μm. The incident field is x-polarized, and the amplitude and phase of y-polarized scattered field from cVMS are simulated. See the left inset in Fig. 2(c). For an incident light with the polarization angle ϕent, the polarization direction of scattered light is along ϕexit=90° − ϕent. See the right inset in Fig. 2(c). The relation between ϕent and ϕexit stems from a symmetry property of V-shape slot antennas. In other words, V-shape of each slot antenna possesses a reflection symmetry with the mirror plane along 45° axis (equation of the mirror plane, xy = 0, ∀z). The induced current on each V-shape antenna is a sum of symmetric and antisymmetric currents with respect to the mirror plane. Therefore, amplitude and phase of the scattered field along ϕexit(=90°−ϕent) for an incident light along with polarization angle ϕent are the same as those of the scattered field along 90°-(90°−ϕent)=ϕent for an incident light with polarization angle 90°−ϕent [4]. As a particular example, for y-polarized incident light, we obtain the same amplitude and phase of x-polarized scattered field from cVMS as those plotted in Fig. 2.

In order to further confirm the occurrence of an extraordinary refraction, plane-wave beam propagation is simulated by FDTD. By placing 2D Y-normal frequency domain power monitor at y = 150nm, the evolution of both co- and cross-polarized scattered fields is calculated upon a 900–1700nm plane wave source impinging normally onto cVMS. See Fig. 3. For a normally incident y-polarized light with λ = 1100nm, the scattered fields with y-polarization (ordinary refraction/reflection) and x-polarization (extraordinary refraction/reflection) are shown in Figs. 3(a) and 3 (b), respectively. The black dashed lines in Figs. 3(b) and 3(d) correspond to the wave fronts of refracted and reflected lights from cVMS. We find θr = θt = −27.3°. The simulation calculation result for λ = 1309nm is shown in Figs. 3(c) and 3(d), and we find θr = θt = −33.1°.

 figure: Fig. 3

Fig. 3 Plane-wave beam propagation is simulated for a normally incident y-polarized light. (a) y-component of electric field is shown corresponding to ordinary refraction, and (b) x-component of electric field is shown corresponding to extraordinary refraction with λ = 1100nm. (c) and (d) are simulation calculation results for λ = 1309nm.

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Prior to constructing a cVMS-TNLC cell, experimental measurements are carried out to find the extraordinary refraction and reflection in the fabricated cVMS sample. In Fig. 4 are plotted the measured refraction and reflection angles versus wavelength. Figure 4(a) shows an extraordinary refraction for the normal incidence in s-polarization, and Fig. 4(b) shows an extraordinary refraction for the incidence angle 15° in p-polarization. Figures 4(c) and 4(d) show extraordinary refraction and reflection for the incidence angle 60° in p-polarization, respectively. We note that the extraordinary refraction and reflection take place over a broad spectral range from 900 nm to 1500nm with deflection angles varying over 20°. The white lines are from a theoretical calculation, θt =θr=arcsin(sinθi − 2π/k0Γ). We find that there is a good agreement between experiment data and theoretical calculation.

 figure: Fig. 4

Fig. 4 Experimental measurements of extraordinary refraction and reflection angles versus wavelength are shown. (a) Refraction is shown for the normal incidence in s-polarization. (b) Refraction is shown for the incidence angle 15° in p-polarization. (c) Refraction is shown for the incidence angle 60° in p-polarization. (d) Reflection is shown for the incidence angle 60° in p-polarization. The white lines are from a theoretical calculation.

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3. Efficiencies of beam deflection and polarization conversion

In an optical device with applications in spatial light modulation and multiplexer/demultiplex, the beam deflection efficiency is a key parameter, and we calculate transmission/reflection efficiencies by FDTD numerical simulation. In order to obtain far-field transmitted and reflected fields, two 2D Z-normal frequency domain power monitors are placed above (z = +3μm) and below (z = −3μm) cVMS.

In Fig. 5 are plotted the efficiencies of beam deflection for y-polarized incident light. Figure 5(a) shows the beam deflection efficiency of reflection, where brown and purple curves correspond to the Au film and green and blue curves correspond to cVMS in co- and cross-polarizations, respectively. Figure 5(b) shows the beam deflection efficiency of transmission, where gray and pink curves correspond to the Au film and black and red curves correspond to cVMS sample in co- and cross-polarizations, respectively. Deflection efficiency is defined as |Ex(a)/Einc|2=Ix(a)/Iinc with (a) = R or T for reflection and transmission. At λ = 1100nm (extraordinary refraction angle −27.28°), the cross-polarization beam deflection efficiencies are found to be IxR/Iinc=15.1% for reflection and IxT/Iinc=14.9% for transmission. As a comparison we find the co-polarization beam deflection efficiencies IyR/Iinc=63.4% for reflection and IyT/Iinc=22.5% for transmission.

 figure: Fig. 5

Fig. 5 Deflection efficiencies are plotted as a function of wavelength for (a) reflection and (b) transmission.

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Negative metasurface is advantageous over positive metasurface by reducing a background noise in the planar optics, since the negative metasurface blocks unscattered co-polarized transmitting light [13, 16]. We compare the polarization conversion efficiency of negative metasur-face cVMS and positive metasurface VMS. Figure 6 shows polar-plots of the transmitted light intensities for cVMS and VMS at λ = 1100nm.

 figure: Fig. 6

Fig. 6 (a) Schematics of beam deflection is shown for y-polarized incident light at λ = 1100nm. (b)&(c) and (d)&(e) correspond to the polar plots of the transmitted light intensities in negative metasurface cVMS and positive metasurface, respectively.

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Figures 6(b) and 6(c) and Figs. 6(d) and 6(e) correspond to the polar plots of the transmitted light intensities in negative metasurface cVMS and positive metasurface VMS, respectively. Comparison of Figs. 6(c) and 6(e) shows that the co-polarized transmission is lower in cVMS than in VMS. We find that polarization conversion efficiency IxT/IyT=69% for cVMS and IxT/IyT=18% for VMS. Importantly, the ratio of extraordinary refraction intensity to ordinary refraction intensity is almost 4 times larger in cVMS than in VMS, which indicates that the complementary design is more useful when a refraction switching device is designed.

4. cVMS-TNLC cell construction and polarization state analysis

Figure 7 shows schematics how an electro-optic control of polarization direction is achieved. TNLC cell of 12μm cell gap is formed with one alignment layer rubbed along y-direction on polyimide(SE-5291, Nissan Chemical Industries, Ltd.)-coated ITO substrate and the other alignment layer rubbed along x-direction on poly-vinyl-alcohol(PVA, Mw ≈ 205K, Aldrich)-coated cVMS substrate. By capillary-filling the TNLC cell gap with nematic, ZLI-2293(Merck) with ne=1.6313 and no=1.4990 at 589.3nm, ε = 14.0 and ε = 4.1 at 1.0kHz, possessing the clearing point 85°C, we obtain a cVMS-TNLC cell as shown in Fig. 7(a) [12].

 figure: Fig. 7

Fig. 7 Schematics of a cVMS-TNLC cell is shown with a y-polarized incident light, when (a) no external voltage is applied and (b) an ac voltage is applied. Linear polarization states are orthogonal for ordinary and extraordinary refractions.

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In the absence of an external voltage, when a y-polarized light is normally incident, the polarization direction is rotated by 90° in the TNLC, ending up as x-polarized on top of cVMS. Upon passing through the cVMS, both ordinary (o) and extraordinary (e) refractions take place. While ordinary (o) refraction with the refraction angle 0° is x-polarized, extraordinary (e) refraction with the refraction angle θr is y-polarized. As shown in Fig. 7(b), when an external voltage is applied, nematic liquid crystals align along the electric field direction, and no polarization rotation takes place, leading to a y-polarized light on top of the cVMS. Now upon passing through the cVMS, ordinary (o) refraction is y-polarized, while extraordinary (e) refraction is x-polarized. Noting that refraction angle θr is wavelength-dependent, we find that cVMS-TNLC structure can be employed for a broadband wavelength demultiplexer with the polarization direction controlled by an electric field.

Before we proceed further, we digress to describe the polarization state in a TNLC cell. As a linearly polarized beam propagates through TNLC cell before entering cVMS, we keep track of changes in the polarization state by employing the Jones matrix [17].

MTNLC=(cosΨsinΨsinΨcosΨ)(cosXiΔ2sinXXΨsinXXΨsinXXcosX+iΔ2sinXX)
where
X=Ψ2+(Δ2)2
Ψ is the total twist angle of the LC director, which is 90° in cVMS-TNLC structure, and the external voltage-dependent phase retardation is Δ(V) = 2π {ne(V) − no}d/λ with d the cell thickness.

We express the input and output polarization states as follows, as determined by the orientation angles of the polarizer transmission axes.

(VxVy)=(cosϕentsinϕent),(VxVy)=(cosϕexitsinϕexit).
The transmission intensity through cVMS-TNLC cell is
T=|V*McVMSMTNLCV|2
where McVMS is the Jones matrix of cVMS,
McVMS=(cos2βsin2βsin2βcos2β).
β is the angle between the mirror symmetry plane and xy plane, which is 45° in cVMS.

Figure 8 shows a photograph of experimental set-up with its schematics. Halogen lamp and near-IR laser diode are employed as light sources, and the beam was focused by an assembly of microscope objectives to have a 50 μm beam diameter on cVMS-TNLC sample. Detectors such as NIR-micro-spectrometer, InGaAs-based detector, and CCD are set on a rotational stage with angular precision 0.5°

 figure: Fig. 8

Fig. 8 (a) Photograph of experimental set-up is shown along with (b) schematics.

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We closely examine the polarization state of extraordinary refraction at λ = 1100nm (extraordinary refraction angle of −27.3°). See Fig. 9. When a linearly polarized light with polarization angle ϕent is incident on cVMS, the extraordinary refraction has a linear polarization with polarization angle 90° − ϕent.

 figure: Fig. 9

Fig. 9 (A) Schematics of a cVMS-TNLC cell is shown with an incident light with polarization angle ϕent. (B) Measurements and (C) theoretical calculations of polarization direction of extraordinary refraction light with ac voltage of (a) 0V, (b) 2.5V, (c) 3.5V, and (d) 4.5V for ϕent=90° are shown.

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First, we examine the external voltage dependence of polarization state. With the incident light polarization fixed as ϕent = 90°, we analyze the polarization states of extraordinary refraction for a series of ac voltage across cVMS-TNLC cell. Figure 9(B) shows the experimental measurements with ac voltage of (a) 0V, (b) 2.5V, (c) 3.5V, and (d) 4.5V. In Fig. 9(B) we find that the extraordinary refraction light is well linearly polarized with the linear polarization direction depending on the applied ac voltage. As comparison, Fig. 9(C) shows the polarization state of the extraordinary refraction light obtained from Jones matrix calculus with the phase retardation of TNLC (a) Δ=Δmax=12, (b) Δ=4, (c) Δ=2, and (d) Δ=0. A full alignment of nematic liquid crystal is achieved at the ac voltage of 8.0V.

Second, we examine how the electric control of polarizations fares when the incident polarization angle ϕent is varied. Polarization states of both ordinary and extraordinary refractions are analyzed in the presence and absence of an external voltage for the incident polarization angle ϕent. In Fig. 10(A) are shown the experimental measurement for the incident polarization angles (a) ϕent=0°, (b) ϕent=30°, (c) ϕent=45°, and (d) ϕent=60° (e) ϕent=90°. Black and red curves correspond to ordinary refraction with ac voltage off and on (V=10V), respectively, and blue and green curves correspond to extraordinary refraction with ac voltage off and on (V=10V), respectively. As comparison, Fig. 10(B) shows the polarization states obtained from Jones matrix calculus. When the external voltage is higher than 8V, the polarization angles of ordinary and extraordinary refractions are ϕent and 90° − ϕent, respectively. On the other hand, in the absence of an external voltage, the polarization angles of ordinary and extraordinary refractions are 90° − ϕent and ϕent, respectively.

 figure: Fig. 10

Fig. 10 (A) Measurements and (B) theoretical calculations of polarization direction of refraction light for the incident polarization angles (a) ϕent=0°, (b) ϕent=30°, (c) ϕent=45°, and (d) ϕent=60° (e) ϕent=90° are shown.

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5. Electro-optic control of refraction in cVMS-TNLC cell

We study electro-optic control of refraction in cVMS-TNLC cell. Figure 11 shows schematics of an electro-optic switching of refraction for a normal incident y-polarized light. The transmitting axis of analyzer is set along x-axis. The analyzer is polarization-selective, and the transmission is allowed for only ordinary refraction in the absence of an external voltage, while only extraordinary refraction goes through the analyzer in the presence of an external voltage.

 figure: Fig. 11

Fig. 11 Schematics of an electro-optic switching of refraction is shown with a y-polarized incident light, when (a) no external voltage is applied and (b) an ac voltage is applied.

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With a combination of cVMS-TNLC cell and analyzer as optical device for y-polarized incident beam, the refraction of the x-polarized exiting beam is electro-optically switched between the refraction angle θt = 0 and θt ≠ 0 in the absence and presence of an external voltage. By attaching a thin-film polarizer sheet on the back side of fused quartz substrate, cVMS-TNLC cell can be easily rendered as a single electro-optic device for a broadband refraction switching device.

In Fig. 12 is shown the experimental data of the voltage dependence of transmission intensities of ordinary refraction (black curve) and extraordinary refraction (red curve) in cVMS-TNLC cell with crossed polarizer configuration for a normal incident y-polarized light. Refraction switching starts to take place from V=2.5V, and a full switching is achieved at an external voltage higher than 8.0V. Measurement of switch-on and switch-off time showed a temporal behavior of refraction switching similar to that reported in [12].

 figure: Fig. 12

Fig. 12 Measurement of an electro-optic switching of refraction is shown in a y-polarized incident light. The light intensity is plotted as a function of an ac voltage.

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In summary, we experimentally demonstrated an electro-optic switching in a complementary V-shape metasurface twisted-nematic liquid crystal cell. Switching operation in the cVMS-TNLC cell provides a new photonic device architecture where spatial light modulation and wave division multiplexer/demultiplexer can be achieved in a broadband near-IR spectral range.

Acknowledgments

This work is supported by the Quantum Metamaterials Research Center Program ( Ministry of Science, ICT and Future Planning, National Research Foundation, Republic of Korea). The authors are grateful to Ji-Hyun Lee at the Daejeon Center of the Korea Basic Science Institute for a focused ion beam (Quanta 3D FEG) milling fabrication of samples.

References and links

1. 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, 333–337 (2011). [CrossRef]   [PubMed]  

2. X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012). [CrossRef]  

3. A. G. Smart, “Phase-shifting surfaces bend the rules of ray optics,” Phys. Today 64, 12 (2011). [CrossRef]  

4. N. Yu, P. Genevet, F. Aieta, M. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: Controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013). [CrossRef]  

5. F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702–1706 (2012). [CrossRef]   [PubMed]  

6. B. Kang, J. H. Woo, E. Choi, H.-H. Lee, E. S. Kim, J. Kim, T.-J. Hwang, Y.-S. Park, D. H. Kim, and J. W. Wu, “Optical switching of near infrared light transmission in metamaterial-liquid crystal cell structure,” Opt. Express 18, 16492–16498 (2010). [CrossRef]   [PubMed]  

7. O. Buchnev, J. Ou, M. Kaczmarek, N. Zheludev, and V. Fedotov, “Electro-optical control in a plasmonic metamaterial hybridised with a liquid-crystal cell,” Opt. Express 21, 1633–1638 (2013). [CrossRef]   [PubMed]  

8. M. Decker, C. Kremers, A. Minovich, I. Staude, A. E. Miroshnichenko, D. Chigrin, D. N. Neshev, C. Jagadish, and Y. S. Kivshar, “Electro-optical switching by liquid-crystal controlled metasurfaces,” Opt. Express 21, 8879–8885 (2013). [CrossRef]   [PubMed]  

9. J. Kim, Y. U. Lee, B. Kang, J. H. Woo, E. Y. Choi, E. S. Kim, M. Gwon, D.-W. Kim, and J. W. Wu, “Fabrication of polarization-dependent reflective metamaterial by focused ion beam milling,” Nanotechnology 24, 015306 (2013). [CrossRef]  

10. H. G. Booker, “Slot aerials and their relation to complementary wire aerials (Babinet’s principle),” J. Inst. Electr. Eng. Part IIIA: Radiolocation 93, 620–626 (1946).

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

12. Y. U. Lee, E. Y. Choi, J. H. Woo, E. S. Kim, and J. W. Wu, “Reflection resonance switching in metamaterial twisted nematics cell,” Opt. Express 21, 17492–17497 (2013). [CrossRef]   [PubMed]  

13. X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, babinet-inverted plasmonic metalenses,” Light-Sci. Appl. 2, e72 (2013). [CrossRef]  

14. S. Larouche and D. R. Smith, “Reconciliation of generalized refraction with diffraction theory,” Opt. Lett. 37, 2391–2393 (2012). [CrossRef]   [PubMed]  

15. See http://www.lumerical.com/

16. D. Hu, X. Wang, S. Feng, J. Ye, W. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1, 186–191 (2013). [CrossRef]  

17. P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley, 2010), Vol. 67.

References

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  1. 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, 333–337 (2011).
    [Crossref] [PubMed]
  2. X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
    [Crossref]
  3. A. G. Smart, “Phase-shifting surfaces bend the rules of ray optics,” Phys. Today 64, 12 (2011).
    [Crossref]
  4. N. Yu, P. Genevet, F. Aieta, M. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: Controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
    [Crossref]
  5. F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702–1706 (2012).
    [Crossref] [PubMed]
  6. B. Kang, J. H. Woo, E. Choi, H.-H. Lee, E. S. Kim, J. Kim, T.-J. Hwang, Y.-S. Park, D. H. Kim, and J. W. Wu, “Optical switching of near infrared light transmission in metamaterial-liquid crystal cell structure,” Opt. Express 18, 16492–16498 (2010).
    [Crossref] [PubMed]
  7. O. Buchnev, J. Ou, M. Kaczmarek, N. Zheludev, and V. Fedotov, “Electro-optical control in a plasmonic metamaterial hybridised with a liquid-crystal cell,” Opt. Express 21, 1633–1638 (2013).
    [Crossref] [PubMed]
  8. M. Decker, C. Kremers, A. Minovich, I. Staude, A. E. Miroshnichenko, D. Chigrin, D. N. Neshev, C. Jagadish, and Y. S. Kivshar, “Electro-optical switching by liquid-crystal controlled metasurfaces,” Opt. Express 21, 8879–8885 (2013).
    [Crossref] [PubMed]
  9. J. Kim, Y. U. Lee, B. Kang, J. H. Woo, E. Y. Choi, E. S. Kim, M. Gwon, D.-W. Kim, and J. W. Wu, “Fabrication of polarization-dependent reflective metamaterial by focused ion beam milling,” Nanotechnology 24, 015306 (2013).
    [Crossref]
  10. H. G. Booker, “Slot aerials and their relation to complementary wire aerials (Babinet’s principle),” J. Inst. Electr. Eng. Part IIIA: Radiolocation 93, 620–626 (1946).
  11. A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).
    [Crossref] [PubMed]
  12. Y. U. Lee, E. Y. Choi, J. H. Woo, E. S. Kim, and J. W. Wu, “Reflection resonance switching in metamaterial twisted nematics cell,” Opt. Express 21, 17492–17497 (2013).
    [Crossref] [PubMed]
  13. X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, babinet-inverted plasmonic metalenses,” Light-Sci. Appl. 2, e72 (2013).
    [Crossref]
  14. S. Larouche and D. R. Smith, “Reconciliation of generalized refraction with diffraction theory,” Opt. Lett. 37, 2391–2393 (2012).
    [Crossref] [PubMed]
  15. See http://www.lumerical.com/
  16. D. Hu, X. Wang, S. Feng, J. Ye, W. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1, 186–191 (2013).
    [Crossref]
  17. P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley, 2010), Vol. 67.

2013 (8)

N. Yu, P. Genevet, F. Aieta, M. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: Controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

O. Buchnev, J. Ou, M. Kaczmarek, N. Zheludev, and V. Fedotov, “Electro-optical control in a plasmonic metamaterial hybridised with a liquid-crystal cell,” Opt. Express 21, 1633–1638 (2013).
[Crossref] [PubMed]

M. Decker, C. Kremers, A. Minovich, I. Staude, A. E. Miroshnichenko, D. Chigrin, D. N. Neshev, C. Jagadish, and Y. S. Kivshar, “Electro-optical switching by liquid-crystal controlled metasurfaces,” Opt. Express 21, 8879–8885 (2013).
[Crossref] [PubMed]

J. Kim, Y. U. Lee, B. Kang, J. H. Woo, E. Y. Choi, E. S. Kim, M. Gwon, D.-W. Kim, and J. W. Wu, “Fabrication of polarization-dependent reflective metamaterial by focused ion beam milling,” Nanotechnology 24, 015306 (2013).
[Crossref]

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

Y. U. Lee, E. Y. Choi, J. H. Woo, E. S. Kim, and J. W. Wu, “Reflection resonance switching in metamaterial twisted nematics cell,” Opt. Express 21, 17492–17497 (2013).
[Crossref] [PubMed]

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, babinet-inverted plasmonic metalenses,” Light-Sci. Appl. 2, e72 (2013).
[Crossref]

D. Hu, X. Wang, S. Feng, J. Ye, W. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1, 186–191 (2013).
[Crossref]

2012 (3)

S. Larouche and D. R. Smith, “Reconciliation of generalized refraction with diffraction theory,” Opt. Lett. 37, 2391–2393 (2012).
[Crossref] [PubMed]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702–1706 (2012).
[Crossref] [PubMed]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

2011 (2)

A. G. Smart, “Phase-shifting surfaces bend the rules of ray optics,” Phys. Today 64, 12 (2011).
[Crossref]

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, 333–337 (2011).
[Crossref] [PubMed]

2010 (1)

1946 (1)

H. G. Booker, “Slot aerials and their relation to complementary wire aerials (Babinet’s principle),” J. Inst. Electr. Eng. Part IIIA: Radiolocation 93, 620–626 (1946).

Aieta, F.

N. Yu, P. Genevet, F. Aieta, M. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: Controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702–1706 (2012).
[Crossref] [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, 333–337 (2011).
[Crossref] [PubMed]

Aoust, G.

N. Yu, P. Genevet, F. Aieta, M. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: Controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

Blanchard, R.

N. Yu, P. Genevet, F. Aieta, M. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: Controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

Boltasseva, A.

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

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

Booker, H. G.

H. G. Booker, “Slot aerials and their relation to complementary wire aerials (Babinet’s principle),” J. Inst. Electr. Eng. Part IIIA: Radiolocation 93, 620–626 (1946).

Buchnev, O.

Capasso, F.

N. Yu, P. Genevet, F. Aieta, M. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: Controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702–1706 (2012).
[Crossref] [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, 333–337 (2011).
[Crossref] [PubMed]

Chigrin, D.

Choi, E.

Choi, E. Y.

Y. U. Lee, E. Y. Choi, J. H. Woo, E. S. Kim, and J. W. Wu, “Reflection resonance switching in metamaterial twisted nematics cell,” Opt. Express 21, 17492–17497 (2013).
[Crossref] [PubMed]

J. Kim, Y. U. Lee, B. Kang, J. H. Woo, E. Y. Choi, E. S. Kim, M. Gwon, D.-W. Kim, and J. W. Wu, “Fabrication of polarization-dependent reflective metamaterial by focused ion beam milling,” Nanotechnology 24, 015306 (2013).
[Crossref]

Decker, M.

Emani, N. K.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

Fedotov, V.

Feng, S.

D. Hu, X. Wang, S. Feng, J. Ye, W. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1, 186–191 (2013).
[Crossref]

Gaburro, Z.

N. Yu, P. Genevet, F. Aieta, M. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: Controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702–1706 (2012).
[Crossref] [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, 333–337 (2011).
[Crossref] [PubMed]

Genevet, P.

N. Yu, P. Genevet, F. Aieta, M. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: Controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702–1706 (2012).
[Crossref] [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, 333–337 (2011).
[Crossref] [PubMed]

Gu, C.

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley, 2010), Vol. 67.

Gwon, M.

J. Kim, Y. U. Lee, B. Kang, J. H. Woo, E. Y. Choi, E. S. Kim, M. Gwon, D.-W. Kim, and J. W. Wu, “Fabrication of polarization-dependent reflective metamaterial by focused ion beam milling,” Nanotechnology 24, 015306 (2013).
[Crossref]

Hu, D.

D. Hu, X. Wang, S. Feng, J. Ye, W. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1, 186–191 (2013).
[Crossref]

Hwang, T.-J.

Ishii, S.

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, babinet-inverted plasmonic metalenses,” Light-Sci. Appl. 2, e72 (2013).
[Crossref]

Jagadish, C.

Kaczmarek, M.

Kan, Q.

D. Hu, X. Wang, S. Feng, J. Ye, W. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1, 186–191 (2013).
[Crossref]

Kang, B.

J. Kim, Y. U. Lee, B. Kang, J. H. Woo, E. Y. Choi, E. S. Kim, M. Gwon, D.-W. Kim, and J. W. Wu, “Fabrication of polarization-dependent reflective metamaterial by focused ion beam milling,” Nanotechnology 24, 015306 (2013).
[Crossref]

B. Kang, J. H. Woo, E. Choi, H.-H. Lee, E. S. Kim, J. Kim, T.-J. Hwang, Y.-S. Park, D. H. Kim, and J. W. Wu, “Optical switching of near infrared light transmission in metamaterial-liquid crystal cell structure,” Opt. Express 18, 16492–16498 (2010).
[Crossref] [PubMed]

Kats, M.

N. Yu, P. Genevet, F. Aieta, M. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: Controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

Kats, M. A.

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702–1706 (2012).
[Crossref] [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, 333–337 (2011).
[Crossref] [PubMed]

Kildishev, A. V.

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

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, babinet-inverted plasmonic metalenses,” Light-Sci. Appl. 2, e72 (2013).
[Crossref]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

Kim, D. H.

Kim, D.-W.

J. Kim, Y. U. Lee, B. Kang, J. H. Woo, E. Y. Choi, E. S. Kim, M. Gwon, D.-W. Kim, and J. W. Wu, “Fabrication of polarization-dependent reflective metamaterial by focused ion beam milling,” Nanotechnology 24, 015306 (2013).
[Crossref]

Kim, E. S.

Kim, J.

J. Kim, Y. U. Lee, B. Kang, J. H. Woo, E. Y. Choi, E. S. Kim, M. Gwon, D.-W. Kim, and J. W. Wu, “Fabrication of polarization-dependent reflective metamaterial by focused ion beam milling,” Nanotechnology 24, 015306 (2013).
[Crossref]

B. Kang, J. H. Woo, E. Choi, H.-H. Lee, E. S. Kim, J. Kim, T.-J. Hwang, Y.-S. Park, D. H. Kim, and J. W. Wu, “Optical switching of near infrared light transmission in metamaterial-liquid crystal cell structure,” Opt. Express 18, 16492–16498 (2010).
[Crossref] [PubMed]

Kivshar, Y. S.

Klar, P. J.

D. Hu, X. Wang, S. Feng, J. Ye, W. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1, 186–191 (2013).
[Crossref]

Kremers, C.

Larouche, S.

Lee, H.-H.

Lee, Y. U.

J. Kim, Y. U. Lee, B. Kang, J. H. Woo, E. Y. Choi, E. S. Kim, M. Gwon, D.-W. Kim, and J. W. Wu, “Fabrication of polarization-dependent reflective metamaterial by focused ion beam milling,” Nanotechnology 24, 015306 (2013).
[Crossref]

Y. U. Lee, E. Y. Choi, J. H. Woo, E. S. Kim, and J. W. Wu, “Reflection resonance switching in metamaterial twisted nematics cell,” Opt. Express 21, 17492–17497 (2013).
[Crossref] [PubMed]

Minovich, A.

Miroshnichenko, A. E.

Neshev, D. N.

Ni, X.

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, babinet-inverted plasmonic metalenses,” Light-Sci. Appl. 2, e72 (2013).
[Crossref]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

Ou, J.

Park, Y.-S.

Shalaev, V. M.

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

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, babinet-inverted plasmonic metalenses,” Light-Sci. Appl. 2, e72 (2013).
[Crossref]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

Smart, A. G.

A. G. Smart, “Phase-shifting surfaces bend the rules of ray optics,” Phys. Today 64, 12 (2011).
[Crossref]

Smith, D. R.

Staude, I.

Sun, W.

D. Hu, X. Wang, S. Feng, J. Ye, W. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1, 186–191 (2013).
[Crossref]

Tetienne, J.-P.

N. Yu, P. Genevet, F. Aieta, M. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: Controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

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, 333–337 (2011).
[Crossref] [PubMed]

Wang, X.

D. Hu, X. Wang, S. Feng, J. Ye, W. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1, 186–191 (2013).
[Crossref]

Woo, J. H.

Wu, J. W.

Ye, J.

D. Hu, X. Wang, S. Feng, J. Ye, W. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1, 186–191 (2013).
[Crossref]

Yeh, P.

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley, 2010), Vol. 67.

Yu, N.

N. Yu, P. Genevet, F. Aieta, M. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: Controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702–1706 (2012).
[Crossref] [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, 333–337 (2011).
[Crossref] [PubMed]

Zhang, Y.

D. Hu, X. Wang, S. Feng, J. Ye, W. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1, 186–191 (2013).
[Crossref]

Zheludev, N.

Adv. Opt. Mater. (1)

D. Hu, X. Wang, S. Feng, J. Ye, W. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1, 186–191 (2013).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

N. Yu, P. Genevet, F. Aieta, M. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: Controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

J. Inst. Electr. Eng. Part IIIA: Radiolocation (1)

H. G. Booker, “Slot aerials and their relation to complementary wire aerials (Babinet’s principle),” J. Inst. Electr. Eng. Part IIIA: Radiolocation 93, 620–626 (1946).

Light-Sci. Appl. (1)

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, babinet-inverted plasmonic metalenses,” Light-Sci. Appl. 2, e72 (2013).
[Crossref]

Nano Lett. (1)

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702–1706 (2012).
[Crossref] [PubMed]

Nanotechnology (1)

J. Kim, Y. U. Lee, B. Kang, J. H. Woo, E. Y. Choi, E. S. Kim, M. Gwon, D.-W. Kim, and J. W. Wu, “Fabrication of polarization-dependent reflective metamaterial by focused ion beam milling,” Nanotechnology 24, 015306 (2013).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Phys. Today (1)

A. G. Smart, “Phase-shifting surfaces bend the rules of ray optics,” Phys. Today 64, 12 (2011).
[Crossref]

Science (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, 333–337 (2011).
[Crossref] [PubMed]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

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

Other (2)

See http://www.lumerical.com/

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley, 2010), Vol. 67.

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Figures (12)

Fig. 1
Fig. 1 (a) SEM image of cVMS fabricated by focused ion beam milling. (b) A row of cVMS is shown with the superlattice periodicity of Γ = 2400nm. Schematics of ordinary/extraordinary reflection and refraction with the reflection angle θr and refraction angle θt are shown in (c) the normal incidence and (d) an incidence angle θi for s-polarized incident beam. In both (c) and (d), θr = θt. See text.
Fig. 2
Fig. 2 2-dimensional plot of (a) normalized amplitude and (b) phase of scattered light in cross-polarization is shown as a function of wavelength and x-position. For a series of wavelengths, (c) normalized amplitude and (d) phase of scattered light in cross-polarization are plotted for each V-shape slot antenna from number 1 to number 8.
Fig. 3
Fig. 3 Plane-wave beam propagation is simulated for a normally incident y-polarized light. (a) y-component of electric field is shown corresponding to ordinary refraction, and (b) x-component of electric field is shown corresponding to extraordinary refraction with λ = 1100nm. (c) and (d) are simulation calculation results for λ = 1309nm.
Fig. 4
Fig. 4 Experimental measurements of extraordinary refraction and reflection angles versus wavelength are shown. (a) Refraction is shown for the normal incidence in s-polarization. (b) Refraction is shown for the incidence angle 15° in p-polarization. (c) Refraction is shown for the incidence angle 60° in p-polarization. (d) Reflection is shown for the incidence angle 60° in p-polarization. The white lines are from a theoretical calculation.
Fig. 5
Fig. 5 Deflection efficiencies are plotted as a function of wavelength for (a) reflection and (b) transmission.
Fig. 6
Fig. 6 (a) Schematics of beam deflection is shown for y-polarized incident light at λ = 1100nm. (b)&(c) and (d)&(e) correspond to the polar plots of the transmitted light intensities in negative metasurface cVMS and positive metasurface, respectively.
Fig. 7
Fig. 7 Schematics of a cVMS-TNLC cell is shown with a y-polarized incident light, when (a) no external voltage is applied and (b) an ac voltage is applied. Linear polarization states are orthogonal for ordinary and extraordinary refractions.
Fig. 8
Fig. 8 (a) Photograph of experimental set-up is shown along with (b) schematics.
Fig. 9
Fig. 9 (A) Schematics of a cVMS-TNLC cell is shown with an incident light with polarization angle ϕent. (B) Measurements and (C) theoretical calculations of polarization direction of extraordinary refraction light with ac voltage of (a) 0V, (b) 2.5V, (c) 3.5V, and (d) 4.5V for ϕent=90° are shown.
Fig. 10
Fig. 10 (A) Measurements and (B) theoretical calculations of polarization direction of refraction light for the incident polarization angles (a) ϕent=0°, (b) ϕent=30°, (c) ϕent=45°, and (d) ϕent=60° (e) ϕent=90° are shown.
Fig. 11
Fig. 11 Schematics of an electro-optic switching of refraction is shown with a y-polarized incident light, when (a) no external voltage is applied and (b) an ac voltage is applied.
Fig. 12
Fig. 12 Measurement of an electro-optic switching of refraction is shown in a y-polarized incident light. The light intensity is plotted as a function of an ac voltage.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

M TNLC = ( cos Ψ sin Ψ sin Ψ cos Ψ ) ( cos X i Δ 2 sin X X Ψ sin X X Ψ sin X X cos X + i Δ 2 sin X X )
X = Ψ 2 + ( Δ 2 ) 2
( V x V y ) = ( cos ϕ ent sin ϕ ent ) , ( V x V y ) = ( cos ϕ exit sin ϕ exit ) .
T = | V * M cVMS M TNLC V | 2
M cVMS = ( cos 2 β sin 2 β sin 2 β cos 2 β ) .

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