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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 14 — Jul. 2, 2012
  • pp: 15882–15890
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Wave front engineering from an array of thin aperture antennas

Ming Kang, Tianhua Feng, Hui-Tian Wang, and Jensen Li  »View Author Affiliations


Optics Express, Vol. 20, Issue 14, pp. 15882-15890 (2012)
http://dx.doi.org/10.1364/OE.20.015882


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Abstract

We propose an ultra-thin metamaterial constructed by an ensemble of the same type of anisotropic aperture antennas with phase discontinuity for wave front manipulation across the metamaterial. A circularly polarized light is completely converted to the cross-polarized light which can either be bent or focused tightly near the diffraction limit. It depends on a precise control of the optical-axis profile of the antennas on a subwavelength scale, in which the rotation angle of the optical axis has a simple linear relationship to the phase discontinuity. Such an approach enables effective wave front engineering within a subwavelength scale.

© 2012 OSA

1. Introduction

Metamaterials (MMs), as a new type of artificially structured materials, have been used to demonstrate exotic phenomena such as negative refraction [1

1. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]

, 2

2. S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102(2), 023901 (2009). [CrossRef] [PubMed]

] and invisibility cloaking [3

3. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]

, 4

4. J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008). [CrossRef] [PubMed]

]. Because metamaterials can provide extreme electromagnetic (EM) response to the incident light with the subwavelength resonating units, it becomes possible to achieve considerable electromagnetic response by just using a slab of metamaterial which is much thinner than a wavelength. For example, an ultra-thin metamaterial can be used to perfectly absorb light [5

5. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008). [CrossRef] [PubMed]

, 6

6. H. T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105(7), 073901 (2010). [CrossRef] [PubMed]

] and to generate large optical chirality for polarization manipulation [7

7. V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006). [CrossRef] [PubMed]

, 8

8. D. H. Kwon, P. L. Werner, and D. H. Werner, “Optical planar chiral metamaterial designs for strong circular dichroism and polarization rotation,” Opt. Express 16(16), 11802–11807 (2008). [CrossRef] [PubMed]

]. Recently, such an approach has been extended to extreme phase control. By using an array of metamaterial units of structural parameters varying on a subwavelength scale, the light incident on an ultra-thin metamaterial can be bent by an angle using the phase discontinuity across the metamaterial, in a way that the Snell's law has been generalized on an inhomogeneous metamaterial surface [9

9. 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). [CrossRef] [PubMed]

13

13. P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012). [CrossRef]

]. In contrast to the ordinary spatial phase modulation devices employing liquid crystals [14

14. F. Gori, “Measuring Stokes parameters by means of a polarization grating,” Opt. Lett. 24(9), 584–586 (1999). [CrossRef] [PubMed]

, 15

15. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006). [CrossRef] [PubMed]

], the phase discontinuity is manipulated on a subwavelength scale (in the transverse direction) and is able to generate a larger bending angle through an array of metamaterial units of deep-subwavelength thickness. In the scheme, the wave front of the cross-polarized transmitted beam is greatly modified by a linear variation of the phase discontinuity which is provided by an array of plasmonic resonators. The large range of phase discontinuity (for the linear variation) is obtained by working at different regimes both near and far from the resonances through a series of plasmonic resonators. In fact, the phase variation across a resonance is always accompanied by the large variation of the amplitude. It is therefore challenging to obtain the desired phase variation with equal amplitude for the transmitted cross-polarized beam. In order to reconcile this dilemma between flexible phase control and equal amplitude, a double-resonance scheme for the plasmonic resonators was previously employed. While the resonances provide the flexible phase discontinuity, the two resonances work cooperatively to compensate each other so that the transmitted amplitude stays fairly constant for the whole series of plasmonic resonators. The scheme normally requires careful optimization of the structural parameters of the resonators [9

9. 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). [CrossRef] [PubMed]

, 10

10. N. Engheta, “ Antenna-Guided Light,” Science 334(6054), 317–318 (2011). [CrossRef] [PubMed]

, 12

12. 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(3), 1702–1706 (2012). [CrossRef] [PubMed]

, 13

13. P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012). [CrossRef]

], and an accurate and efficient method has been developed in order to achieve the whole series of design [16

16. R. Blanchard, G. Aoust, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Modeling nanoscale V-shaped antennas for the design of optical phased arrays,” Phys. Rev. B 85(15), 155457 (2012). [CrossRef]

]. Here, we investigate an alternative scheme in generating the phase discontinuity by an ultra-thin metamaterial constructed by an ensemble of the same type of anisotropic aperture antennas. In our design, all the anisotropic antennas have only one resonance at the same frequency in order to avoid the amplitude dispersion of the antennas working across resonance. We only need to engineer the orientation of the optical axes of the same type of antennas at different positions on a subwavelength scale. By using a circularly polarized light (instead of linear polarization) impinging on the metamaterial, it can be completely converted to the cross-polarized light without the residual power in the original polarization, which can occupy larger than half of the transmitted power in the double-resonance scheme with linear polarization. Moreover, the phase control becomes intuitive that the spatial variation of the phase discontinuity has a simple linear relationship to the rotation angle of the optical-axis profile, as in one type of Q-plates [15

15. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006). [CrossRef] [PubMed]

]. Linear and parabolic phase variations for the optical-axis profile are investigated in order to bend or tightly focus the incident light near the diffraction limit.

2. Phase discontinuity through rotation of optical axes

Up to now, we could design and manipulate the output wave front though spatial rotation of the resonator arrays. As examples to demonstrate our proposal, we investigate two kinds of one dimensional phase profiles to demonstrate general manipulation of the wave front:

A: Linear phase discontinuity:

The generalized version of Snell’s Law is in the form [9

9. 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). [CrossRef] [PubMed]

, 10

10. N. Engheta, “ Antenna-Guided Light,” Science 334(6054), 317–318 (2011). [CrossRef] [PubMed]

, 12

12. 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(3), 1702–1706 (2012). [CrossRef] [PubMed]

, 13

13. P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012). [CrossRef]

]:
ntsinαtnisinαi=λ2πdΦdx
(3)
where αi(αt) corresponds to the incident (refraction) angle of the plane wave, ni(nt)is the refractive index in the incident (refracted) region. If we assume the plane wave is normally incident to the metamaterial surface, the refraction angle is governed by sinαt=(λ/2π)dΦ/dx, where the refractive index in the refracted region is assumed to be vacuum, i.e. nt=1. The linear phase variation, i.e. the gradient of the linear phase variation dΦ/dx being constant, can bend the incident wave at an angle. According to our scheme for the linear phase variation, the gradient of the phase variation iskG=dΦ/dx=2π/D, where D is the total width of the antennas array and the rotation angle ranges from 0 toπ.

B: Parabolic phase discontinuity:

In fact, the linear phase relationship is only one possibility to manipulate the wave front. As another representative example, as a one-dimensional variation, we can generate a phase discontinuity profile according to:
Φ(x)=2πfλ2πf2+x2λ
(4)
With such a parabolic profile, we can focus the incident light (wavelengthλ) to a distance f beyond the metamaterial surface, where f is the focal length. Ordinary lens, e.g. a cylinder convex lens, accumulates the phase along the optical path with different thicknesses of material. In contrary, we can generate such a phase discontinuity by an ultra-thin metamaterial surface in the subwavelength scale. Moreover, due to the abrupt phase control, we can focus the light to a tight focus near the diffraction limit as we will see later.

Taking into account of the linear and parabolic phase discontinuity along the metamaterial surface through an array of split ring aperture antenna with defined profiles of the rotation angles, as depicted in Fig. 1(c), one representative structure (A) is designed and is composed of 11 rotating antennas to realize the linear phase variation from 0 to 2π. Considering the finite size of the unit cell, the phase variation is not continuous but is discrete. For structure A, each unit cell only needs a discrete rotation with step size of 0.1π to realize the linear phase variation from 0 to 2π. The case of structure B contains 15 rotating resonators with defined rotation angle to realize the parabolic phase variation in Eq. (4). Here, we emphasize that phase variation acquired by rotating optical axis is free of dispersion of the resonator, as we could keep the desired anisotropic behavior.

To verify our proposed scheme, we have performed full-wave simulations using CST Microwave Studio, based on the finite difference time domain (FDTD) algorithm [28

28. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008). [CrossRef] [PubMed]

]. We utilize the perfect conductor approximation (PCA) for simplicity. The results presented here can be extended to other frequency regimes, when the dispersion of metal is taken into consideration. We focus on the wavelength λ = 2.21a(3.68b), where the element of transmission matrix fulfills t1t2. In the y direction, we adopt periodic condition, while in the x direction, perfectly matched layer absorbing boundary condition is adopted. We set the mesh size to be 0.01a-0.02a in the transverse direction and 0.02a-0.05a in the longitudinal z direction. The mesh size with high precision enables us to model the array of the metallic apertures exhibiting inhomogeneous and anisotropic EM responses with high accuracy.

3. Light bending through phase discontinuities across an ultra-thin metamaterial surface

4. Tight Light Focusing through phase discontinuities across an ultra-thin metamaterial surface

To further demonstrate the feasibility of the additional phase discontinuities in our scheme, we modulate the metamaterial surface to focus the incident plane wave through additional convex phase discontinuity. According to Eq. (4), the interface is created by arranging 15 antennas at various angles, as shown in Fig. 1. As viewed in the Fig. 3(a)
Fig. 3 Numerical and theoretical illustration of the additional parabolic phase discontinuity through structured metamaterial surface. The region exhibiting the numerical results is from 0 to 20a along the z direction, and the region of the theoretical results is from 2a to 20a along the z direction, where the transverse direction is from −8a to 8a. One of the electric field component(x) numerical and theoretical distributions for the left-handed circular polarization incidence (a), (b) and right-handed circular polarization normal incidence (e), (f) indicates the convex and concave wave front across the resonator interface. The corresponding theoretical results are The numerical and theoretical electric field energy density illuminates the focusing (defocusing) phenomenon due to the induced convex phase discontinuity through rotating optical axis for left-handed circular polarization incidence(c), (d)and right-handed circular polarization incidence (g),(h).
and 3(e), for left-handed circular polarization incidence, we can create a converging wave front; while for right-handed circular polarization incidence, we can create a diverging wave front. The focusing (defocusing) behavior of the metamaterial surface can also be viewed in the electric field energy density distribution, see Fig. 3(c) and 3(g), the focus length (f) is f = 10a, which is slightly different from the targeted focus length f = 11a in Eq. (4). The full width of the half maximum energy density is w=0.77λ for left-handed circular incidence, which is in the region of tight focus in the far field focusing. In contrary, the transverse energy density distribution does not concentrate energy for the incident light of right-handed circular polarization, the transverse energy density becomes broad in the entire transverse region, shown in Fig. 3(g), due to the introduced diverging wave front through the metamaterial. Visual understanding of the EM evolution through the metallic resonator arrays can be obtained by formulating the E field after the metallic surface. When the left-handed circular polarization is normally incident, the transverse E field at the observation plane can be approximately described by
E=Ainri1ejk0riej2θi(1,i)T
(5)
where ri is the distance between the i th aperture element to the observation point, A is the scale factor to reveal the transmission behavior of each unit, and the field at the observation point is the summation of the contribution from each aperture element. The phase associated with the incident polarization state leads to the optical spin dependent phenomenon in our proposed metamaterial structures [14

14. F. Gori, “Measuring Stokes parameters by means of a polarization grating,” Opt. Lett. 24(9), 584–586 (1999). [CrossRef] [PubMed]

]. The analytical prediction could map the main feature of the numerical results, as shown in Fig. 3(b), 3(d), 3(f), 3(h), where the displayed region in analytical description is from 2a to 20a along the z direction. By far, we can model the most representative parabolic phase to realize the convex or concave wave front through rotating the optic axes of the antennas investigated, which is different from conventional optical components, where the spatial phase profile relies on light propagation over different optical lengths.

5. Conclusion

We have proposed an ultra-thin metamaterial constructed by an ensemble of the same type of anisotropic aperture antennas with phase discontinuity for wave front manipulation across the metamaterial. The phase discontinuity only depends on a precise control of the optical-axis rotation profile of the antennas on a subwavelength scale, in which the rotation angle of the optical axis has a simple linear relationship to the phase discontinuity. By simply manipulating the rotation of the optical axes, an abrupt beam bending (linear phase variation case) and tight focusing (parabolic phase variation case) across the ultra thin metamaterial are numerically demonstrated. Such a simple approach enables effective wave front engineering within a subwavelength scale. Our proposal would enrich the functionality of the state-of-art metamaterial design, illuminates new ways in designing metmaterials, and the exotic EM response generated would encourage the precise manipulation of the light in the subwavelength region [29

29. A. A. Yanik, R. Adato, S. Erramilli, and H. Altug, “Hybridized nanocavities as single-polarized plasmonic antennas,” Opt. Express 17(23), 20900–20910 (2009). [CrossRef] [PubMed]

].

Acknowledgment

This work was supported by Hong Kong Research Grants Council (GRF grant CityU 102211 and Project No. HKUST2/CRF/11G). This work is also supported by the 973 Program of China under Grant No. 2012CB921900 and the National Natural Science Foundation of China under Grants 10934003.

References and links

1.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]

2.

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102(2), 023901 (2009). [CrossRef] [PubMed]

3.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]

4.

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008). [CrossRef] [PubMed]

5.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008). [CrossRef] [PubMed]

6.

H. T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105(7), 073901 (2010). [CrossRef] [PubMed]

7.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006). [CrossRef] [PubMed]

8.

D. H. Kwon, P. L. Werner, and D. H. Werner, “Optical planar chiral metamaterial designs for strong circular dichroism and polarization rotation,” Opt. Express 16(16), 11802–11807 (2008). [CrossRef] [PubMed]

9.

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). [CrossRef] [PubMed]

10.

N. Engheta, “ Antenna-Guided Light,” Science 334(6054), 317–318 (2011). [CrossRef] [PubMed]

11.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335(6067), 427 (2012). [CrossRef] [PubMed]

12.

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(3), 1702–1706 (2012). [CrossRef] [PubMed]

13.

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012). [CrossRef]

14.

F. Gori, “Measuring Stokes parameters by means of a polarization grating,” Opt. Lett. 24(9), 584–586 (1999). [CrossRef] [PubMed]

15.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006). [CrossRef] [PubMed]

16.

R. Blanchard, G. Aoust, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Modeling nanoscale V-shaped antennas for the design of optical phased arrays,” Phys. Rev. B 85(15), 155457 (2012). [CrossRef]

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C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005). [CrossRef] [PubMed]

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28.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008). [CrossRef] [PubMed]

29.

A. A. Yanik, R. Adato, S. Erramilli, and H. Altug, “Hybridized nanocavities as single-polarized plasmonic antennas,” Opt. Express 17(23), 20900–20910 (2009). [CrossRef] [PubMed]

OCIS Codes
(260.2110) Physical optics : Electromagnetic optics
(310.6860) Thin films : Thin films, optical properties
(160.3918) Materials : Metamaterials

ToC Category:
Metamaterials

History
Original Manuscript: May 11, 2012
Revised Manuscript: June 5, 2012
Manuscript Accepted: June 6, 2012
Published: June 27, 2012

Citation
Ming Kang, Tianhua Feng, Hui-Tian Wang, and Jensen Li, "Wave front engineering from an array of thin aperture antennas," Opt. Express 20, 15882-15890 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-14-15882


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References

  1. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science292(5514), 77–79 (2001). [CrossRef] [PubMed]
  2. S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett.102(2), 023901 (2009). [CrossRef] [PubMed]
  3. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
  4. J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett.101(20), 203901 (2008). [CrossRef] [PubMed]
  5. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett.100(20), 207402 (2008). [CrossRef] [PubMed]
  6. H. T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett.105(7), 073901 (2010). [CrossRef] [PubMed]
  7. V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett.97(16), 167401 (2006). [CrossRef] [PubMed]
  8. D. H. Kwon, P. L. Werner, and D. H. Werner, “Optical planar chiral metamaterial designs for strong circular dichroism and polarization rotation,” Opt. Express16(16), 11802–11807 (2008). [CrossRef] [PubMed]
  9. 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,” Science334(6054), 333–337 (2011). [CrossRef] [PubMed]
  10. N. Engheta, “ Antenna-Guided Light,” Science334(6054), 317–318 (2011). [CrossRef] [PubMed]
  11. X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science335(6067), 427 (2012). [CrossRef] [PubMed]
  12. 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(3), 1702–1706 (2012). [CrossRef] [PubMed]
  13. P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett.100(1), 013101 (2012). [CrossRef]
  14. F. Gori, “Measuring Stokes parameters by means of a polarization grating,” Opt. Lett.24(9), 584–586 (1999). [CrossRef] [PubMed]
  15. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett.96(16), 163905 (2006). [CrossRef] [PubMed]
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