Abstract

Measuring light’s state of polarization is an inherently difficult problem since the phase information between orthogonal polarization states is typically lost in the detection process. In this work, we bring to the fore the equivalence between normalized Stokes parameters and diffraction contrasts in appropriately designed phase-gradient birefringent metasurfaces and introduce a concept of all-polarization birefringent metagratings. The metagrating, which consists of three interweaved metasurfaces, allows one to easily analyze an arbitrary state of light polarization by conducting simultaneous (i.e., parallel) measurements of the correspondent diffraction intensities that reveal immediately the Stokes parameters of the polarization state under examination. Based on plasmonic metasurfaces operating in reflection at a wavelength of 800 nm, we design and realize phase-gradient birefringent metasurfaces and the correspondent metagrating, while experimental characterization of the fabricated components convincingly demonstrates the expected functionalities. We foresee the use of the metagrating in compact polarimetric setups at any frequency regime of interest.

© 2015 Optical Society of America

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References

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2015 (4)

D. Wen, F. Yue, S. Kumar, Y. Ma, M. Chen, X. Ren, P. E. Kremer, B. D. Gerardot, M. R. Taghizadeh, G. S. Buller, and X. Chen, “Metasurface for characterization of the polarization state of light,” Opt. Express 23, 10272–10281 (2015).
[Crossref]

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[Crossref]

F. Ding, Z. Wang, S. He, V. M. Shalaev, and A. V. Kildishev, “Broadband high-efficiency half-wave plate: a supercell-based plasmonic metasurface approach,” ACS Nano 9, 4111–4119 (2015).
[Crossref]

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).

2014 (7)

A. Shaltout, J. Liu, V. M. Shalaev, and A. V. Kildishev, “Optically active metasurface with non-chiral plasmonic nanoantennas,” Nano Lett. 14, 4426–4431 (2014).
[Crossref]

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

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, 1394–1399 (2014).
[Crossref]

F. J. Rodríguez-Fortuño, D. Puerto, A. Griol, L. Bellieres, J. Martí, and A. Martínez, “Universal method for the synthesis of arbitrary polarization states radiated by a nanoantenna,” Laser Photon. Rev. 8, L27–L31 (2014).
[Crossref]

J. Carbonell, F. J. Rodríguez-Fortuño, A. Díaz-Rubio, A. Martínez, F. Cervera, and J. Sánchez-Dehesa, “Directive excitation of guided electromagnetic waves through polarization control,” Phys. Rev. B 89, 155121 (2014).
[Crossref]

F. J. Rodríguez-Fortuño, I. Barber-Sanz, D. Puerto, A. Griol, and A. Martínez, “Resolving light handedness with an on-chip silicon microdisk,” ACS Photon. 1, 762–767 (2014).
[Crossref]

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

2013 (5)

2012 (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, 6328–6333 (2012).
[Crossref]

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

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, 4932–4936 (2012).
[Crossref]

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012).
[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]

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, 6223–6229 (2012).
[Crossref]

M. Kang, T. Feng, H.-T. Wang, and J. Li, “Wave front engineering from an array of thin aperture antennas,” Opt. Express 20, 15882–15890 (2012).
[Crossref]

A. Roberts and L. Lin, “Plasmonic quarter-wave plate,” Opt. Lett. 37, 1820–1822 (2012).
[Crossref]

2011 (5)

2010 (2)

K.-P. Chen, V. P. Drachev, J. D. Borneman, A. V. Kildishev, and V. M. Shalaev, “Drude relaxation rate in grained gold nanoantennas,” Nano Lett. 10, 916–922 (2010).
[Crossref]

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10, 1936–1940 (2010).
[Crossref]

2009 (2)

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[Crossref]

J. Hao, Q. Ren, Z. An, X. Huang, Z. Chen, M. Qiu, and L. Zhou, “Optical metamaterial for polarization control,” Phys. Rev. A 80, 023807 (2009).
[Crossref]

2007 (1)

2002 (1)

2001 (1)

1999 (1)

1998 (1)

1997 (2)

A. F. Collings and F. Caruso, “Biosensors: recent advances,” Rep. Prog. Phys. 60, 1397–1445 (1997).
[Crossref]

D. M. Pozar, S. D. Targonski, and H. Syrigos, “Design of millimeter wave microstrip reflectarrays,” IEEE Trans. Antennas Propag. 45, 287–296 (1997).
[Crossref]

1984 (1)

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. A 392, 45–57 (1984).
[Crossref]

1979 (1)

A. Rzhanov and K. Svitashev, “Ellipsometric techniques to study surfaces and thin films,” Adv. Electron. Electron Phys. 49, 1–84 (1979).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

1956 (1)

S. Pancharatnam, “Generalized theory of interference and its applications,” Proc. Indian Acad. Sci. A 44, 247–262 (1956).

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, 4932–4936 (2012).
[Crossref]

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, 6328–6333 (2012).
[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]

Albrektsen, O.

Alú, A.

Y. Zhao and A. Alú, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
[Crossref]

An, Z.

J. Hao, Q. Ren, Z. An, X. Huang, Z. Chen, M. Qiu, and L. Zhou, “Optical metamaterial for polarization control,” Phys. Rev. A 80, 023807 (2009).
[Crossref]

Bai, B.

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012).
[Crossref]

Barber-Sanz, I.

F. J. Rodríguez-Fortuño, I. Barber-Sanz, D. Puerto, A. Griol, and A. Martínez, “Resolving light handedness with an on-chip silicon microdisk,” ACS Photon. 1, 762–767 (2014).
[Crossref]

Barnard, E. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[Crossref]

Bellieres, L.

F. J. Rodríguez-Fortuño, D. Puerto, A. Griol, L. Bellieres, J. Martí, and A. Martínez, “Universal method for the synthesis of arbitrary polarization states radiated by a nanoantenna,” Laser Photon. Rev. 8, L27–L31 (2014).
[Crossref]

Berry, M. V.

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. A 392, 45–57 (1984).
[Crossref]

Biener, G.

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, 4932–4936 (2012).
[Crossref]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 2004).

Boltasseva, A.

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]

Bomzon, Z.

Borneman, J. D.

K.-P. Chen, V. P. Drachev, J. D. Borneman, A. V. Kildishev, and V. M. Shalaev, “Drude relaxation rate in grained gold nanoantennas,” Nano Lett. 10, 916–922 (2010).
[Crossref]

Bozhevolnyi, S. I.

Brener, I.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).

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, 1394–1399 (2014).
[Crossref]

Brongersma, M. L.

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

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[Crossref]

Buller, G. S.

Capasso, F.

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

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, 4932–4936 (2012).
[Crossref]

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, 6328–6333 (2012).
[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]

Carbonell, J.

J. Carbonell, F. J. Rodríguez-Fortuño, A. Díaz-Rubio, A. Martínez, F. Cervera, and J. Sánchez-Dehesa, “Directive excitation of guided electromagnetic waves through polarization control,” Phys. Rev. B 89, 155121 (2014).
[Crossref]

Caruso, F.

A. F. Collings and F. Caruso, “Biosensors: recent advances,” Rep. Prog. Phys. 60, 1397–1445 (1997).
[Crossref]

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[Crossref]

Cervera, F.

J. Carbonell, F. J. Rodríguez-Fortuño, A. Díaz-Rubio, A. Martínez, F. Cervera, and J. Sánchez-Dehesa, “Directive excitation of guided electromagnetic waves through polarization control,” Phys. Rev. B 89, 155121 (2014).
[Crossref]

Chen, K.-P.

S. Ishii, A. V. Kildishev, V. M. Shalaev, K.-P. Chen, and V. P. Drachev, “Metal nanoslit lenses with polarization-selective design,” Opt. Lett. 36, 451–453 (2011).
[Crossref]

K.-P. Chen, V. P. Drachev, J. D. Borneman, A. V. Kildishev, and V. M. Shalaev, “Drude relaxation rate in grained gold nanoantennas,” Nano Lett. 10, 916–922 (2010).
[Crossref]

Chen, M.

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, 6223–6229 (2012).
[Crossref]

Chen, X.

D. Wen, F. Yue, S. Kumar, Y. Ma, M. Chen, X. Ren, P. E. Kremer, B. D. Gerardot, M. R. Taghizadeh, G. S. Buller, and X. Chen, “Metasurface for characterization of the polarization state of light,” Opt. Express 23, 10272–10281 (2015).
[Crossref]

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012).
[Crossref]

Chen, Z.

J. Hao, Q. Ren, Z. An, X. Huang, Z. Chen, M. Qiu, and L. Zhou, “Optical metamaterial for polarization control,” Phys. Rev. A 80, 023807 (2009).
[Crossref]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
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Supplementary Material (1)

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» Supplement 1: PDF (1945 KB)      Supplemental Document

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Figures (6)

Fig. 1.
Fig. 1. Illustration of the metagrating’s working principle. An incoming beam with an unknown polarization state |u is on reflection represented in the bases (x^,y^), (a^,b^), and (r^,l^), thereby allowing one to determine the Stokes parameters and, hence, the state of polarization without the need of multiple measurements or an interferometric setup.
Fig. 2.
Fig. 2. Design of the birefringent phase-gradient metasurfaces. (a) Sketch of a basic unit cell consisting of a gold nanobrick on top of a glass spacer and gold substrate. Panels (b) and (c) show the calculated reflection coefficient as a function of nanobrick widths for x- and y-polarized light, respectively, and geometrical parameters Λx=320nm, Λy=250nm, t=40nm, ts=50nm, and wavelength λ=800nm. The color maps show the reflection coefficient amplitude, whereas the solid green lines are contours of the corresponding reflection phase. The square, circle, and triangular markers indicate the nanobrick sizes constituting the metasurface supercells depicted in (d). (e) Reflection coefficient amplitude along the three metasurfaces, as extracted from panels (b) and (c), for the polarization bases (x^,y^), (a^,b^), and (r^,l^).
Fig. 3.
Fig. 3. Theoretical performance of the phase-gradient metasurfaces. (a)–(c) Diffraction contrasts for the three metasurfaces as a function of the polarization state of incident light. Here, the amplitude of the electric field is defined as (Ax,Ay)=(cosθ,sinθ) and δ is the phase difference. (d) Three-dimensional plot of the diffraction contrasts, clearly illustrating that the associated surface closely resembles a unit sphere. (e) Plot of the difference between the calculated diffraction contrasts and the Stokes parameters, with the color bar representing the two-norm error SD2 [here, S=(s1,s2,s3)/s0 and D=(D1,D2,D3)].
Fig. 4.
Fig. 4. Fabricated metasurfaces and the experimental setup. Representative scanning electron microscopy images (a)–(c) of metasurfaces 1, 2, and 3, respectively, and (d) of the metagrating. (e) Schematic of the experimental setup for optical characterization.
Fig. 5.
Fig. 5. Experimental verification of the metasurface polarization splitters. (a) Normalized optical images of the diffraction spots for the two orthogonal polarizations that the metasurfaces are designed to split. The incident polarization state is denoted by |u in each panel. (b) Measured diffraction contrasts for the six polarizations that represent the extreme values of the three Stokes parameters.
Fig. 6.
Fig. 6. Experimental verification of the all-polarization birefringent metagrating. (a) Normalized optical images of the diffraction spots for the six polarizations representing the extreme values of the Stokes parameters. The incident polarization state is denoted by |u in each panel. (b) Measured diffraction contrasts (denoted by filled circles) for polarization states along the main axes of the Poincaré sphere (indicated by asterisks). The measured diffraction contrasts can be found tabulated in Supplement 1.

Equations (8)

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

E0=(AxAyeiδ),
s0=Ax2+Ay2I,
s1=Ax2Ay2,
s2=2AxAycosδ=Aa2Ab2,
s3=2AxAysinδ=Ar2Al2.
r¯¯=r(ei2πx/Λ00ei2πx/Λ),
I+1r2Au2andI1r2Av2,
D=I+1I1I+1+I1=Au2Av2Au2+Av2.

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