Abstract

In this work a new technique for synthesizing metamaterials using Bézier surfaces is introduced. First, the computational efficiency for the optimization of a reconfigurable Bézier quarter-wave plate metasurface is compared to the popular technique of optimizing pixelized surfaces via a binary Genetic Algorithm (GA). For the presented design methodology, a real valued optimization technique is employed which is based on the Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES). When compared to the GA, the optimizations of Bézier surfaces using CMA-ES are shown to consistently arrive at better solutions with an order of magnitude reduction in the required number of function evaluations. Additionally, more examples of Bézier metasurfaces are presented in the form of broadband quarter-wave and half-wave plate designs operating at optical wavelengths, subsequently exhibiting bandwidths which outperform metasurface designs found in the current literature.

© 2014 Optical Society of America

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2014 (4)

Q. Lévesque, M. Makhsiyan, P. Bouchon, F. Pardo, J. Jaeck, N. Bardou, and J. L. Pelouard, “Plasmonic planar antenna for wideband and efficient linear polarization conversion,” Appl. Phys. Lett. 104(11), 111105 (2014).
[Crossref]

Y. Wang, M. Pu, C. Hu, Z. Zhao, C. Wang, and X. Luo, “Dynamic manipulation of polarization states using anisotropic meta-surface,” Opt. Commun. 319, 14–16 (2014).
[Crossref]

S. C. Jiang, X. Xiong, Y. S. Hu, Y. H. Hu, G. B. Ma, R. W. Peng, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4(2), 021026 (2014).

H. F. Ma, G. Z. Wang, G. S. Kong, and T. J. Cui, “Broadband circular and linear polarization conversions realized by thin birefringent reflective metasurfaces,” Opt. Mater. Express 4(8), 1717–1724 (2014).
[Crossref]

2013 (6)

P. E. Sieber and D. H. Werner, “Reconfigurable broadband infrared circularly polarizing reflectors based on phase changing birefringent metasurfaces,” Opt. Express 21(1), 1087–1100 (2013).
[Crossref] [PubMed]

J. A. Bossard and D. H. Werner, “Metamaterials with custom emissivity polarization in the near-infrared,” Opt. Express 21(3), 3872–3884 (2013).
[Crossref] [PubMed]

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Broadband plasmonic half-wave plates in reflection,” Opt. Lett. 38(4), 513–515 (2013).
[Crossref] [PubMed]

A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband focusing flat mirrors based on plasmonic gradient metasurfaces,” Nano Lett. 13(2), 829–834 (2013).
[Crossref] [PubMed]

Y. Zhao and A. Alù, “Tailoring the dispersion of plasmonic nanorods to realize broadband optical meta-waveplates,” Nano Lett. 13(3), 1086–1091 (2013).
[Crossref] [PubMed]

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

2012 (10)

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat Commun 3, 870 (2012).
[Crossref] [PubMed]

J. K. Gansel, M. Latzel, A. Frölich, J. Kaschke, M. Theil, and M. Wegener, “Tapered gold-helix metamaterials as improved circular polarizers,” Appl. Phys. Lett. 100(10), 101109 (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(12), 6223–6229 (2012).
[Crossref] [PubMed]

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

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]

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

A. B. Khanikaev, S. H. Mousavi, C. Wu, N. Dabidian, K. B. Alici, and G. Shvets, “Electromagnetically induced polarization conversion,” Opt. Commun. 285(16), 3423–3427 (2012).
[Crossref]

E. Doumanis, G. Goussetis, J. L. Gomez-Tornero, R. Cahill, and V. Fusco, “Anisotropic impedance surfaces for linear to circular polarization conversion,” IEEE Trans. Antenn. Propag. 60(1), 212–219 (2012).
[Crossref]

R. T. Farouki, “The Bernstein polynomial basis: A centennial retrospective,” Comput. Aided Geom. Des. 29(6), 379–419 (2012).
[Crossref]

M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. Mumtaz Qazilbash, D. N. Basov, S. Ramanathan, and F. Caspasso, “Ultra-thin perfect absorber employing a tunable phase change material,” Appl. Phys. Lett. 101(22), 221101 (2012).
[Crossref]

2011 (9)

J. B. Kana Kana, J. M. Ndjaka, G. Vignaud, A. Gibaud, and M. Maaza, “Thermally tunable optical constants of vanadium dioxide thin films measured by spectroscopic ellipsometry,” Opt. Commun. 284(3), 807–812 (2011).
[Crossref]

M. D. Goldflam, T. Driscoll, B. Chapler, O. Khatib, N. Marie Jokerst, S. Palit, D. R. Smith, B. J. Kim, G. Seo, H. T. Kim, M. Di Ventra, and D. N. Basov, “Reconfigurable gradient index using VO2 memory metamaterials,” Appl. Phys. Lett. 99(4), 044103 (2011).
[Crossref]

J. Y. Ou, E. Plum, L. Jiang, and N. I. Zheludev, “Reconfigurable photonic metamaterials,” Nano Lett. 11(5), 2142–2144 (2011).
[Crossref] [PubMed]

W. Withayachumnankul, C. Fumeaux, and D. Abbott, “Planar array of electric-LC resonators with broadband tunability,” IEEE Antennas Wirel. Propag. Lett. 10, 577–580 (2011).
[Crossref]

M. D. Gregory, Z. Bayraktar, and D. H. Werner, “Fast optimization of electromagnetic design problems using the covariance matrix adaptation evolutionary strategy,” IEEE Trans. Antenn. Propag. 59(4), 1275–1285 (2011).
[Crossref]

C. Wu, H. Li, X. Yu, F. Li, H. Chen, and C. T. Chan, “Metallic helix array as a broadband wave plate,” Phys. Rev. Lett. 107(17), 177401 (2011).
[Crossref] [PubMed]

Z. Wei, Y. Cao, Y. Fan, X. Yu, and H. Li, “Broadband polarization transformation via enhanced asymmetric transmission through arrays of twisted complementary split-ring resonators,” Appl. Phys. Lett. 99(22), 221907 (2011).
[Crossref]

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84(20), 205428 (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(6054), 333–337 (2011).
[Crossref] [PubMed]

2010 (10)

M. Euler, V. Fusco, R. Cahill, and R. Dickie, “325 GHz single layer sub-millimeter wave FSS based split slot ring linear to circular polarization convertor,” IEEE Trans. Antenn. Propag. 58(7), 2457–2459 (2010).
[Crossref]

Y. Ye and S. He, “90 polarization rotator using a bilayered chiral metamaterial with giant optical activity,” Appl. Phys. Lett. 96(20), 203501 (2010).
[Crossref]

B. Zhu, Y. Feng, J. Zhao, C. Huang, and T. Jiang, “Switchable metamaterial reflector/absorber for different polarized electromagnetic waves,” Appl. Phys. Lett. 97(5), 051906 (2010).
[Crossref]

Z. L. Samson, K. F. MacDonald, F. De Angelis, B. Gholipour, K. Knight, C. C. Huang, E. Di Fabrizio, D. W. Hewak, and N. I. Zheludev, “Metamaterial electro-optic switch of nanoscale thickness,” Appl. Phys. Lett. 96(14), 143105 (2010).
[Crossref]

M. Seo, J. Kyoung, H. Park, S. Koo, H. S. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H. T. Kim, N. Park, Q. H. Park, K. Ahn, and D. S. Kim, “Active terahertz nanoantennas based on VO2 phase transition,” Nano Lett. 10(6), 2064–2068 (2010).
[Crossref] [PubMed]

Q. Y. Wen, H. W. Zhang, Q. H. Yang, Y. S. Xie, K. Chen, and Y. L. Liu, “Terahertz metamaterials with VO 2 cut-wires for thermal tunability,” Appl. Phys. Lett. 97(2), 021111 (2010).
[Crossref]

W.-X. Huang, X. G. Yin, C. P. Huang, Q. J. Wang, T. F. Miao, and Y. Y. Zhu, “Optical switching of a metamaterial by temperature controlling,” Appl. Phys. Lett. 96(26), 261908 (2010).
[Crossref]

D. J. Shelton, K. R. Coffey, and G. D. Boreman, “Experimental demonstration of tunable phase in a thermochromic infrared-reflectarray metamaterial,” Opt. Express 18(2), 1330–1335 (2010).
[Crossref] [PubMed]

M. Liu, Y. Zhang, X. Wang, and C. Jin, “Incident-angle-insensitive and polarization independent polarization rotator,” Opt. Express 18(11), 11990–12001 (2010).
[Crossref] [PubMed]

Z. Y. Yang, M. Zhao, P. X. Lu, and Y. F. Lu, “Ultrabroadband optical circular polarizers consisting of double-helical nanowire structures,” Opt. Lett. 35(15), 2588–2590 (2010).
[Crossref] [PubMed]

2009 (6)

2008 (4)

E. V. Plum, A. Fedotov, and N. I. Zheludev, “Optical activity in extrinsically chiral metamaterial,” Appl. Phys. Lett. 93(19), 191911 (2008).
[Crossref]

H.-T. Chen, J. F. O Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials,” Nat. Photonics 2(5), 295–298 (2008).
[Crossref]

J. Hegedüs and S. R. Elliott, “Microscopic origin of the fast crystallization ability of Ge-Sb-Te phase-change memory materials,” Nat. Mater. 7(5), 399–405 (2008).
[Crossref] [PubMed]

K. Shportko, S. Kremers, M. Woda, D. Lencer, J. Robertson, and M. Wuttig, “Resonant bonding in crystalline phase-change materials,” Nat. Mater. 7(8), 653–658 (2008).
[Crossref] [PubMed]

2007 (1)

J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. 99(6), 063908 (2007).
[Crossref] [PubMed]

2006 (2)

A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, “Giant gyrotropy due to electromagnetic-field coupling in a bilayered chiral structure,” Phys. Rev. Lett. 97(17), 177401 (2006).
[Crossref] [PubMed]

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

2003 (2)

D. J. Kern and D. H. Werner, “A genetic algorithm approach to the design of ultra‐thin electromagnetic bandgap absorbers,” Microw. Opt. Technol. Lett. 38(1), 61–64 (2003).
[Crossref]

N. Hansen, S. D. Müller, and P. Koumoutsakos, “Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES),” Evol. Comput. 11(1), 1–18 (2003).
[Crossref] [PubMed]

2002 (1)

K. Karkkainen and M. Stuchly, “Frequency selective surface as a polarization transformer,” Proc. Inst. Elect Eng. Microw. Antennas Propag. 149(5), 248–252 (2002).
[Crossref]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
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1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

1997 (2)

J. M. Johnson and V. Rahmat-Samii, “Genetic algorithms in engineering electromagnetics,” IEEE Antennas and Prop. Magazine 39(4), 7–21 (1997).
[Crossref]

D. S. Weile and E. Michielssen, “Genetic algorithm optimization applied to electromagnetics: A review,” IEEE Trans. Antenn. Propag. 45(3), 343–353 (1997).
[Crossref]

1995 (1)

R. L. Haupt, “An introduction to genetic algorithms for electromagnetics,” IEEE Antennas and Prop. Magazine 37(2), 7–15 (1995).
[Crossref]

1988 (1)

D. E. Goldberg and J. H. Holland, “Genetic algorithms and machine learning,” Mach. Learn. 3(2), 95–99 (1988).
[Crossref]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative value of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[Crossref]

1965 (1)

D. S. Lerner, “A wave polarization converter for circular polarization,” IEEE Trans. Antenn. Propag. 13(1), 3–7 (1965).
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1956 (1)

1948 (1)

1947 (1)

1941 (1)

Abbott, D.

W. Withayachumnankul, C. Fumeaux, and D. Abbott, “Planar array of electric-LC resonators with broadband tunability,” IEEE Antennas Wirel. Propag. Lett. 10, 577–580 (2011).
[Crossref]

Ahn, K.

M. Seo, J. Kyoung, H. Park, S. Koo, H. S. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H. T. Kim, N. Park, Q. H. Park, K. Ahn, and D. S. Kim, “Active terahertz nanoantennas based on VO2 phase transition,” Nano Lett. 10(6), 2064–2068 (2010).
[Crossref] [PubMed]

Ahn, Y. H.

M. Seo, J. Kyoung, H. Park, S. Koo, H. S. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H. T. Kim, N. Park, Q. H. Park, K. Ahn, and D. S. Kim, “Active terahertz nanoantennas based on VO2 phase transition,” Nano Lett. 10(6), 2064–2068 (2010).
[Crossref] [PubMed]

Aieta, F.

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

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (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(6054), 333–337 (2011).
[Crossref] [PubMed]

Alici, K. B.

A. B. Khanikaev, S. H. Mousavi, C. Wu, N. Dabidian, K. B. Alici, and G. Shvets, “Electromagnetically induced polarization conversion,” Opt. Commun. 285(16), 3423–3427 (2012).
[Crossref]

Alù, A.

Y. Zhao and A. Alù, “Tailoring the dispersion of plasmonic nanorods to realize broadband optical meta-waveplates,” Nano Lett. 13(3), 1086–1091 (2013).
[Crossref] [PubMed]

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat Commun 3, 870 (2012).
[Crossref] [PubMed]

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84(20), 205428 (2011).
[Crossref]

Atwater, H. A.

Averitt, R. D.

H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable terahertz metamaterials,” Phys. Rev. Lett. 103(14), 147401 (2009).
[Crossref] [PubMed]

A. C. Strikwerda, K. Fan, H. Tao, D. V. Pilon, X. Zhang, and R. D. Averitt, “Comparison of birefringent electric split-ring resonator and meanderline structures as quarter-wave plates at terahertz frequencies,” Opt. Express 17(1), 136–149 (2009).
[PubMed]

H.-T. Chen, J. F. O Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials,” Nat. Photonics 2(5), 295–298 (2008).
[Crossref]

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

Aydin, K.

Azad, A. K.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

H.-T. Chen, J. F. O Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials,” Nat. Photonics 2(5), 295–298 (2008).
[Crossref]

Bade, K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Bardou, N.

Q. Lévesque, M. Makhsiyan, P. Bouchon, F. Pardo, J. Jaeck, N. Bardou, and J. L. Pelouard, “Plasmonic planar antenna for wideband and efficient linear polarization conversion,” Appl. Phys. Lett. 104(11), 111105 (2014).
[Crossref]

Basov, D. N.

M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. Mumtaz Qazilbash, D. N. Basov, S. Ramanathan, and F. Caspasso, “Ultra-thin perfect absorber employing a tunable phase change material,” Appl. Phys. Lett. 101(22), 221101 (2012).
[Crossref]

M. D. Goldflam, T. Driscoll, B. Chapler, O. Khatib, N. Marie Jokerst, S. Palit, D. R. Smith, B. J. Kim, G. Seo, H. T. Kim, M. Di Ventra, and D. N. Basov, “Reconfigurable gradient index using VO2 memory metamaterials,” Appl. Phys. Lett. 99(4), 044103 (2011).
[Crossref]

Bayraktar, Z.

M. D. Gregory, Z. Bayraktar, and D. H. Werner, “Fast optimization of electromagnetic design problems using the covariance matrix adaptation evolutionary strategy,” IEEE Trans. Antenn. Propag. 59(4), 1275–1285 (2011).
[Crossref]

Belkin, M. A.

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat Commun 3, 870 (2012).
[Crossref] [PubMed]

Bernien, H.

M. Seo, J. Kyoung, H. Park, S. Koo, H. S. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H. T. Kim, N. Park, Q. H. Park, K. Ahn, and D. S. Kim, “Active terahertz nanoantennas based on VO2 phase transition,” Nano Lett. 10(6), 2064–2068 (2010).
[Crossref] [PubMed]

Blanchard, R.

M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. Mumtaz Qazilbash, D. N. Basov, S. Ramanathan, and F. Caspasso, “Ultra-thin perfect absorber employing a tunable phase change material,” Appl. Phys. Lett. 101(22), 221101 (2012).
[Crossref]

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

Boltasseva, A.

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]

Boreman, G. D.

Bossard, J. A.

Bouchon, P.

Q. Lévesque, M. Makhsiyan, P. Bouchon, F. Pardo, J. Jaeck, N. Bardou, and J. L. Pelouard, “Plasmonic planar antenna for wideband and efficient linear polarization conversion,” Appl. Phys. Lett. 104(11), 111105 (2014).
[Crossref]

Boyd, E. M.

Bozhevolnyi, S. I.

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Broadband plasmonic half-wave plates in reflection,” Opt. Lett. 38(4), 513–515 (2013).
[Crossref] [PubMed]

A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband focusing flat mirrors based on plasmonic gradient metasurfaces,” Nano Lett. 13(2), 829–834 (2013).
[Crossref] [PubMed]

Cahill, R.

E. Doumanis, G. Goussetis, J. L. Gomez-Tornero, R. Cahill, and V. Fusco, “Anisotropic impedance surfaces for linear to circular polarization conversion,” IEEE Trans. Antenn. Propag. 60(1), 212–219 (2012).
[Crossref]

M. Euler, V. Fusco, R. Cahill, and R. Dickie, “325 GHz single layer sub-millimeter wave FSS based split slot ring linear to circular polarization convertor,” IEEE Trans. Antenn. Propag. 58(7), 2457–2459 (2010).
[Crossref]

Cao, Y.

Z. Wei, Y. Cao, Y. Fan, X. Yu, and H. Li, “Broadband polarization transformation via enhanced asymmetric transmission through arrays of twisted complementary split-ring resonators,” Appl. Phys. Lett. 99(22), 221907 (2011).
[Crossref]

Capasso, F.

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

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (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(6054), 333–337 (2011).
[Crossref] [PubMed]

Caspasso, F.

M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. Mumtaz Qazilbash, D. N. Basov, S. Ramanathan, and F. Caspasso, “Ultra-thin perfect absorber employing a tunable phase change material,” Appl. Phys. Lett. 101(22), 221101 (2012).
[Crossref]

Chan, C. T.

C. Wu, H. Li, X. Yu, F. Li, H. Chen, and C. T. Chan, “Metallic helix array as a broadband wave plate,” Phys. Rev. Lett. 107(17), 177401 (2011).
[Crossref] [PubMed]

J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. 99(6), 063908 (2007).
[Crossref] [PubMed]

Chapler, B.

M. D. Goldflam, T. Driscoll, B. Chapler, O. Khatib, N. Marie Jokerst, S. Palit, D. R. Smith, B. J. Kim, G. Seo, H. T. Kim, M. Di Ventra, and D. N. Basov, “Reconfigurable gradient index using VO2 memory metamaterials,” Appl. Phys. Lett. 99(4), 044103 (2011).
[Crossref]

Chen, H.

C. Wu, H. Li, X. Yu, F. Li, H. Chen, and C. T. Chan, “Metallic helix array as a broadband wave plate,” Phys. Rev. Lett. 107(17), 177401 (2011).
[Crossref] [PubMed]

Chen, H. T.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

Chen, H.-T.

H.-T. Chen, J. F. O Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials,” Nat. Photonics 2(5), 295–298 (2008).
[Crossref]

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

Chen, K.

Q. Y. Wen, H. W. Zhang, Q. H. Yang, Y. S. Xie, K. Chen, and Y. L. Liu, “Terahertz metamaterials with VO 2 cut-wires for thermal tunability,” Appl. Phys. Lett. 97(2), 021111 (2010).
[Crossref]

Chen, W. T.

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

Chin, J. Y.

Choe, J. H.

M. Seo, J. Kyoung, H. Park, S. Koo, H. S. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H. T. Kim, N. Park, Q. H. Park, K. Ahn, and D. S. Kim, “Active terahertz nanoantennas based on VO2 phase transition,” Nano Lett. 10(6), 2064–2068 (2010).
[Crossref] [PubMed]

Chowdhury, D. R.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

Coffey, K. R.

Cui, T. J.

Dabidian, N.

A. B. Khanikaev, S. H. Mousavi, C. Wu, N. Dabidian, K. B. Alici, and G. Shvets, “Electromagnetically induced polarization conversion,” Opt. Commun. 285(16), 3423–3427 (2012).
[Crossref]

Dalvit, D. A.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

De Angelis, F.

Z. L. Samson, K. F. MacDonald, F. De Angelis, B. Gholipour, K. Knight, C. C. Huang, E. Di Fabrizio, D. W. Hewak, and N. I. Zheludev, “Metamaterial electro-optic switch of nanoscale thickness,” Appl. Phys. Lett. 96(14), 143105 (2010).
[Crossref]

Decker, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Di Fabrizio, E.

Z. L. Samson, K. F. MacDonald, F. De Angelis, B. Gholipour, K. Knight, C. C. Huang, E. Di Fabrizio, D. W. Hewak, and N. I. Zheludev, “Metamaterial electro-optic switch of nanoscale thickness,” Appl. Phys. Lett. 96(14), 143105 (2010).
[Crossref]

Di Ventra, M.

M. D. Goldflam, T. Driscoll, B. Chapler, O. Khatib, N. Marie Jokerst, S. Palit, D. R. Smith, B. J. Kim, G. Seo, H. T. Kim, M. Di Ventra, and D. N. Basov, “Reconfigurable gradient index using VO2 memory metamaterials,” Appl. Phys. Lett. 99(4), 044103 (2011).
[Crossref]

Dicken, M. J.

Dickie, R.

M. Euler, V. Fusco, R. Cahill, and R. Dickie, “325 GHz single layer sub-millimeter wave FSS based split slot ring linear to circular polarization convertor,” IEEE Trans. Antenn. Propag. 58(7), 2457–2459 (2010).
[Crossref]

Doumanis, E.

E. Doumanis, G. Goussetis, J. L. Gomez-Tornero, R. Cahill, and V. Fusco, “Anisotropic impedance surfaces for linear to circular polarization conversion,” IEEE Trans. Antenn. Propag. 60(1), 212–219 (2012).
[Crossref]

Driscoll, T.

M. D. Goldflam, T. Driscoll, B. Chapler, O. Khatib, N. Marie Jokerst, S. Palit, D. R. Smith, B. J. Kim, G. Seo, H. T. Kim, M. Di Ventra, and D. N. Basov, “Reconfigurable gradient index using VO2 memory metamaterials,” Appl. Phys. Lett. 99(4), 044103 (2011).
[Crossref]

Elliott, S. R.

J. Hegedüs and S. R. Elliott, “Microscopic origin of the fast crystallization ability of Ge-Sb-Te phase-change memory materials,” Nat. Mater. 7(5), 399–405 (2008).
[Crossref] [PubMed]

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(6067), 427 (2012).
[Crossref] [PubMed]

Eriksen, R. L.

A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband focusing flat mirrors based on plasmonic gradient metasurfaces,” Nano Lett. 13(2), 829–834 (2013).
[Crossref] [PubMed]

Euler, M.

M. Euler, V. Fusco, R. Cahill, and R. Dickie, “325 GHz single layer sub-millimeter wave FSS based split slot ring linear to circular polarization convertor,” IEEE Trans. Antenn. Propag. 58(7), 2457–2459 (2010).
[Crossref]

Fan, K.

Fan, Y.

Z. Wei, Y. Cao, Y. Fan, X. Yu, and H. Li, “Broadband polarization transformation via enhanced asymmetric transmission through arrays of twisted complementary split-ring resonators,” Appl. Phys. Lett. 99(22), 221907 (2011).
[Crossref]

Farouki, R. T.

R. T. Farouki, “The Bernstein polynomial basis: A centennial retrospective,” Comput. Aided Geom. Des. 29(6), 379–419 (2012).
[Crossref]

Fedotov, A.

E. V. Plum, A. Fedotov, and N. I. Zheludev, “Optical activity in extrinsically chiral metamaterial,” Appl. Phys. Lett. 93(19), 191911 (2008).
[Crossref]

Fedotov, V. A.

A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, “Giant gyrotropy due to electromagnetic-field coupling in a bilayered chiral structure,” Phys. Rev. Lett. 97(17), 177401 (2006).
[Crossref] [PubMed]

Feng, Y.

B. Zhu, Y. Feng, J. Zhao, C. Huang, and T. Jiang, “Switchable metamaterial reflector/absorber for different polarized electromagnetic waves,” Appl. Phys. Lett. 97(5), 051906 (2010).
[Crossref]

Frölich, A.

J. K. Gansel, M. Latzel, A. Frölich, J. Kaschke, M. Theil, and M. Wegener, “Tapered gold-helix metamaterials as improved circular polarizers,” Appl. Phys. Lett. 100(10), 101109 (2012).
[Crossref]

Fumeaux, C.

W. Withayachumnankul, C. Fumeaux, and D. Abbott, “Planar array of electric-LC resonators with broadband tunability,” IEEE Antennas Wirel. Propag. Lett. 10, 577–580 (2011).
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Figures (8)

Fig. 1
Fig. 1 Scattered field handedness, amplitude, and propagation direction for an anisotropic metasurface illuminated by a linearly polarized incident field.
Fig. 2
Fig. 2 A Bézier curve (blue) plotted as a function of x with n = 5 control points (black).
Fig. 3
Fig. 3 Plot of a m = 5, n = 5 Bézier surface. (a) Three dimensional surface plot (color) with control points shown (black). (b) Projection of positive values of the Bézier surface onto the z = 0 axis.
Fig. 4
Fig. 4 Performance comparison of pixelized structure GA optimizations versus Bézier surface CMA-ES optimizations. (a) Average mean and best fitness over 20 seeds for GA and CMA-ES optimizations. (b) Stokes parameters for the best GA optimized seed. (c) Stokes parameters for the best CMA-ES optimized seed.
Fig. 5
Fig. 5 Full wave simulations at normal incidence comparing the SR’s CP response versus that of the optimized Bézier metasurface (a). Full wave simulations of the Bézier metasurface’s CP response as a function of oblique incidence angle (b).
Fig. 6
Fig. 6 Normalized Stokes parameters as a function of azimuthal rotation when GST is in (a) the amorphous state and (b) the crystalline state.
Fig. 7
Fig. 7 Full wave simulation results of an optimized quarter-wave plate Bézier metasurface (inset) expressed in terms of the Stokes parameters (a) as a function of frequency and (b) as a function of azimuthal rotation.
Fig. 8
Fig. 8 Full wave simulation results of an optimized half-wave plate Bézier metasurface (inset) expressed in terms of the Stokes parameters (a) as a function of frequency and (b) as a function of azimuthal rotation.

Equations (31)

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( Γ xx Γ xy Γ yx Γ yy )=( a b c d ).
det( a λ s b c d λ s )=( a λ s )( d λ s )bc=0,
λ 1,2 s =a±| b | e iθ ,
θ= π 2 .
S=a= cos 2 ( θ 2 ),
a=1/2.
| a+ 1 2 | 2 + | b | 2 = ( 1 2 ) 2 .
λ 1,2 s = 1 2 ( 1±i ).
Γ φ=0 = 2 2 ( e i 3π 4 0 0 e i 3π 4 ).
Γ( φ )=R( φ ) Γ φ=0 R( φ ),
R( φ )=( cosφ sinφ sinφ cosφ ).
E ¯ inc = E 0 ( x ^ cosφ+ y ^ sinφ ) e i( kzωt ) ,
E inc =( 1 0 ),
E r = 1 2 ( 1 i i 1 )( 1 0 )= 1 2 ( 1 i )= 2 2 E RHCP
E t = 1 2 ( 1 i i 1 )( 1 0 )= 1 2 ( 1 i )= 2 2 E LHCP .
E r, ground = 1 2 ( 1 0 0 1 )( 1 i )= 1 2 ( 1 i ).
E r, total = ( 1 2 ( 1 i ) ) 2 + ( 1 2 ( 1 i ) ) 2 = 2 2 ( 1 i )= E RHCP ,
Γ φ= π 4 =( 1 2 Γ x + 1 2 Γ y 1 2 Γ x 1 2 Γ y 1 2 Γ x 1 2 Γ y 1 2 Γ x + 1 2 Γ y ).
E r =( 1 2 Γ x + 1 2 Γ y 1 2 Γ x 1 2 Γ y 1 2 Γ x 1 2 Γ y 1 2 Γ x + 1 2 Γ y )( 1 0 )=( 0 1 ).
Γ x =1 and Γ y =1.
E r = 1 2 ( 0 1 1 0 )( 1 0 )=( 0 1 )= E y .
P n ( x )= k=0 n f( k/n ) B k n ( x )
B k n ( x )=( n k ) x k (1x) ( nk ) , k=0,...,n.
P n ( x )= k=0 n C k B k n ( x )
P n,m ( x,y )= i=0 n j=0 m C i,j B i n ( x ) B j n ( y ).
C i,j =( C 11 C 12 C 1m C 21 C 22 C 2m C n1 C n2 C nm )
fitness= frequency ( (1I) 2 + (Q) 2 + (U) 2 + (1| V |) 2 ) ,
I= | E x | 2 + | E y | 2 ,
Q= | E x | 2 | E y | 2 ,
U=2Re ( E x E y * ),
V=2Im ( E x E y * ).

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