Abstract

We deduce by the monomode modal method the analytical expressions of the transmission and reflection Jones matrices of an infinitely conducting metallic screen periodically pierced by subwavelength holes. The study is restricted to normal incidence and to the case of neglected evanescent fields (far-field), which covers many common cases. When only one nondegenerate mode propagates in cavities, they take identical forms to those of a polarizer, with Fabry–Perot-like spectral resonant factors depending on the bigrating parameters. The isotropic or birefringent properties are then obtained when holes support two orthogonal polarization modes. This basic formalism is finally applied to design compact and efficient metallic half-wave plates.

© 2014 Optical Society of America

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  1. M. Iwanaga, “Photonic metamaterials: a new class of materials for manipulating light waves,” Sci. Tech. Adv. Mater. 13, 053002 (2012).
    [CrossRef]
  2. X.-F. Ren, P. Zhang, G.-P. Guo, Y.-F. Huang, Z.-W. Wang, and G.-C. Guo, “Polarization properties of subwavelength hole arrays consisting of rectangular holes,” Appl. Phys. B 91, 601–604 (2008).
    [CrossRef]
  3. Y.-L. Zhang, W. Jin, X.-Z. Dong, Z.-S. Zhao, and X.-M. Duan, “Asymmetric fishnet metamaterials with strong optical activity,” Opt. Express 20, 10776–10787 (2012).
    [CrossRef]
  4. J. Xu, T. Li, F. F. Lu, S. M. Wang, and S. N. Zhu, “Manipulating optical polarization by stereo plasmonic structure,” Opt. Express 19, 748–756 (2011).
    [CrossRef]
  5. Ph. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A 2, 48–51 (2000).
    [CrossRef]
  6. F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
    [CrossRef]
  7. P. Boyer and D. Van Labeke, “Analytical study of resonance conditions in planar resonators,” J. Opt. Soc. Am. A 29, 1659–1666 (2012).
    [CrossRef]
  8. R. C. McPhedran and D. Maystre, “On the theory and solar application of inductive grids,” Appl. Phys. 14, 1–20 (1977).
    [CrossRef]
  9. R. Petit, Electromagnetic Theory of Gratings, Topics in Current Physics (Springer-Verlag, 1980).
  10. R. Ulrich, K. F. Renk, and L. Genzel, “Tunable submillimeter interferometers of the Fabry–Perot type,” IEEE Trans. Microwave Theor. Tech. 11, 363–371 (1963).
    [CrossRef]
  11. R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37–55 (1967).
    [CrossRef]
  12. T. Li, S. M. Wang, J. X. Cao, H. Liu, and S. N. Zhu, “Cavity-involved plasmonic metamaterial for optical polarization conversion,” Appl. Phys. Lett. 97, 261113 (2010).
    [CrossRef]
  13. F. I. Baida, M. Boutria, R. Oussaid, and D. Van Labeke, “Enhanced-transmission metamaterials as anisotropic plates,” Phys. Rev. B 84, 035107 (2011).
    [CrossRef]
  14. M. Boutria, R. Oussaid, D. Van Labeke, and F. I. Baida, “Tunable artificial chirality with extraordinary transmission metamaterials,” Phys. Rev. B 86, 155428 (2012).
    [CrossRef]
  15. P. R. McIsaac, “Symmetry-induced modal characteristics of uniform waveguides I: summary of results,” IEEE Trans. Microwave Theor. Tech. 23, 421–429 (1975).
    [CrossRef]
  16. A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garca-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76, 195414 (2007).
    [CrossRef]
  17. 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, 221907 (2011).
    [CrossRef]
  18. N. Kanda, K. Konishi, and M. Kuwata-Gonokami, “Terahertz wave polarization rotation with double layered metal grating of complimentary chiral patterns,” Opt. Express 15, 11117 (2007).
    [CrossRef]
  19. R. Ortuno, C. Garcia-Meca, F. J. Rodriguez-Fortuno, J. Marti, and A. Martinez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075425 (2009).
    [CrossRef]
  20. T. D. Nguyen, S. Liu, Z. V. Vardeny, and A. Nahata, “Engineering the properties of terahertz filters using multilayer aperture arrays,” Opt. Express 19, 18678–18686 (2011).
    [CrossRef]
  21. A. Mary, S. G. Rodrigo, L. Martn-Moreno, and F. J. Garca-Vidal, “Holey metal films: from extraordinary transmission to negative-index behavior,” Phys. Rev. B 80, 165431 (2009).
    [CrossRef]
  22. T. W. H. Oates, B. Dastmalchi, C. Helgert, L. Reissmann, U. Huebner, E.-B. Kley, M. A. Verschuuren, I. Bergmair, T. Pertsch, K. Hinger, and K. Hinrichs, “Optical activity in sub-wavelength metallic grids and fishnet metamaterials in the conical mount,” Opt. Mater. Express 3, 439–451 (2013).
    [CrossRef]
  23. F. I. Baida and D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun. 209, 17–22 (2002).
    [CrossRef]
  24. Z. Chen, C. Wang, Y. Lou, B. Cao, and X. Li, “Quarter-wave plate with subwavelength rectangular annular arrays,” Opt. Commun. 297, 198–203 (2013).
    [CrossRef]

2013

2012

Y.-L. Zhang, W. Jin, X.-Z. Dong, Z.-S. Zhao, and X.-M. Duan, “Asymmetric fishnet metamaterials with strong optical activity,” Opt. Express 20, 10776–10787 (2012).
[CrossRef]

P. Boyer and D. Van Labeke, “Analytical study of resonance conditions in planar resonators,” J. Opt. Soc. Am. A 29, 1659–1666 (2012).
[CrossRef]

M. Iwanaga, “Photonic metamaterials: a new class of materials for manipulating light waves,” Sci. Tech. Adv. Mater. 13, 053002 (2012).
[CrossRef]

M. Boutria, R. Oussaid, D. Van Labeke, and F. I. Baida, “Tunable artificial chirality with extraordinary transmission metamaterials,” Phys. Rev. B 86, 155428 (2012).
[CrossRef]

2011

F. I. Baida, M. Boutria, R. Oussaid, and D. Van Labeke, “Enhanced-transmission metamaterials as anisotropic plates,” Phys. Rev. B 84, 035107 (2011).
[CrossRef]

J. Xu, T. Li, F. F. Lu, S. M. Wang, and S. N. Zhu, “Manipulating optical polarization by stereo plasmonic structure,” Opt. Express 19, 748–756 (2011).
[CrossRef]

T. D. Nguyen, S. Liu, Z. V. Vardeny, and A. Nahata, “Engineering the properties of terahertz filters using multilayer aperture arrays,” Opt. Express 19, 18678–18686 (2011).
[CrossRef]

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, 221907 (2011).
[CrossRef]

2010

T. Li, S. M. Wang, J. X. Cao, H. Liu, and S. N. Zhu, “Cavity-involved plasmonic metamaterial for optical polarization conversion,” Appl. Phys. Lett. 97, 261113 (2010).
[CrossRef]

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

2009

R. Ortuno, C. Garcia-Meca, F. J. Rodriguez-Fortuno, J. Marti, and A. Martinez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075425 (2009).
[CrossRef]

A. Mary, S. G. Rodrigo, L. Martn-Moreno, and F. J. Garca-Vidal, “Holey metal films: from extraordinary transmission to negative-index behavior,” Phys. Rev. B 80, 165431 (2009).
[CrossRef]

2008

X.-F. Ren, P. Zhang, G.-P. Guo, Y.-F. Huang, Z.-W. Wang, and G.-C. Guo, “Polarization properties of subwavelength hole arrays consisting of rectangular holes,” Appl. Phys. B 91, 601–604 (2008).
[CrossRef]

2007

N. Kanda, K. Konishi, and M. Kuwata-Gonokami, “Terahertz wave polarization rotation with double layered metal grating of complimentary chiral patterns,” Opt. Express 15, 11117 (2007).
[CrossRef]

A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garca-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76, 195414 (2007).
[CrossRef]

2002

F. I. Baida and D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun. 209, 17–22 (2002).
[CrossRef]

2000

Ph. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A 2, 48–51 (2000).
[CrossRef]

1977

R. C. McPhedran and D. Maystre, “On the theory and solar application of inductive grids,” Appl. Phys. 14, 1–20 (1977).
[CrossRef]

1975

P. R. McIsaac, “Symmetry-induced modal characteristics of uniform waveguides I: summary of results,” IEEE Trans. Microwave Theor. Tech. 23, 421–429 (1975).
[CrossRef]

1967

R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37–55 (1967).
[CrossRef]

1963

R. Ulrich, K. F. Renk, and L. Genzel, “Tunable submillimeter interferometers of the Fabry–Perot type,” IEEE Trans. Microwave Theor. Tech. 11, 363–371 (1963).
[CrossRef]

Astilean, S.

Ph. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A 2, 48–51 (2000).
[CrossRef]

Baida, F. I.

M. Boutria, R. Oussaid, D. Van Labeke, and F. I. Baida, “Tunable artificial chirality with extraordinary transmission metamaterials,” Phys. Rev. B 86, 155428 (2012).
[CrossRef]

F. I. Baida, M. Boutria, R. Oussaid, and D. Van Labeke, “Enhanced-transmission metamaterials as anisotropic plates,” Phys. Rev. B 84, 035107 (2011).
[CrossRef]

F. I. Baida and D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun. 209, 17–22 (2002).
[CrossRef]

Bergmair, I.

Boutria, M.

M. Boutria, R. Oussaid, D. Van Labeke, and F. I. Baida, “Tunable artificial chirality with extraordinary transmission metamaterials,” Phys. Rev. B 86, 155428 (2012).
[CrossRef]

F. I. Baida, M. Boutria, R. Oussaid, and D. Van Labeke, “Enhanced-transmission metamaterials as anisotropic plates,” Phys. Rev. B 84, 035107 (2011).
[CrossRef]

Boyer, P.

Cao, B.

Z. Chen, C. Wang, Y. Lou, B. Cao, and X. Li, “Quarter-wave plate with subwavelength rectangular annular arrays,” Opt. Commun. 297, 198–203 (2013).
[CrossRef]

Cao, J. X.

T. Li, S. M. Wang, J. X. Cao, H. Liu, and S. N. Zhu, “Cavity-involved plasmonic metamaterial for optical polarization conversion,” Appl. Phys. Lett. 97, 261113 (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, 221907 (2011).
[CrossRef]

Chen, Z.

Z. Chen, C. Wang, Y. Lou, B. Cao, and X. Li, “Quarter-wave plate with subwavelength rectangular annular arrays,” Opt. Commun. 297, 198–203 (2013).
[CrossRef]

Dastmalchi, B.

Dong, X.-Z.

Duan, X.-M.

Ebbesen, T. W.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

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, 221907 (2011).
[CrossRef]

Garca-Vidal, F. J.

A. Mary, S. G. Rodrigo, L. Martn-Moreno, and F. J. Garca-Vidal, “Holey metal films: from extraordinary transmission to negative-index behavior,” Phys. Rev. B 80, 165431 (2009).
[CrossRef]

A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garca-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76, 195414 (2007).
[CrossRef]

Garcia-Meca, C.

R. Ortuno, C. Garcia-Meca, F. J. Rodriguez-Fortuno, J. Marti, and A. Martinez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075425 (2009).
[CrossRef]

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

Genzel, L.

R. Ulrich, K. F. Renk, and L. Genzel, “Tunable submillimeter interferometers of the Fabry–Perot type,” IEEE Trans. Microwave Theor. Tech. 11, 363–371 (1963).
[CrossRef]

Guo, G.-C.

X.-F. Ren, P. Zhang, G.-P. Guo, Y.-F. Huang, Z.-W. Wang, and G.-C. Guo, “Polarization properties of subwavelength hole arrays consisting of rectangular holes,” Appl. Phys. B 91, 601–604 (2008).
[CrossRef]

Guo, G.-P.

X.-F. Ren, P. Zhang, G.-P. Guo, Y.-F. Huang, Z.-W. Wang, and G.-C. Guo, “Polarization properties of subwavelength hole arrays consisting of rectangular holes,” Appl. Phys. B 91, 601–604 (2008).
[CrossRef]

Helgert, C.

Hinger, K.

Hinrichs, K.

Huang, Y.-F.

X.-F. Ren, P. Zhang, G.-P. Guo, Y.-F. Huang, Z.-W. Wang, and G.-C. Guo, “Polarization properties of subwavelength hole arrays consisting of rectangular holes,” Appl. Phys. B 91, 601–604 (2008).
[CrossRef]

Huebner, U.

Hugonin, J. P.

Ph. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A 2, 48–51 (2000).
[CrossRef]

Iwanaga, M.

M. Iwanaga, “Photonic metamaterials: a new class of materials for manipulating light waves,” Sci. Tech. Adv. Mater. 13, 053002 (2012).
[CrossRef]

Jin, W.

Kanda, N.

Kley, E.-B.

Konishi, K.

Kuipers, L.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

Kuwata-Gonokami, M.

Lalanne, Ph.

Ph. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A 2, 48–51 (2000).
[CrossRef]

Li, H.

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, 221907 (2011).
[CrossRef]

Li, T.

J. Xu, T. Li, F. F. Lu, S. M. Wang, and S. N. Zhu, “Manipulating optical polarization by stereo plasmonic structure,” Opt. Express 19, 748–756 (2011).
[CrossRef]

T. Li, S. M. Wang, J. X. Cao, H. Liu, and S. N. Zhu, “Cavity-involved plasmonic metamaterial for optical polarization conversion,” Appl. Phys. Lett. 97, 261113 (2010).
[CrossRef]

Li, X.

Z. Chen, C. Wang, Y. Lou, B. Cao, and X. Li, “Quarter-wave plate with subwavelength rectangular annular arrays,” Opt. Commun. 297, 198–203 (2013).
[CrossRef]

Liu, H.

T. Li, S. M. Wang, J. X. Cao, H. Liu, and S. N. Zhu, “Cavity-involved plasmonic metamaterial for optical polarization conversion,” Appl. Phys. Lett. 97, 261113 (2010).
[CrossRef]

Liu, S.

Lou, Y.

Z. Chen, C. Wang, Y. Lou, B. Cao, and X. Li, “Quarter-wave plate with subwavelength rectangular annular arrays,” Opt. Commun. 297, 198–203 (2013).
[CrossRef]

Lu, F. F.

Marti, J.

R. Ortuno, C. Garcia-Meca, F. J. Rodriguez-Fortuno, J. Marti, and A. Martinez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075425 (2009).
[CrossRef]

Martinez, A.

R. Ortuno, C. Garcia-Meca, F. J. Rodriguez-Fortuno, J. Marti, and A. Martinez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075425 (2009).
[CrossRef]

Martin-Moreno, L.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garca-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76, 195414 (2007).
[CrossRef]

Martn-Moreno, L.

A. Mary, S. G. Rodrigo, L. Martn-Moreno, and F. J. Garca-Vidal, “Holey metal films: from extraordinary transmission to negative-index behavior,” Phys. Rev. B 80, 165431 (2009).
[CrossRef]

Mary, A.

A. Mary, S. G. Rodrigo, L. Martn-Moreno, and F. J. Garca-Vidal, “Holey metal films: from extraordinary transmission to negative-index behavior,” Phys. Rev. B 80, 165431 (2009).
[CrossRef]

A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garca-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76, 195414 (2007).
[CrossRef]

Maystre, D.

R. C. McPhedran and D. Maystre, “On the theory and solar application of inductive grids,” Appl. Phys. 14, 1–20 (1977).
[CrossRef]

McIsaac, P. R.

P. R. McIsaac, “Symmetry-induced modal characteristics of uniform waveguides I: summary of results,” IEEE Trans. Microwave Theor. Tech. 23, 421–429 (1975).
[CrossRef]

McPhedran, R. C.

R. C. McPhedran and D. Maystre, “On the theory and solar application of inductive grids,” Appl. Phys. 14, 1–20 (1977).
[CrossRef]

Möller, K. D.

Ph. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A 2, 48–51 (2000).
[CrossRef]

Nahata, A.

Nguyen, T. D.

Oates, T. W. H.

Ortuno, R.

R. Ortuno, C. Garcia-Meca, F. J. Rodriguez-Fortuno, J. Marti, and A. Martinez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075425 (2009).
[CrossRef]

Oussaid, R.

M. Boutria, R. Oussaid, D. Van Labeke, and F. I. Baida, “Tunable artificial chirality with extraordinary transmission metamaterials,” Phys. Rev. B 86, 155428 (2012).
[CrossRef]

F. I. Baida, M. Boutria, R. Oussaid, and D. Van Labeke, “Enhanced-transmission metamaterials as anisotropic plates,” Phys. Rev. B 84, 035107 (2011).
[CrossRef]

Palamaru, M.

Ph. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A 2, 48–51 (2000).
[CrossRef]

Pertsch, T.

Petit, R.

R. Petit, Electromagnetic Theory of Gratings, Topics in Current Physics (Springer-Verlag, 1980).

Reissmann, L.

Ren, X.-F.

X.-F. Ren, P. Zhang, G.-P. Guo, Y.-F. Huang, Z.-W. Wang, and G.-C. Guo, “Polarization properties of subwavelength hole arrays consisting of rectangular holes,” Appl. Phys. B 91, 601–604 (2008).
[CrossRef]

Renk, K. F.

R. Ulrich, K. F. Renk, and L. Genzel, “Tunable submillimeter interferometers of the Fabry–Perot type,” IEEE Trans. Microwave Theor. Tech. 11, 363–371 (1963).
[CrossRef]

Rodrigo, S. G.

A. Mary, S. G. Rodrigo, L. Martn-Moreno, and F. J. Garca-Vidal, “Holey metal films: from extraordinary transmission to negative-index behavior,” Phys. Rev. B 80, 165431 (2009).
[CrossRef]

A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garca-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76, 195414 (2007).
[CrossRef]

Rodriguez-Fortuno, F. J.

R. Ortuno, C. Garcia-Meca, F. J. Rodriguez-Fortuno, J. Marti, and A. Martinez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075425 (2009).
[CrossRef]

Ulrich, R.

R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37–55 (1967).
[CrossRef]

R. Ulrich, K. F. Renk, and L. Genzel, “Tunable submillimeter interferometers of the Fabry–Perot type,” IEEE Trans. Microwave Theor. Tech. 11, 363–371 (1963).
[CrossRef]

Van Labeke, D.

M. Boutria, R. Oussaid, D. Van Labeke, and F. I. Baida, “Tunable artificial chirality with extraordinary transmission metamaterials,” Phys. Rev. B 86, 155428 (2012).
[CrossRef]

P. Boyer and D. Van Labeke, “Analytical study of resonance conditions in planar resonators,” J. Opt. Soc. Am. A 29, 1659–1666 (2012).
[CrossRef]

F. I. Baida, M. Boutria, R. Oussaid, and D. Van Labeke, “Enhanced-transmission metamaterials as anisotropic plates,” Phys. Rev. B 84, 035107 (2011).
[CrossRef]

F. I. Baida and D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun. 209, 17–22 (2002).
[CrossRef]

Vardeny, Z. V.

Verschuuren, M. A.

Wang, C.

Z. Chen, C. Wang, Y. Lou, B. Cao, and X. Li, “Quarter-wave plate with subwavelength rectangular annular arrays,” Opt. Commun. 297, 198–203 (2013).
[CrossRef]

Wang, S. M.

J. Xu, T. Li, F. F. Lu, S. M. Wang, and S. N. Zhu, “Manipulating optical polarization by stereo plasmonic structure,” Opt. Express 19, 748–756 (2011).
[CrossRef]

T. Li, S. M. Wang, J. X. Cao, H. Liu, and S. N. Zhu, “Cavity-involved plasmonic metamaterial for optical polarization conversion,” Appl. Phys. Lett. 97, 261113 (2010).
[CrossRef]

Wang, Z.-W.

X.-F. Ren, P. Zhang, G.-P. Guo, Y.-F. Huang, Z.-W. Wang, and G.-C. Guo, “Polarization properties of subwavelength hole arrays consisting of rectangular holes,” Appl. Phys. B 91, 601–604 (2008).
[CrossRef]

Wei, Z.

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, 221907 (2011).
[CrossRef]

Xu, J.

Yu, X.

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, 221907 (2011).
[CrossRef]

Zhang, P.

X.-F. Ren, P. Zhang, G.-P. Guo, Y.-F. Huang, Z.-W. Wang, and G.-C. Guo, “Polarization properties of subwavelength hole arrays consisting of rectangular holes,” Appl. Phys. B 91, 601–604 (2008).
[CrossRef]

Zhang, Y.-L.

Zhao, Z.-S.

Zhu, S. N.

J. Xu, T. Li, F. F. Lu, S. M. Wang, and S. N. Zhu, “Manipulating optical polarization by stereo plasmonic structure,” Opt. Express 19, 748–756 (2011).
[CrossRef]

T. Li, S. M. Wang, J. X. Cao, H. Liu, and S. N. Zhu, “Cavity-involved plasmonic metamaterial for optical polarization conversion,” Appl. Phys. Lett. 97, 261113 (2010).
[CrossRef]

Appl. Phys.

R. C. McPhedran and D. Maystre, “On the theory and solar application of inductive grids,” Appl. Phys. 14, 1–20 (1977).
[CrossRef]

Appl. Phys. B

X.-F. Ren, P. Zhang, G.-P. Guo, Y.-F. Huang, Z.-W. Wang, and G.-C. Guo, “Polarization properties of subwavelength hole arrays consisting of rectangular holes,” Appl. Phys. B 91, 601–604 (2008).
[CrossRef]

Appl. Phys. Lett.

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, 221907 (2011).
[CrossRef]

T. Li, S. M. Wang, J. X. Cao, H. Liu, and S. N. Zhu, “Cavity-involved plasmonic metamaterial for optical polarization conversion,” Appl. Phys. Lett. 97, 261113 (2010).
[CrossRef]

IEEE Trans. Microwave Theor. Tech.

P. R. McIsaac, “Symmetry-induced modal characteristics of uniform waveguides I: summary of results,” IEEE Trans. Microwave Theor. Tech. 23, 421–429 (1975).
[CrossRef]

R. Ulrich, K. F. Renk, and L. Genzel, “Tunable submillimeter interferometers of the Fabry–Perot type,” IEEE Trans. Microwave Theor. Tech. 11, 363–371 (1963).
[CrossRef]

Infrared Phys.

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Figures (9)

Fig. 1.
Fig. 1.

Metallic screen periodically pierced by subwavelength holes.

Fig. 2.
Fig. 2.

Some examples of common SMBG pattern cross sections considered in the present work. E1 set: one hole with one nondegenerate mode. E2 set: one hole with two degenerate modes. E3 set: two holes, each having a nondegenerate mode.

Fig. 3.
Fig. 3.

Resonant coefficients α˜T,R(λ,ψ) versus wavelength for different values of ψ. The width of the rectangular hole is ax=0.2 and its length is ay=0.7. Other parameters are dx=dy=1, h/d=0.8, n1=n2=n3=1, and N=5.

Fig. 4.
Fig. 4.

Variation of λmax at |α˜T,R(λ,ψ)| maxima according to ψ. See Fig. 3 for parameter values.

Fig. 5.
Fig. 5.

Coupling analysis between the modes of each cavity for L-shape pattern made of two orthogonal rectangular apertures: τq,q|q(1) and |C˜q,q| versus λ/d. The transmission spectrum is plotted in gray color (scale not mentioned).

Fig. 6.
Fig. 6.

PD between txx and tyy versus λ/d and ay/d for a SMBG with C1v pattern made of two orthogonal rectangular apertures. The white contour plots show the couples (λ, ay) that correspond to |txx|=|tyy|. The black line corresponds to PD=π, the blue line to PD=π/2, and the red lines to |txx| maxima. Point A represents the case of a half-wave plate. The parameters are h/d=0.83, ax/d=0.73, cx/d=0.067, ay/d=0.58, by/d=0.2, and cy/d=0.45.

Fig. 7.
Fig. 7.

Design of one optimized half-wave plate: L1L3 and L computed at point A (see Fig. 6) as functions of h/d. The gray lines refer to equivalent Baida’s waveplate (h/d=0.83) [13] and to the optimized one (h/d=0.5484).

Fig. 8.
Fig. 8.

Variations of ay/d, Tmax, λmax/d, and PD at each minimum of L depicted in Fig. 7.

Fig. 9.
Fig. 9.

Transmission spectra of the retained metallic plate (h/d=0.5484 and ay/d=0.5008).

Equations (24)

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JT,R=α˜T,RJθ(pol,ex)ξT,RId
Jθ(pol,ex)=(cos2θcosθsinθcosθsinθsin2θ)
JjT,R=f˜jT,R(g˜0,tmg˜0,tm*g˜0,tmg˜0,te*g˜0,teg˜0,tm*g˜0,teg˜0,te*)ξT,R(1001),
f˜jT=4uη0(j)η˜[C˜(1)+η˜][C˜(3)+η˜]u2[C˜(1)η˜][C˜(3)η˜]
f˜jR=2η0(j){[C˜(j)+η˜]+u2[η˜C˜(j)]}[C˜(1)+η˜][C˜(3)+η˜]u2[C˜(1)η˜][C˜(3)η˜],
C˜(j)=ph˜p(j)·g˜p,
{Ep,σ(x,y)=eikp·ρSep,σ,Hp,σ(x,y)=η0ηp,σ(j)ezEp,σ(x,y),
ep,tm={kpkpif|kp|0,cosφGex+sinφGeyif|kp|=0,
ep,te={ezkpkpif|kp|0,sinφGex+cosφGeyif|kp|=0.
g˜p,σ=SEp,σ*(x,y)·E˜(x,y)ds=ep,σ·g˜p.
g˜p=SE˜(x,y)eikp·ρSds=g˜pvp,
ep,te·vp={mdxcos(ψp)ndysin(ψp)n2dy2+m2dx2if|kp|0,sin(φGψp)if|kp|=0,
ep,tm·vp={ndycos(ψp)+mdxsin(ψp)n2dy2+m2dx2if|kp|0,cos(φGψp)if|kp|=0,
α˜T,R(λ,ψ)=f˜jT,R(λ,ψ)|g˜0|2.
C˜(j)=nj|g˜0|2+p0h˜p(j)·g˜p,
{J1T=2[(ug˜)tM11+g˜tM21]g˜*η(1),J1R=2[g˜tM11+(ug˜)tM21]g˜*η(1)Id,J3T=2[(ug˜)tM12+g˜tM22]g˜*η(3),J3R=2[g˜tM21+(ug˜)tM22]g˜*η(3)Id,
M=(C˜1,1(1)+η˜1C˜1,2(1)[C˜1,1(1)η˜1]u1C˜1,2(1)u2C˜2,1(1)C˜2,2(1)+η˜2C˜2,1(1)u1[C˜2,2(1)η˜2]u2[C˜1,1(3)η˜1]u1C˜1,2(3)u2C˜1,1(3)+η˜1C˜1,2(3)C˜2,1(3)u1[C˜2,2(3)η˜2]u2C˜2,1(3)C˜2,2(3)+η˜2).
C˜q,q(j)=ph˜p,q(j)·g˜p,q,
JjT,R=q=12α˜T,R(λ,ψ(q))Jψ0,qφG(pol,ex)ξT,RId,
JjT,R=(α˜R,T(λ,ψ(1))ξT,R00α˜R,T(λ,ψ(2))ξT,R).
τq,q|q(j)=|C˜q,q(j)/C˜q,q(j)|,
T=12(|txx+txy|2+|tyx+tyy|2),
{L1=arg(txx/tyy)/π1=0:PD condition,L2=|txx||tyy|=0:identical transmission moduli condition,L3=|txx|1=0:total transmission condition,
L=l=13|Ll|.

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