Abstract

Dissymmetric, periodically nanostructured metal films can show non-reciprocal transmission of polarized light, in apparent violation of the Lorentz reciprocity theorem. The wave vector dependence of the extraordinary optical transmission in gold films with square and oblique subwavelength hole arrays was examined for the full range of polarized light input states. In normal incidence, the oblique lattice, in contrast to square lattice, showed strong asymmetric, non-reciprocal transmission of circularly polarized light. By analyzing the polarization of the input and the output with a complete Mueller matrix polarimeter the mechanisms that permits asymmetric transmission while preserving the requirement of electromagnetic reciprocity is revealed: the coupling of the linear anisotropies induced by misaligned surface plasmons in the film. The square lattice also shows asymmetric transmission at non-normal incidence, whenever the plane of incidence does not coincide with a mirror line.

© 2014 Optical Society of America

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  1. R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67(5), 717–754 (2004).
    [CrossRef]
  2. V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
    [CrossRef] [PubMed]
  3. V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, S. L. Prosvirnin, “Asymmetric transmission of light and enantiomerically sensitive plasmon resonance in planar chiral nanostructures,” Nano Lett. 7(7), 1996–1999 (2007).
    [CrossRef]
  4. A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, N. I. Zheludev, “Nanostructured metal film with asymmetric optical transmission,” Nano Lett. 8(9), 2940–2943 (2008).
    [CrossRef] [PubMed]
  5. R. Zhao, L. Zhang, J. Zhou, T. Kochny, C. M. Soukoulis, “Conjugated gammadion chiral metamaterial with uniaxial optical activity and negative refractive index,” Phys. Rev. B 83(3), 035105 (2011).
    [CrossRef]
  6. E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
    [CrossRef] [PubMed]
  7. B. Gompf, J. Braun, T. Weiss, H. Giessen, M. Dressel, U. Hübner, “Periodic nanostructures: spatial dispersion mimics chirality,” Phys. Rev. Lett. 106(18), 185501 (2011).
    [CrossRef] [PubMed]
  8. N. Berova, P. Polavarapu, K. Nakanishi, and R. W. Woody, eds., Comprehensive Chiroptical Spectroscopy, Volumes 1 & 2, (Wiley VCH, 2012).
  9. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
    [CrossRef]
  10. P. Lalanne, J. P. Hugonin, “Microscopic theory of the extraordinary optical transmission,” Nat. Phys. 2, 551 (2006).
    [CrossRef]
  11. F. van Beijnum, C. Rétif, C. B. Smiet, H. Liu, P. Lalanne, M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
    [CrossRef] [PubMed]
  12. D. A. Goldstein, Polarized Light (Marcel Dekker, New York,2003).
  13. O. Arteaga, “Number of independent parameters in the Mueller matrix representation of homogeneous depolarizing media,” Opt. Lett. 38(7), 1131–1133 (2013).
    [CrossRef] [PubMed]
  14. A. Schönhofer, H.-G. Kuball, “Symmetry properties of the Mueller matrix,” Chem. Phys. 115(2), 159–167 (1987).
    [CrossRef]
  15. O. Arteaga, J. Freudenthal, B. Wang, B. Kahr, “Mueller matrix polarimetry with four photoelastic modulators: theory and calibration,” Appl. Opt. 51(28), 6805–6817 (2012).
    [CrossRef] [PubMed]
  16. To determine the intensity of transmitted RCPL and LCPL it is necessary to multiply the output Stokes vector by the Mueller matrix of a right and left circular polarizer. This operation is equivalent to multiply the first Stokes parameters by the last (negated in the case of LCPL).
  17. R. Ossikovski, “Differential matrix formalism for depolarizing anisotropic media,” Opt. Lett. 36(12), 2330–2332 (2011).
    [CrossRef] [PubMed]
  18. O. Arteaga, B. Kahr, “Characterization of homogenous depolarizing media based on Mueller matrix differential decomposition,” Opt. Lett. 38(7), 1134–1136 (2013).
    [CrossRef] [PubMed]
  19. We use the word “dichroism” to be consistent with published literature. However, it should be reminded that the transmissions peaks observed in CD and LD can be due not only to absorption but also correspond to reflection/scattering peaks for the incoming light.
  20. J. Schellman, H. P. Jensen, “Optical spectroscopy of oriented molecules,” Chem. Rev. 87(6), 1359–1399 (1987).
    [CrossRef]
  21. O. Arteaga, A. Canillas, “Pseudopolar decomposition of the Jones and Mueller-Jones exponential polarization matrices,” J. Opt. Soc. Am. A 26(4), 783–793 (2009).
    [CrossRef] [PubMed]
  22. K. Claborn, A.-S. Chu, S.-H. Jang, F. Su, W. Kaminsky, B. Kahr, “Circular extinction imaging: determination of the absolute orientation of embedded chromophores in enantiomorphously twinned LiKSO4 crystals,” Cryst. Growth Des. 5(6), 2117–2123 (2005).
    [CrossRef]
  23. A. Shtukenberg, Y. Punin, and B. Kahr, Optically anomalous crystals, (Springer, 2007).
  24. A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, N. I. Zheludev, “Optical manifestations of planar chirality,” Phys. Rev. Lett. 90(10), 107404 (2003).
    [CrossRef] [PubMed]
  25. L. Wu, Z. Y. Yang, Y. Cheng, Z. Lu, P. Zhang, M. Zhao, R. Gong, X. Yuan, Y. Zheng, J. Duan, “Electromagnetic manifestation of chirality in layer-by-layer chiral metamaterials,” Opt. Express 21(5), 5239–5246 (2013).
    [CrossRef] [PubMed]
  26. C. Genet, T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
    [CrossRef] [PubMed]
  27. V. V. Temnov, U. Woggon, J. Dintinger, E. Devaux, T. W. Ebbesen, “Surface plasmon interferometry: measuring group velocity of surface plasmons,” Opt. Lett. 32(10), 1235–1237 (2007).
    [CrossRef] [PubMed]
  28. E. Altewischer, M. P. van Exter, J. P. Woerdman, “Polarization analysis of propagating surface plasmons in a subwavelength hole arrays,” J. Opt. Soc. Am. B 20(9), 1927 (2003).
    [CrossRef]
  29. K. L. van der Molen, F. B. Segerink, N. F. van Hulst, L. Kuipers, “Influence of hole size on theextraordinary transmission through subwavelength hole arrays,” Appl. Phys. Lett. 85(19), 4316–4318 (2004).
    [CrossRef]
  30. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
    [CrossRef] [PubMed]

2013 (3)

2012 (2)

O. Arteaga, J. Freudenthal, B. Wang, B. Kahr, “Mueller matrix polarimetry with four photoelastic modulators: theory and calibration,” Appl. Opt. 51(28), 6805–6817 (2012).
[CrossRef] [PubMed]

F. van Beijnum, C. Rétif, C. B. Smiet, H. Liu, P. Lalanne, M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
[CrossRef] [PubMed]

2011 (3)

R. Ossikovski, “Differential matrix formalism for depolarizing anisotropic media,” Opt. Lett. 36(12), 2330–2332 (2011).
[CrossRef] [PubMed]

R. Zhao, L. Zhang, J. Zhou, T. Kochny, C. M. Soukoulis, “Conjugated gammadion chiral metamaterial with uniaxial optical activity and negative refractive index,” Phys. Rev. B 83(3), 035105 (2011).
[CrossRef]

B. Gompf, J. Braun, T. Weiss, H. Giessen, M. Dressel, U. Hübner, “Periodic nanostructures: spatial dispersion mimics chirality,” Phys. Rev. Lett. 106(18), 185501 (2011).
[CrossRef] [PubMed]

2009 (2)

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[CrossRef] [PubMed]

O. Arteaga, A. Canillas, “Pseudopolar decomposition of the Jones and Mueller-Jones exponential polarization matrices,” J. Opt. Soc. Am. A 26(4), 783–793 (2009).
[CrossRef] [PubMed]

2008 (1)

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, N. I. Zheludev, “Nanostructured metal film with asymmetric optical transmission,” Nano Lett. 8(9), 2940–2943 (2008).
[CrossRef] [PubMed]

2007 (3)

V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, S. L. Prosvirnin, “Asymmetric transmission of light and enantiomerically sensitive plasmon resonance in planar chiral nanostructures,” Nano Lett. 7(7), 1996–1999 (2007).
[CrossRef]

C. Genet, T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
[CrossRef] [PubMed]

V. V. Temnov, U. Woggon, J. Dintinger, E. Devaux, T. W. Ebbesen, “Surface plasmon interferometry: measuring group velocity of surface plasmons,” Opt. Lett. 32(10), 1235–1237 (2007).
[CrossRef] [PubMed]

2006 (2)

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

P. Lalanne, J. P. Hugonin, “Microscopic theory of the extraordinary optical transmission,” Nat. Phys. 2, 551 (2006).
[CrossRef]

2005 (1)

K. Claborn, A.-S. Chu, S.-H. Jang, F. Su, W. Kaminsky, B. Kahr, “Circular extinction imaging: determination of the absolute orientation of embedded chromophores in enantiomorphously twinned LiKSO4 crystals,” Cryst. Growth Des. 5(6), 2117–2123 (2005).
[CrossRef]

2004 (2)

K. L. van der Molen, F. B. Segerink, N. F. van Hulst, L. Kuipers, “Influence of hole size on theextraordinary transmission through subwavelength hole arrays,” Appl. Phys. Lett. 85(19), 4316–4318 (2004).
[CrossRef]

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67(5), 717–754 (2004).
[CrossRef]

2003 (2)

A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, N. I. Zheludev, “Optical manifestations of planar chirality,” Phys. Rev. Lett. 90(10), 107404 (2003).
[CrossRef] [PubMed]

E. Altewischer, M. P. van Exter, J. P. Woerdman, “Polarization analysis of propagating surface plasmons in a subwavelength hole arrays,” J. Opt. Soc. Am. B 20(9), 1927 (2003).
[CrossRef]

2001 (1)

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

1987 (2)

A. Schönhofer, H.-G. Kuball, “Symmetry properties of the Mueller matrix,” Chem. Phys. 115(2), 159–167 (1987).
[CrossRef]

J. Schellman, H. P. Jensen, “Optical spectroscopy of oriented molecules,” Chem. Rev. 87(6), 1359–1399 (1987).
[CrossRef]

Altewischer, E.

Arteaga, O.

Bagnall, D. M.

A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, N. I. Zheludev, “Optical manifestations of planar chirality,” Phys. Rev. Lett. 90(10), 107404 (2003).
[CrossRef] [PubMed]

Braun, J.

B. Gompf, J. Braun, T. Weiss, H. Giessen, M. Dressel, U. Hübner, “Periodic nanostructures: spatial dispersion mimics chirality,” Phys. Rev. Lett. 106(18), 185501 (2011).
[CrossRef] [PubMed]

Canillas, A.

Chen, Y.

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[CrossRef] [PubMed]

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, N. I. Zheludev, “Nanostructured metal film with asymmetric optical transmission,” Nano Lett. 8(9), 2940–2943 (2008).
[CrossRef] [PubMed]

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

Cheng, Y.

Chu, A.-S.

K. Claborn, A.-S. Chu, S.-H. Jang, F. Su, W. Kaminsky, B. Kahr, “Circular extinction imaging: determination of the absolute orientation of embedded chromophores in enantiomorphously twinned LiKSO4 crystals,” Cryst. Growth Des. 5(6), 2117–2123 (2005).
[CrossRef]

Claborn, K.

K. Claborn, A.-S. Chu, S.-H. Jang, F. Su, W. Kaminsky, B. Kahr, “Circular extinction imaging: determination of the absolute orientation of embedded chromophores in enantiomorphously twinned LiKSO4 crystals,” Cryst. Growth Des. 5(6), 2117–2123 (2005).
[CrossRef]

Coles, H. J.

A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, N. I. Zheludev, “Optical manifestations of planar chirality,” Phys. Rev. Lett. 90(10), 107404 (2003).
[CrossRef] [PubMed]

Devaux, E.

Dintinger, J.

Dressel, M.

B. Gompf, J. Braun, T. Weiss, H. Giessen, M. Dressel, U. Hübner, “Periodic nanostructures: spatial dispersion mimics chirality,” Phys. Rev. Lett. 106(18), 185501 (2011).
[CrossRef] [PubMed]

Duan, J.

Ebbesen, T. W.

V. V. Temnov, U. Woggon, J. Dintinger, E. Devaux, T. W. Ebbesen, “Surface plasmon interferometry: measuring group velocity of surface plasmons,” Opt. Lett. 32(10), 1235–1237 (2007).
[CrossRef] [PubMed]

C. Genet, T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Fedotov, V. A.

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[CrossRef] [PubMed]

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, N. I. Zheludev, “Nanostructured metal film with asymmetric optical transmission,” Nano Lett. 8(9), 2940–2943 (2008).
[CrossRef] [PubMed]

V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, S. L. Prosvirnin, “Asymmetric transmission of light and enantiomerically sensitive plasmon resonance in planar chiral nanostructures,” Nano Lett. 7(7), 1996–1999 (2007).
[CrossRef]

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

Freudenthal, J.

García-Vidal, F. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

Genet, C.

C. Genet, T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
[CrossRef] [PubMed]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Giessen, H.

B. Gompf, J. Braun, T. Weiss, H. Giessen, M. Dressel, U. Hübner, “Periodic nanostructures: spatial dispersion mimics chirality,” Phys. Rev. Lett. 106(18), 185501 (2011).
[CrossRef] [PubMed]

Gompf, B.

B. Gompf, J. Braun, T. Weiss, H. Giessen, M. Dressel, U. Hübner, “Periodic nanostructures: spatial dispersion mimics chirality,” Phys. Rev. Lett. 106(18), 185501 (2011).
[CrossRef] [PubMed]

Gong, R.

Hübner, U.

B. Gompf, J. Braun, T. Weiss, H. Giessen, M. Dressel, U. Hübner, “Periodic nanostructures: spatial dispersion mimics chirality,” Phys. Rev. Lett. 106(18), 185501 (2011).
[CrossRef] [PubMed]

Hugonin, J. P.

P. Lalanne, J. P. Hugonin, “Microscopic theory of the extraordinary optical transmission,” Nat. Phys. 2, 551 (2006).
[CrossRef]

Jang, S.-H.

K. Claborn, A.-S. Chu, S.-H. Jang, F. Su, W. Kaminsky, B. Kahr, “Circular extinction imaging: determination of the absolute orientation of embedded chromophores in enantiomorphously twinned LiKSO4 crystals,” Cryst. Growth Des. 5(6), 2117–2123 (2005).
[CrossRef]

Jensen, H. P.

J. Schellman, H. P. Jensen, “Optical spectroscopy of oriented molecules,” Chem. Rev. 87(6), 1359–1399 (1987).
[CrossRef]

Kahr, B.

Kaminsky, W.

K. Claborn, A.-S. Chu, S.-H. Jang, F. Su, W. Kaminsky, B. Kahr, “Circular extinction imaging: determination of the absolute orientation of embedded chromophores in enantiomorphously twinned LiKSO4 crystals,” Cryst. Growth Des. 5(6), 2117–2123 (2005).
[CrossRef]

Khardikov, V. V.

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, N. I. Zheludev, “Nanostructured metal film with asymmetric optical transmission,” Nano Lett. 8(9), 2940–2943 (2008).
[CrossRef] [PubMed]

V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, S. L. Prosvirnin, “Asymmetric transmission of light and enantiomerically sensitive plasmon resonance in planar chiral nanostructures,” Nano Lett. 7(7), 1996–1999 (2007).
[CrossRef]

Kochny, T.

R. Zhao, L. Zhang, J. Zhou, T. Kochny, C. M. Soukoulis, “Conjugated gammadion chiral metamaterial with uniaxial optical activity and negative refractive index,” Phys. Rev. B 83(3), 035105 (2011).
[CrossRef]

Kuball, H.-G.

A. Schönhofer, H.-G. Kuball, “Symmetry properties of the Mueller matrix,” Chem. Phys. 115(2), 159–167 (1987).
[CrossRef]

Kuipers, L.

K. L. van der Molen, F. B. Segerink, N. F. van Hulst, L. Kuipers, “Influence of hole size on theextraordinary transmission through subwavelength hole arrays,” Appl. Phys. Lett. 85(19), 4316–4318 (2004).
[CrossRef]

Lalanne, P.

F. van Beijnum, C. Rétif, C. B. Smiet, H. Liu, P. Lalanne, M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
[CrossRef] [PubMed]

P. Lalanne, J. P. Hugonin, “Microscopic theory of the extraordinary optical transmission,” Nat. Phys. 2, 551 (2006).
[CrossRef]

Lezec, H. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Liu, H.

F. van Beijnum, C. Rétif, C. B. Smiet, H. Liu, P. Lalanne, M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
[CrossRef] [PubMed]

Liu, X. X.

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[CrossRef] [PubMed]

Lu, Z.

Martín-Moreno, L.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

Mladyonov, P. L.

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

Ossikovski, R.

Papakostas, A.

A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, N. I. Zheludev, “Optical manifestations of planar chirality,” Phys. Rev. Lett. 90(10), 107404 (2003).
[CrossRef] [PubMed]

Pellerin, K. M.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

Pendry, J. B.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

Plum, E.

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[CrossRef] [PubMed]

Potton, R. J.

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67(5), 717–754 (2004).
[CrossRef]

Potts, A.

A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, N. I. Zheludev, “Optical manifestations of planar chirality,” Phys. Rev. Lett. 90(10), 107404 (2003).
[CrossRef] [PubMed]

Prosvirnin, S. L.

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, N. I. Zheludev, “Nanostructured metal film with asymmetric optical transmission,” Nano Lett. 8(9), 2940–2943 (2008).
[CrossRef] [PubMed]

V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, S. L. Prosvirnin, “Asymmetric transmission of light and enantiomerically sensitive plasmon resonance in planar chiral nanostructures,” Nano Lett. 7(7), 1996–1999 (2007).
[CrossRef]

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

A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, N. I. Zheludev, “Optical manifestations of planar chirality,” Phys. Rev. Lett. 90(10), 107404 (2003).
[CrossRef] [PubMed]

Rétif, C.

F. van Beijnum, C. Rétif, C. B. Smiet, H. Liu, P. Lalanne, M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
[CrossRef] [PubMed]

Rogacheva, A. V.

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

Schellman, J.

J. Schellman, H. P. Jensen, “Optical spectroscopy of oriented molecules,” Chem. Rev. 87(6), 1359–1399 (1987).
[CrossRef]

Schönhofer, A.

A. Schönhofer, H.-G. Kuball, “Symmetry properties of the Mueller matrix,” Chem. Phys. 115(2), 159–167 (1987).
[CrossRef]

Schwanecke, A. S.

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, N. I. Zheludev, “Nanostructured metal film with asymmetric optical transmission,” Nano Lett. 8(9), 2940–2943 (2008).
[CrossRef] [PubMed]

V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, S. L. Prosvirnin, “Asymmetric transmission of light and enantiomerically sensitive plasmon resonance in planar chiral nanostructures,” Nano Lett. 7(7), 1996–1999 (2007).
[CrossRef]

Segerink, F. B.

K. L. van der Molen, F. B. Segerink, N. F. van Hulst, L. Kuipers, “Influence of hole size on theextraordinary transmission through subwavelength hole arrays,” Appl. Phys. Lett. 85(19), 4316–4318 (2004).
[CrossRef]

Smiet, C. B.

F. van Beijnum, C. Rétif, C. B. Smiet, H. Liu, P. Lalanne, M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
[CrossRef] [PubMed]

Soukoulis, C. M.

R. Zhao, L. Zhang, J. Zhou, T. Kochny, C. M. Soukoulis, “Conjugated gammadion chiral metamaterial with uniaxial optical activity and negative refractive index,” Phys. Rev. B 83(3), 035105 (2011).
[CrossRef]

Su, F.

K. Claborn, A.-S. Chu, S.-H. Jang, F. Su, W. Kaminsky, B. Kahr, “Circular extinction imaging: determination of the absolute orientation of embedded chromophores in enantiomorphously twinned LiKSO4 crystals,” Cryst. Growth Des. 5(6), 2117–2123 (2005).
[CrossRef]

Temnov, V. V.

Thio, T.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Tsai, D. P.

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[CrossRef] [PubMed]

van Beijnum, F.

F. van Beijnum, C. Rétif, C. B. Smiet, H. Liu, P. Lalanne, M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
[CrossRef] [PubMed]

van der Molen, K. L.

K. L. van der Molen, F. B. Segerink, N. F. van Hulst, L. Kuipers, “Influence of hole size on theextraordinary transmission through subwavelength hole arrays,” Appl. Phys. Lett. 85(19), 4316–4318 (2004).
[CrossRef]

van Exter, M. P.

F. van Beijnum, C. Rétif, C. B. Smiet, H. Liu, P. Lalanne, M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
[CrossRef] [PubMed]

E. Altewischer, M. P. van Exter, J. P. Woerdman, “Polarization analysis of propagating surface plasmons in a subwavelength hole arrays,” J. Opt. Soc. Am. B 20(9), 1927 (2003).
[CrossRef]

van Hulst, N. F.

K. L. van der Molen, F. B. Segerink, N. F. van Hulst, L. Kuipers, “Influence of hole size on theextraordinary transmission through subwavelength hole arrays,” Appl. Phys. Lett. 85(19), 4316–4318 (2004).
[CrossRef]

Wang, B.

Weiss, T.

B. Gompf, J. Braun, T. Weiss, H. Giessen, M. Dressel, U. Hübner, “Periodic nanostructures: spatial dispersion mimics chirality,” Phys. Rev. Lett. 106(18), 185501 (2011).
[CrossRef] [PubMed]

Woerdman, J. P.

Woggon, U.

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Wu, L.

Yang, Z. Y.

Yuan, X.

Zhang, L.

R. Zhao, L. Zhang, J. Zhou, T. Kochny, C. M. Soukoulis, “Conjugated gammadion chiral metamaterial with uniaxial optical activity and negative refractive index,” Phys. Rev. B 83(3), 035105 (2011).
[CrossRef]

Zhang, P.

Zhao, M.

Zhao, R.

R. Zhao, L. Zhang, J. Zhou, T. Kochny, C. M. Soukoulis, “Conjugated gammadion chiral metamaterial with uniaxial optical activity and negative refractive index,” Phys. Rev. B 83(3), 035105 (2011).
[CrossRef]

Zheludev, N. I.

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[CrossRef] [PubMed]

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, N. I. Zheludev, “Nanostructured metal film with asymmetric optical transmission,” Nano Lett. 8(9), 2940–2943 (2008).
[CrossRef] [PubMed]

V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, S. L. Prosvirnin, “Asymmetric transmission of light and enantiomerically sensitive plasmon resonance in planar chiral nanostructures,” Nano Lett. 7(7), 1996–1999 (2007).
[CrossRef]

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

A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, N. I. Zheludev, “Optical manifestations of planar chirality,” Phys. Rev. Lett. 90(10), 107404 (2003).
[CrossRef] [PubMed]

Zheng, Y.

Zhou, J.

R. Zhao, L. Zhang, J. Zhou, T. Kochny, C. M. Soukoulis, “Conjugated gammadion chiral metamaterial with uniaxial optical activity and negative refractive index,” Phys. Rev. B 83(3), 035105 (2011).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

K. L. van der Molen, F. B. Segerink, N. F. van Hulst, L. Kuipers, “Influence of hole size on theextraordinary transmission through subwavelength hole arrays,” Appl. Phys. Lett. 85(19), 4316–4318 (2004).
[CrossRef]

Chem. Phys. (1)

A. Schönhofer, H.-G. Kuball, “Symmetry properties of the Mueller matrix,” Chem. Phys. 115(2), 159–167 (1987).
[CrossRef]

Chem. Rev. (1)

J. Schellman, H. P. Jensen, “Optical spectroscopy of oriented molecules,” Chem. Rev. 87(6), 1359–1399 (1987).
[CrossRef]

Cryst. Growth Des. (1)

K. Claborn, A.-S. Chu, S.-H. Jang, F. Su, W. Kaminsky, B. Kahr, “Circular extinction imaging: determination of the absolute orientation of embedded chromophores in enantiomorphously twinned LiKSO4 crystals,” Cryst. Growth Des. 5(6), 2117–2123 (2005).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Nano Lett. (2)

V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, S. L. Prosvirnin, “Asymmetric transmission of light and enantiomerically sensitive plasmon resonance in planar chiral nanostructures,” Nano Lett. 7(7), 1996–1999 (2007).
[CrossRef]

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, N. I. Zheludev, “Nanostructured metal film with asymmetric optical transmission,” Nano Lett. 8(9), 2940–2943 (2008).
[CrossRef] [PubMed]

Nat. Phys. (1)

P. Lalanne, J. P. Hugonin, “Microscopic theory of the extraordinary optical transmission,” Nat. Phys. 2, 551 (2006).
[CrossRef]

Nature (3)

F. van Beijnum, C. Rétif, C. B. Smiet, H. Liu, P. Lalanne, M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

C. Genet, T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. B (1)

R. Zhao, L. Zhang, J. Zhou, T. Kochny, C. M. Soukoulis, “Conjugated gammadion chiral metamaterial with uniaxial optical activity and negative refractive index,” Phys. Rev. B 83(3), 035105 (2011).
[CrossRef]

Phys. Rev. Lett. (5)

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[CrossRef] [PubMed]

B. Gompf, J. Braun, T. Weiss, H. Giessen, M. Dressel, U. Hübner, “Periodic nanostructures: spatial dispersion mimics chirality,” Phys. Rev. Lett. 106(18), 185501 (2011).
[CrossRef] [PubMed]

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

A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, N. I. Zheludev, “Optical manifestations of planar chirality,” Phys. Rev. Lett. 90(10), 107404 (2003).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67(5), 717–754 (2004).
[CrossRef]

Other (5)

D. A. Goldstein, Polarized Light (Marcel Dekker, New York,2003).

N. Berova, P. Polavarapu, K. Nakanishi, and R. W. Woody, eds., Comprehensive Chiroptical Spectroscopy, Volumes 1 & 2, (Wiley VCH, 2012).

We use the word “dichroism” to be consistent with published literature. However, it should be reminded that the transmissions peaks observed in CD and LD can be due not only to absorption but also correspond to reflection/scattering peaks for the incoming light.

To determine the intensity of transmitted RCPL and LCPL it is necessary to multiply the output Stokes vector by the Mueller matrix of a right and left circular polarizer. This operation is equivalent to multiply the first Stokes parameters by the last (negated in the case of LCPL).

A. Shtukenberg, Y. Punin, and B. Kahr, Optically anomalous crystals, (Springer, 2007).

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Figures (13)

Fig. 1
Fig. 1

Scanning electron michrographs.Square (left) and oblique (right) arrays. The lattice parameters are a = 530 nm, b = 730 nm, d = 250 nm and φ = 65°. The thickness of the gold layer is 250 nm.

Fig. 2
Fig. 2

Normalized spectroscopic Mueller matrix measurement of the oblique array lattice in the forward and backward configurations.

Fig. 3
Fig. 3

Intensity of transmitted LCPL and RCPL in the forward and backward configurations for the oblique hole array illuminated with LCPL and RCPL. The difference in the line shape between (a) and (b) is a manifestation of the natural optical activity contribution.

Fig. 4
Fig. 4

Reciprocal (a,b) and non-reciprocal (c,d) contributions to the chiroptical response of the oblique array of nanoholes.(a) CD, (b) CB, (c) µ and (d) ν are compared in the forward (red, from gold to substrate) and backward (blue) directions. (a,b) emphasize that the film with an oblique array displays some natural, wave vector invariant, optical activity, as would any 3D enantiomorph. (c,d) emphasize the “apparent” non-reciprocal chiroptical contributions, that reverse sign as the wave vector is reversed. These contributions are retrieved from the Mueller calculus as combinations of L and L’.

Fig. 5
Fig. 5

Asymmetric transmission of CPL. Cartoon of the transmission of CPL through an ideal 2D oblique array. The solid black arrows represent the portion of the transmitted light that has a polarization different from the incoming. In the limit of a 2D material, the intensity of RCPL and LCPL transmitted through the sample is the same (because no optical activity is possible) and independent of the sense of wavevector. The different amounts of other forms of polarized light generated for LCPL and RCPL in forward and backward configurations give rise to the asymmetric transmission.

Fig. 6
Fig. 6

SPs in hole arrays with plane group symmetries p4mm (a) and p2 (b).Colored double-headed arrows represent plasmons of unique energies. In (a) at normal incidence, there is perfect polarization preservation; M is proportional to the identity matrix. For (b), the optically response is anisotropic, with non-zero linear dichroism and linear birefringence. For SP modes associated with similar lattice constants (w and v), the plasmon moments are similar, and the transmitted is affected by the scattering of distinct, misaligned SPs. Reversing the sense of the wavector initially propagating along positive Z is equivalent to rotating 180° around Y the sample (c). In the laboratory/instrument system of reference, a SP mode initially oriented at 135° has an orientation of 45° after the sample turn.

Fig. 7
Fig. 7

Oblique incidence measurements through the square nanohole array. Angle of incidence θ and azimuthal orientation α (a). Lattice projections as function of α and θ (b). Polar plots measured at 615 nm and 640 nm showing the evolution of µ and CD with α and θ (c). Asymmetric transmission (a direct consequence of µ) is only non-zero for values of α in which the square lattice has an oblique projection.

Fig. 8
Fig. 8

Normalized Mueller matrix mapping at 495 nm.

Fig. 9
Fig. 9

Normalized Mueller matrix mapping at 570 nm.

Fig. 10
Fig. 10

Normalized Mueller matrix mapping at 615 nm.

Fig. 11
Fig. 11

Normalized Mueller matrix mapping at 640 nm.

Fig. 12
Fig. 12

Normalized Mueller matrix mapping at 687 nm.

Fig. 13
Fig. 13

Normalized Mueller matrix mapping at 750 nm.

Equations (3)

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M B =O M F T O 1 ,
μ=(LBLD'LB'LD)/2
ν=(LBLB'+LD'LD)/2

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