Abstract

Understanding gyrotropic effects in the mid-infrared (MIR) spectral range is of high technological interest because it is the fingerprint region of many metamaterials and organic compounds. We present experimental and simulated ellipsometric measurements of gyrotropy in the MIR region upon reflection from an ordered array of split-ring resonators, which are inherently non-chiral. We use the symmetry properties of the Mueller matrix for interpretation of the ellipsometric measurements and to identify gyrotropy. When the plane of incidence coincides with the low-symmetry optical axis, we observe gyrotropy at oblique incidence. The origin of the gyrotropy is explained by considering not only the electric dipole–magnetic dipole interaction, as in natural optical activity, but by retaining the electric dipole–electric quadrupole contributions. In isotropic systems these average to zero, however they are significant in ordered systems such as crystals and metamaterials.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]
  4. K. Claborn, C. Isborn, W. Kaminsky, and B. Kahr, “Optical rotation of achiral compounds,” Angew. Chem. Int. Ed. Engl. 47(31), 5706–5717 (2008).
    [Crossref] [PubMed]
  5. E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]

2014 (1)

T. W. H. Oates, T. Shaykhutdinov, T. Wagner, A. Furchner, and K. Hinrichs, “Gyrotropy in achiral materials: the coupled oscillator model,” Adv. Mater. 26(42), 7197–7201 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (3)

T. W. H. Oates, B. Dastmalchi, G. Isic, S. Tollabimazraehno, C. Helgert, T. Pertsch, E. B. Kley, M. A. Verschuuren, I. Bergmair, K. Hingerl, and K. Hinrichs, “Oblique incidence ellipsometric characterization and the substrate dependence of visible frequency fishnet metamaterials,” Opt. Express 20(10), 11166–11177 (2012).
[Crossref] [PubMed]

M. M. Jakovljević, G. Isic, B. Vasic, T. W. H. Oates, K. Hinrichs, I. Bergmair, K. Hingerl, and R. Gajic, “Spectroscopic ellipsometry of split ring resonators at infrared frequencies,” Appl. Phys. Lett. 100(16), 161105 (2012).
[Crossref]

M. Ren, E. Plum, J. Xu, and N. I. Zheludev, “Giant nonlinear optical activity in a plasmonic metamaterial,” Nat Commun 3, 833 (2012).
[Crossref] [PubMed]

2011 (4)

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

I. Bergmair, B. Dastmalchi, M. Bergmair, A. Saeed, W. Hilber, G. Hesser, C. Helgert, E. Pshenay-Severin, T. Pertsch, E. B. Kley, U. Hübner, N. H. Shen, R. Penciu, M. Kafesaki, C. M. Soukoulis, K. Hingerl, M. Muehlberger, and R. Schoeftner, “Single and multilayer metamaterials fabricated by nanoimprint lithography,” Nanotechnology 22(32), 325301 (2011).
[Crossref] [PubMed]

T. W. H. Oates, H. Wormeester, and H. Arwin, “Characterization of plasmonic effects in thin films and metamaterials using spectroscopic ellipsometry,” Prog. Surf. Sci. 86(11–12), 328–376 (2011).
[Crossref]

T. W. H. Oates, M. Ranjan, S. Facsko, and H. Arwin, “Highly anisotropic effective dielectric functions of silver nanoparticle arrays,” Opt. Express 19(3), 2014–2028 (2011).
[Crossref] [PubMed]

2010 (1)

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref] [PubMed]

2009 (1)

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

2008 (2)

2007 (2)

W. J. Padilla, “Group theoretical description of artificial electromagnetic metamaterials,” Opt. Express 15(4), 1639–1646 (2007).
[Crossref] [PubMed]

C. Isborn, K. Claborn, and B. Kahr, “The optical rotatory power of water,” J. Phys. Chem. A 111(32), 7800–7804 (2007).
[Crossref] [PubMed]

2006 (3)

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

C. Gautier and T. Bürgi, “Chiral N-isobutyryl-cysteine protected gold nanoparticles: preparation, size selection, and optical activity in the UV-vis and infrared,” J. Am. Chem. Soc. 128(34), 11079–11087 (2006).
[Crossref] [PubMed]

M. Krykunov, M. D. Kundrat, and J. Autschbach, “Calculation of circular dichroism spectra from optical rotatory dispersion, and vice versa, as complementary tools for theoretical studies of optical activity using time-dependent density functional theory,” J. Chem. Phys. 125(19), 194110 (2006).
[Crossref] [PubMed]

2002 (1)

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B 65(14), 144440 (2002).
[Crossref]

1991 (1)

P. A. Thomas, I. J. Tebbutt, and A. M. Glazer, “Potassium titanyl phosphate, KTiOPO4. I. Experimental investigation of optical gyration, absolute optical chirality and twinning,” J. Appl. Cryst. 24(5), 963–967 (1991).
[Crossref]

1990 (1)

1987 (1)

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

1971 (1)

A. D. Buckingham and M. B. Dunn, “Optical activity of oriented molecules,” J. Chem. Soc. A 0, 1988–1991 (1971).
[Crossref]

Arteaga, O.

O. Arteaga, “Useful Mueller matrix symmetries for ellipsometry,” Thin Solid Films. in press).

Arwin, H.

T. W. H. Oates, H. Wormeester, and H. Arwin, “Characterization of plasmonic effects in thin films and metamaterials using spectroscopic ellipsometry,” Prog. Surf. Sci. 86(11–12), 328–376 (2011).
[Crossref]

T. W. H. Oates, M. Ranjan, S. Facsko, and H. Arwin, “Highly anisotropic effective dielectric functions of silver nanoparticle arrays,” Opt. Express 19(3), 2014–2028 (2011).
[Crossref] [PubMed]

Autschbach, J.

M. Krykunov, M. D. Kundrat, and J. Autschbach, “Calculation of circular dichroism spectra from optical rotatory dispersion, and vice versa, as complementary tools for theoretical studies of optical activity using time-dependent density functional theory,” J. Chem. Phys. 125(19), 194110 (2006).
[Crossref] [PubMed]

Badoz, J.

Barron, L. D.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref] [PubMed]

Baumberg, J. J.

V. K. Valev, J. J. Baumberg, C. Sibilia, and T. Verbiest, “Chirality and chiroptical effects in plasmonic nanostructures: fundamentals, recent progress, and outlook,” Adv. Mater. 25(18), 2517–2534 (2013).
[Crossref] [PubMed]

Bergmair, I.

T. W. H. Oates, B. Dastmalchi, C. Helgert, L. Reissmann, U. Huebner, E. B. Kley, M. A. Verschuuren, I. Bergmair, T. Pertsch, K. Hingerl, and K. Hinrichs, “Optical activity in sub-wavelength metallic grids and fishnet metamaterials in the conical mount,” Opt. Mater. Express 3(4), 439–451 (2013).
[Crossref]

M. M. Jakovljević, G. Isic, B. Vasic, T. W. H. Oates, K. Hinrichs, I. Bergmair, K. Hingerl, and R. Gajic, “Spectroscopic ellipsometry of split ring resonators at infrared frequencies,” Appl. Phys. Lett. 100(16), 161105 (2012).
[Crossref]

T. W. H. Oates, B. Dastmalchi, G. Isic, S. Tollabimazraehno, C. Helgert, T. Pertsch, E. B. Kley, M. A. Verschuuren, I. Bergmair, K. Hingerl, and K. Hinrichs, “Oblique incidence ellipsometric characterization and the substrate dependence of visible frequency fishnet metamaterials,” Opt. Express 20(10), 11166–11177 (2012).
[Crossref] [PubMed]

I. Bergmair, B. Dastmalchi, M. Bergmair, A. Saeed, W. Hilber, G. Hesser, C. Helgert, E. Pshenay-Severin, T. Pertsch, E. B. Kley, U. Hübner, N. H. Shen, R. Penciu, M. Kafesaki, C. M. Soukoulis, K. Hingerl, M. Muehlberger, and R. Schoeftner, “Single and multilayer metamaterials fabricated by nanoimprint lithography,” Nanotechnology 22(32), 325301 (2011).
[Crossref] [PubMed]

Bergmair, M.

I. Bergmair, B. Dastmalchi, M. Bergmair, A. Saeed, W. Hilber, G. Hesser, C. Helgert, E. Pshenay-Severin, T. Pertsch, E. B. Kley, U. Hübner, N. H. Shen, R. Penciu, M. Kafesaki, C. M. Soukoulis, K. Hingerl, M. Muehlberger, and R. Schoeftner, “Single and multilayer metamaterials fabricated by nanoimprint lithography,” Nanotechnology 22(32), 325301 (2011).
[Crossref] [PubMed]

Braun, J.

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

Buckingham, A. D.

A. D. Buckingham and M. B. Dunn, “Optical activity of oriented molecules,” J. Chem. Soc. A 0, 1988–1991 (1971).
[Crossref]

Bürgi, T.

C. Gautier and T. Bürgi, “Chiral N-isobutyryl-cysteine protected gold nanoparticles: preparation, size selection, and optical activity in the UV-vis and infrared,” J. Am. Chem. Soc. 128(34), 11079–11087 (2006).
[Crossref] [PubMed]

Carpy, T.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref] [PubMed]

Chen, Y.

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

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

Claborn, K.

K. Claborn, C. Isborn, W. Kaminsky, and B. Kahr, “Optical rotation of achiral compounds,” Angew. Chem. Int. Ed. Engl. 47(31), 5706–5717 (2008).
[Crossref] [PubMed]

C. Isborn, K. Claborn, and B. Kahr, “The optical rotatory power of water,” J. Phys. Chem. A 111(32), 7800–7804 (2007).
[Crossref] [PubMed]

Dastmalchi, B.

Dressel, M.

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

Dunn, M. B.

A. D. Buckingham and M. B. Dunn, “Optical activity of oriented molecules,” J. Chem. Soc. A 0, 1988–1991 (1971).
[Crossref]

Facsko, S.

Fedotov, V. A.

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

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

Furchner, A.

T. W. H. Oates, T. Shaykhutdinov, T. Wagner, A. Furchner, and K. Hinrichs, “Gyrotropy in achiral materials: the coupled oscillator model,” Adv. Mater. 26(42), 7197–7201 (2014).
[Crossref] [PubMed]

Gadegaard, N.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref] [PubMed]

Gajic, R.

M. M. Jakovljević, G. Isic, B. Vasic, T. W. H. Oates, K. Hinrichs, I. Bergmair, K. Hingerl, and R. Gajic, “Spectroscopic ellipsometry of split ring resonators at infrared frequencies,” Appl. Phys. Lett. 100(16), 161105 (2012).
[Crossref]

Gautier, C.

C. Gautier and T. Bürgi, “Chiral N-isobutyryl-cysteine protected gold nanoparticles: preparation, size selection, and optical activity in the UV-vis and infrared,” J. Am. Chem. Soc. 128(34), 11079–11087 (2006).
[Crossref] [PubMed]

Giessen, H.

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

Glazer, A. M.

P. A. Thomas, I. J. Tebbutt, and A. M. Glazer, “Potassium titanyl phosphate, KTiOPO4. I. Experimental investigation of optical gyration, absolute optical chirality and twinning,” J. Appl. Cryst. 24(5), 963–967 (1991).
[Crossref]

Gompf, B.

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

Helgert, C.

Hendry, E.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref] [PubMed]

Hesser, G.

I. Bergmair, B. Dastmalchi, M. Bergmair, A. Saeed, W. Hilber, G. Hesser, C. Helgert, E. Pshenay-Severin, T. Pertsch, E. B. Kley, U. Hübner, N. H. Shen, R. Penciu, M. Kafesaki, C. M. Soukoulis, K. Hingerl, M. Muehlberger, and R. Schoeftner, “Single and multilayer metamaterials fabricated by nanoimprint lithography,” Nanotechnology 22(32), 325301 (2011).
[Crossref] [PubMed]

Hilber, W.

I. Bergmair, B. Dastmalchi, M. Bergmair, A. Saeed, W. Hilber, G. Hesser, C. Helgert, E. Pshenay-Severin, T. Pertsch, E. B. Kley, U. Hübner, N. H. Shen, R. Penciu, M. Kafesaki, C. M. Soukoulis, K. Hingerl, M. Muehlberger, and R. Schoeftner, “Single and multilayer metamaterials fabricated by nanoimprint lithography,” Nanotechnology 22(32), 325301 (2011).
[Crossref] [PubMed]

Hingerl, K.

T. W. H. Oates, B. Dastmalchi, C. Helgert, L. Reissmann, U. Huebner, E. B. Kley, M. A. Verschuuren, I. Bergmair, T. Pertsch, K. Hingerl, and K. Hinrichs, “Optical activity in sub-wavelength metallic grids and fishnet metamaterials in the conical mount,” Opt. Mater. Express 3(4), 439–451 (2013).
[Crossref]

M. M. Jakovljević, G. Isic, B. Vasic, T. W. H. Oates, K. Hinrichs, I. Bergmair, K. Hingerl, and R. Gajic, “Spectroscopic ellipsometry of split ring resonators at infrared frequencies,” Appl. Phys. Lett. 100(16), 161105 (2012).
[Crossref]

T. W. H. Oates, B. Dastmalchi, G. Isic, S. Tollabimazraehno, C. Helgert, T. Pertsch, E. B. Kley, M. A. Verschuuren, I. Bergmair, K. Hingerl, and K. Hinrichs, “Oblique incidence ellipsometric characterization and the substrate dependence of visible frequency fishnet metamaterials,” Opt. Express 20(10), 11166–11177 (2012).
[Crossref] [PubMed]

I. Bergmair, B. Dastmalchi, M. Bergmair, A. Saeed, W. Hilber, G. Hesser, C. Helgert, E. Pshenay-Severin, T. Pertsch, E. B. Kley, U. Hübner, N. H. Shen, R. Penciu, M. Kafesaki, C. M. Soukoulis, K. Hingerl, M. Muehlberger, and R. Schoeftner, “Single and multilayer metamaterials fabricated by nanoimprint lithography,” Nanotechnology 22(32), 325301 (2011).
[Crossref] [PubMed]

Hinrichs, K.

Hübner, U.

I. Bergmair, B. Dastmalchi, M. Bergmair, A. Saeed, W. Hilber, G. Hesser, C. Helgert, E. Pshenay-Severin, T. Pertsch, E. B. Kley, U. Hübner, N. H. Shen, R. Penciu, M. Kafesaki, C. M. Soukoulis, K. Hingerl, M. Muehlberger, and R. Schoeftner, “Single and multilayer metamaterials fabricated by nanoimprint lithography,” Nanotechnology 22(32), 325301 (2011).
[Crossref] [PubMed]

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

Huebner, U.

Isborn, C.

K. Claborn, C. Isborn, W. Kaminsky, and B. Kahr, “Optical rotation of achiral compounds,” Angew. Chem. Int. Ed. Engl. 47(31), 5706–5717 (2008).
[Crossref] [PubMed]

C. Isborn, K. Claborn, and B. Kahr, “The optical rotatory power of water,” J. Phys. Chem. A 111(32), 7800–7804 (2007).
[Crossref] [PubMed]

Isic, G.

Jakovljevic, M. M.

M. M. Jakovljević, G. Isic, B. Vasic, T. W. H. Oates, K. Hinrichs, I. Bergmair, K. Hingerl, and R. Gajic, “Spectroscopic ellipsometry of split ring resonators at infrared frequencies,” Appl. Phys. Lett. 100(16), 161105 (2012).
[Crossref]

Jensen, H. P.

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

Johnston, J.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref] [PubMed]

Kadodwala, M.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref] [PubMed]

Kafesaki, M.

I. Bergmair, B. Dastmalchi, M. Bergmair, A. Saeed, W. Hilber, G. Hesser, C. Helgert, E. Pshenay-Severin, T. Pertsch, E. B. Kley, U. Hübner, N. H. Shen, R. Penciu, M. Kafesaki, C. M. Soukoulis, K. Hingerl, M. Muehlberger, and R. Schoeftner, “Single and multilayer metamaterials fabricated by nanoimprint lithography,” Nanotechnology 22(32), 325301 (2011).
[Crossref] [PubMed]

Kahr, B.

K. Claborn, C. Isborn, W. Kaminsky, and B. Kahr, “Optical rotation of achiral compounds,” Angew. Chem. Int. Ed. Engl. 47(31), 5706–5717 (2008).
[Crossref] [PubMed]

C. Isborn, K. Claborn, and B. Kahr, “The optical rotatory power of water,” J. Phys. Chem. A 111(32), 7800–7804 (2007).
[Crossref] [PubMed]

Kaminsky, W.

K. Claborn, C. Isborn, W. Kaminsky, and B. Kahr, “Optical rotation of achiral compounds,” Angew. Chem. Int. Ed. Engl. 47(31), 5706–5717 (2008).
[Crossref] [PubMed]

Kelly, S. M.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref] [PubMed]

Kley, E. B.

Krykunov, M.

M. Krykunov, M. D. Kundrat, and J. Autschbach, “Calculation of circular dichroism spectra from optical rotatory dispersion, and vice versa, as complementary tools for theoretical studies of optical activity using time-dependent density functional theory,” J. Chem. Phys. 125(19), 194110 (2006).
[Crossref] [PubMed]

Kundrat, M. D.

M. Krykunov, M. D. Kundrat, and J. Autschbach, “Calculation of circular dichroism spectra from optical rotatory dispersion, and vice versa, as complementary tools for theoretical studies of optical activity using time-dependent density functional theory,” J. Chem. Phys. 125(19), 194110 (2006).
[Crossref] [PubMed]

Lapthorn, A. J.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref] [PubMed]

Liu, X. X.

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

Marqués, R.

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B 65(14), 144440 (2002).
[Crossref]

Medina, F.

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B 65(14), 144440 (2002).
[Crossref]

Mikhaylovskiy, R. V.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref] [PubMed]

Mladyonov, P. L.

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

Muehlberger, M.

I. Bergmair, B. Dastmalchi, M. Bergmair, A. Saeed, W. Hilber, G. Hesser, C. Helgert, E. Pshenay-Severin, T. Pertsch, E. B. Kley, U. Hübner, N. H. Shen, R. Penciu, M. Kafesaki, C. M. Soukoulis, K. Hingerl, M. Muehlberger, and R. Schoeftner, “Single and multilayer metamaterials fabricated by nanoimprint lithography,” Nanotechnology 22(32), 325301 (2011).
[Crossref] [PubMed]

Oates, T. W. H.

T. W. H. Oates, T. Shaykhutdinov, T. Wagner, A. Furchner, and K. Hinrichs, “Gyrotropy in achiral materials: the coupled oscillator model,” Adv. Mater. 26(42), 7197–7201 (2014).
[Crossref] [PubMed]

T. W. H. Oates, B. Dastmalchi, C. Helgert, L. Reissmann, U. Huebner, E. B. Kley, M. A. Verschuuren, I. Bergmair, T. Pertsch, K. Hingerl, and K. Hinrichs, “Optical activity in sub-wavelength metallic grids and fishnet metamaterials in the conical mount,” Opt. Mater. Express 3(4), 439–451 (2013).
[Crossref]

M. M. Jakovljević, G. Isic, B. Vasic, T. W. H. Oates, K. Hinrichs, I. Bergmair, K. Hingerl, and R. Gajic, “Spectroscopic ellipsometry of split ring resonators at infrared frequencies,” Appl. Phys. Lett. 100(16), 161105 (2012).
[Crossref]

T. W. H. Oates, B. Dastmalchi, G. Isic, S. Tollabimazraehno, C. Helgert, T. Pertsch, E. B. Kley, M. A. Verschuuren, I. Bergmair, K. Hingerl, and K. Hinrichs, “Oblique incidence ellipsometric characterization and the substrate dependence of visible frequency fishnet metamaterials,” Opt. Express 20(10), 11166–11177 (2012).
[Crossref] [PubMed]

T. W. H. Oates, H. Wormeester, and H. Arwin, “Characterization of plasmonic effects in thin films and metamaterials using spectroscopic ellipsometry,” Prog. Surf. Sci. 86(11–12), 328–376 (2011).
[Crossref]

T. W. H. Oates, M. Ranjan, S. Facsko, and H. Arwin, “Highly anisotropic effective dielectric functions of silver nanoparticle arrays,” Opt. Express 19(3), 2014–2028 (2011).
[Crossref] [PubMed]

Padilla, W. J.

Penciu, R.

I. Bergmair, B. Dastmalchi, M. Bergmair, A. Saeed, W. Hilber, G. Hesser, C. Helgert, E. Pshenay-Severin, T. Pertsch, E. B. Kley, U. Hübner, N. H. Shen, R. Penciu, M. Kafesaki, C. M. Soukoulis, K. Hingerl, M. Muehlberger, and R. Schoeftner, “Single and multilayer metamaterials fabricated by nanoimprint lithography,” Nanotechnology 22(32), 325301 (2011).
[Crossref] [PubMed]

Pertsch, T.

Plum, E.

M. Ren, E. Plum, J. Xu, and N. I. Zheludev, “Giant nonlinear optical activity in a plasmonic metamaterial,” Nat Commun 3, 833 (2012).
[Crossref] [PubMed]

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

Popland, M.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref] [PubMed]

Prosvirnin, S. L.

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

Pshenay-Severin, E.

I. Bergmair, B. Dastmalchi, M. Bergmair, A. Saeed, W. Hilber, G. Hesser, C. Helgert, E. Pshenay-Severin, T. Pertsch, E. B. Kley, U. Hübner, N. H. Shen, R. Penciu, M. Kafesaki, C. M. Soukoulis, K. Hingerl, M. Muehlberger, and R. Schoeftner, “Single and multilayer metamaterials fabricated by nanoimprint lithography,” Nanotechnology 22(32), 325301 (2011).
[Crossref] [PubMed]

Rafii-El-Idrissi, R.

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B 65(14), 144440 (2002).
[Crossref]

Ranjan, M.

Rappich, J.

Reissmann, L.

Ren, M.

M. Ren, E. Plum, J. Xu, and N. I. Zheludev, “Giant nonlinear optical activity in a plasmonic metamaterial,” Nat Commun 3, 833 (2012).
[Crossref] [PubMed]

Rogacheva, A. V.

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

Roodenko, K.

Röseler, A.

Saeed, A.

I. Bergmair, B. Dastmalchi, M. Bergmair, A. Saeed, W. Hilber, G. Hesser, C. Helgert, E. Pshenay-Severin, T. Pertsch, E. B. Kley, U. Hübner, N. H. Shen, R. Penciu, M. Kafesaki, C. M. Soukoulis, K. Hingerl, M. Muehlberger, and R. Schoeftner, “Single and multilayer metamaterials fabricated by nanoimprint lithography,” Nanotechnology 22(32), 325301 (2011).
[Crossref] [PubMed]

Schellman, J.

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

Schoeftner, R.

I. Bergmair, B. Dastmalchi, M. Bergmair, A. Saeed, W. Hilber, G. Hesser, C. Helgert, E. Pshenay-Severin, T. Pertsch, E. B. Kley, U. Hübner, N. H. Shen, R. Penciu, M. Kafesaki, C. M. Soukoulis, K. Hingerl, M. Muehlberger, and R. Schoeftner, “Single and multilayer metamaterials fabricated by nanoimprint lithography,” Nanotechnology 22(32), 325301 (2011).
[Crossref] [PubMed]

Shaykhutdinov, T.

T. W. H. Oates, T. Shaykhutdinov, T. Wagner, A. Furchner, and K. Hinrichs, “Gyrotropy in achiral materials: the coupled oscillator model,” Adv. Mater. 26(42), 7197–7201 (2014).
[Crossref] [PubMed]

Shen, N. H.

I. Bergmair, B. Dastmalchi, M. Bergmair, A. Saeed, W. Hilber, G. Hesser, C. Helgert, E. Pshenay-Severin, T. Pertsch, E. B. Kley, U. Hübner, N. H. Shen, R. Penciu, M. Kafesaki, C. M. Soukoulis, K. Hingerl, M. Muehlberger, and R. Schoeftner, “Single and multilayer metamaterials fabricated by nanoimprint lithography,” Nanotechnology 22(32), 325301 (2011).
[Crossref] [PubMed]

Sibilia, C.

V. K. Valev, J. J. Baumberg, C. Sibilia, and T. Verbiest, “Chirality and chiroptical effects in plasmonic nanostructures: fundamentals, recent progress, and outlook,” Adv. Mater. 25(18), 2517–2534 (2013).
[Crossref] [PubMed]

Silverman, M. P.

Soukoulis, C. M.

I. Bergmair, B. Dastmalchi, M. Bergmair, A. Saeed, W. Hilber, G. Hesser, C. Helgert, E. Pshenay-Severin, T. Pertsch, E. B. Kley, U. Hübner, N. H. Shen, R. Penciu, M. Kafesaki, C. M. Soukoulis, K. Hingerl, M. Muehlberger, and R. Schoeftner, “Single and multilayer metamaterials fabricated by nanoimprint lithography,” Nanotechnology 22(32), 325301 (2011).
[Crossref] [PubMed]

Tebbutt, I. J.

P. A. Thomas, I. J. Tebbutt, and A. M. Glazer, “Potassium titanyl phosphate, KTiOPO4. I. Experimental investigation of optical gyration, absolute optical chirality and twinning,” J. Appl. Cryst. 24(5), 963–967 (1991).
[Crossref]

Thomas, P. A.

P. A. Thomas, I. J. Tebbutt, and A. M. Glazer, “Potassium titanyl phosphate, KTiOPO4. I. Experimental investigation of optical gyration, absolute optical chirality and twinning,” J. Appl. Cryst. 24(5), 963–967 (1991).
[Crossref]

Tollabimazraehno, S.

Tsai, D. P.

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

Valev, V. K.

V. K. Valev, J. J. Baumberg, C. Sibilia, and T. Verbiest, “Chirality and chiroptical effects in plasmonic nanostructures: fundamentals, recent progress, and outlook,” Adv. Mater. 25(18), 2517–2534 (2013).
[Crossref] [PubMed]

Vasic, B.

M. M. Jakovljević, G. Isic, B. Vasic, T. W. H. Oates, K. Hinrichs, I. Bergmair, K. Hingerl, and R. Gajic, “Spectroscopic ellipsometry of split ring resonators at infrared frequencies,” Appl. Phys. Lett. 100(16), 161105 (2012).
[Crossref]

Verbiest, T.

V. K. Valev, J. J. Baumberg, C. Sibilia, and T. Verbiest, “Chirality and chiroptical effects in plasmonic nanostructures: fundamentals, recent progress, and outlook,” Adv. Mater. 25(18), 2517–2534 (2013).
[Crossref] [PubMed]

Verschuuren, M. A.

Wagner, T.

T. W. H. Oates, T. Shaykhutdinov, T. Wagner, A. Furchner, and K. Hinrichs, “Gyrotropy in achiral materials: the coupled oscillator model,” Adv. Mater. 26(42), 7197–7201 (2014).
[Crossref] [PubMed]

Weiss, T.

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

Wormeester, H.

T. W. H. Oates, H. Wormeester, and H. Arwin, “Characterization of plasmonic effects in thin films and metamaterials using spectroscopic ellipsometry,” Prog. Surf. Sci. 86(11–12), 328–376 (2011).
[Crossref]

Xu, J.

M. Ren, E. Plum, J. Xu, and N. I. Zheludev, “Giant nonlinear optical activity in a plasmonic metamaterial,” Nat Commun 3, 833 (2012).
[Crossref] [PubMed]

Zheludev, N. I.

M. Ren, E. Plum, J. Xu, and N. I. Zheludev, “Giant nonlinear optical activity in a plasmonic metamaterial,” Nat Commun 3, 833 (2012).
[Crossref] [PubMed]

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

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

Adv. Mater. (2)

V. K. Valev, J. J. Baumberg, C. Sibilia, and T. Verbiest, “Chirality and chiroptical effects in plasmonic nanostructures: fundamentals, recent progress, and outlook,” Adv. Mater. 25(18), 2517–2534 (2013).
[Crossref] [PubMed]

T. W. H. Oates, T. Shaykhutdinov, T. Wagner, A. Furchner, and K. Hinrichs, “Gyrotropy in achiral materials: the coupled oscillator model,” Adv. Mater. 26(42), 7197–7201 (2014).
[Crossref] [PubMed]

Angew. Chem. Int. Ed. Engl. (1)

K. Claborn, C. Isborn, W. Kaminsky, and B. Kahr, “Optical rotation of achiral compounds,” Angew. Chem. Int. Ed. Engl. 47(31), 5706–5717 (2008).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

M. M. Jakovljević, G. Isic, B. Vasic, T. W. H. Oates, K. Hinrichs, I. Bergmair, K. Hingerl, and R. Gajic, “Spectroscopic ellipsometry of split ring resonators at infrared frequencies,” Appl. Phys. Lett. 100(16), 161105 (2012).
[Crossref]

Appl. Spectrosc. (1)

Chem. Rev. (1)

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

J. Am. Chem. Soc. (1)

C. Gautier and T. Bürgi, “Chiral N-isobutyryl-cysteine protected gold nanoparticles: preparation, size selection, and optical activity in the UV-vis and infrared,” J. Am. Chem. Soc. 128(34), 11079–11087 (2006).
[Crossref] [PubMed]

J. Appl. Cryst. (1)

P. A. Thomas, I. J. Tebbutt, and A. M. Glazer, “Potassium titanyl phosphate, KTiOPO4. I. Experimental investigation of optical gyration, absolute optical chirality and twinning,” J. Appl. Cryst. 24(5), 963–967 (1991).
[Crossref]

J. Chem. Phys. (1)

M. Krykunov, M. D. Kundrat, and J. Autschbach, “Calculation of circular dichroism spectra from optical rotatory dispersion, and vice versa, as complementary tools for theoretical studies of optical activity using time-dependent density functional theory,” J. Chem. Phys. 125(19), 194110 (2006).
[Crossref] [PubMed]

J. Chem. Soc. A (1)

A. D. Buckingham and M. B. Dunn, “Optical activity of oriented molecules,” J. Chem. Soc. A 0, 1988–1991 (1971).
[Crossref]

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

J. Phys. Chem. A (1)

C. Isborn, K. Claborn, and B. Kahr, “The optical rotatory power of water,” J. Phys. Chem. A 111(32), 7800–7804 (2007).
[Crossref] [PubMed]

Nanotechnology (1)

I. Bergmair, B. Dastmalchi, M. Bergmair, A. Saeed, W. Hilber, G. Hesser, C. Helgert, E. Pshenay-Severin, T. Pertsch, E. B. Kley, U. Hübner, N. H. Shen, R. Penciu, M. Kafesaki, C. M. Soukoulis, K. Hingerl, M. Muehlberger, and R. Schoeftner, “Single and multilayer metamaterials fabricated by nanoimprint lithography,” Nanotechnology 22(32), 325301 (2011).
[Crossref] [PubMed]

Nat Commun (1)

M. Ren, E. Plum, J. Xu, and N. I. Zheludev, “Giant nonlinear optical activity in a plasmonic metamaterial,” Nat Commun 3, 833 (2012).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Mater. Express (1)

Phys. Rev. B (1)

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B 65(14), 144440 (2002).
[Crossref]

Phys. Rev. Lett. (3)

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

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

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

Prog. Surf. Sci. (1)

T. W. H. Oates, H. Wormeester, and H. Arwin, “Characterization of plasmonic effects in thin films and metamaterials using spectroscopic ellipsometry,” Prog. Surf. Sci. 86(11–12), 328–376 (2011).
[Crossref]

Other (4)

O. Arteaga, Mueller matrix polarimetry of anisotropic chiral media (Universitat de Barcelona, Departament de Física Aplicada i Òptica, 2010).

R. Scarmozzino, “Simulation tools for devices, systems, and networks,” in Optical Fiber Telecommunications V Part B: Systems and Networks, I. P. Kaminow, T. Li, and A. E. Willner, eds. (Academic Press, 2008).

O. Arteaga, “Useful Mueller matrix symmetries for ellipsometry,” Thin Solid Films. in press).

L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge University Press, 2004).

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic of a unit cell of the SRR array showing the Cartesian axes and the polar (θ) and azimuthal (ϕ) co-ordinates. The simulated normalized modulus of the z-component of the electric field for the; (b) first resonance mode at 800 cm−1; (c) second resonance mode at 1700 cm−1; (d) third resonance mode at 2200 cm−1. The sign of the phase at the maximum values are shown with “+” and “–“.
Fig. 2
Fig. 2 Simulated (a) and measured (b) values of Rps at polar angle θ = 50° for azimuth angle ϕ from −90° to + 95°. The measured values are normalized to Rpp from gold.
Fig. 3
Fig. 3 Measured (a-c) and simulated (d-f) Mueller matrix elements m12 and m21, and (m12 + m21)/2, at ϕ = 0°-90° and θ = 50°. The anisotropic gyrotropic resonances at the first and third resonance mode wavenumbers are clearly resolved in (c) and (f). The resonances are maximum at the low-symmetry optical axis ϕ = 0°.
Fig. 4
Fig. 4 The MM element m12 as the polar angle θ is varied from 0° to 90°, for azimuths ϕ = 0° and 180°. A maximum in the gyrotropy is observed at the third resonance mode at around 60°.
Fig. 5
Fig. 5 Schematic of the modes shown in Figs. 1(b)-1(d), built up from individual dipoles. (a) corresponds to the first resonance mode, (b) the second mode and (c) the third mode. The combination of dipoles creates transition moments of electric dipole, μ, magnetic dipole, m, and electric quadrupole, Θ , character.

Equations (10)

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S out = [ S 0 S 1 S 2 S 3 ] out =[ m 00 m 10 m 20 m 30 m 01 m 11 m 21 m 31 m 02 m 12 m 22 m 32 m 03 m 13 m 23 m 33 ] [ S 0 S 1 S 2 S 3 ] in =M S in .
μ α = α αβ E β + 1 ω G αβ B ˙ β + 1 3 A αβγ E βγ +...,
m α = χ αβ B β 1 ω G βα E ˙ β +...,
Θ αβ = A γαβ E γ +...,
G αβ = 2 jn ω ω jn 2 ω 2 Im( n| μ α |jj| m β |n ) ,
A αβγ = 2 jn ω jn ω jn 2 ω 2 Re( n| μ α |jj| Θ βγ |n ) .
g αβ = 1 2 i[ G αβ + G βα 1 3 ω( ε αγδ A γδβ + ε βγδ A γδα ) ],
θ= 1 2 μ 0 NLω[ G xx + G yy ],
g zx ( B 2 )= 1 2 i[ G xz 1 3 ω A xxy ].
g zx ( A 1 )= 1 2 i[ 1 3 ω( A yxx + A yzz ) ].

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