Abstract

Novel ways to detect the handedness in chiral optical metamaterials by means of the second harmonic generation (SHG) process have recently been proposed. However, the precise origin of the SHG emission has yet to be unambiguously established. In this paper, we present computational simulations of both the electric currents and the electromagnetic fields in chiral planar metamaterials, at the fundamental frequency (FF), and discuss the implications of our results on the characteristics of experimentally measured SHG. In particular, we show that the results of our numerical simulations are in good agreement with the experimental mapping of SHG sources. Thus, the SHG in these metamaterials can be attributed to a strong local enhancement of the electromagnetic fields at the FF, which depends on the particular structure of the patterned metamaterial.

© 2011 OSA

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    [CrossRef]
  37. M. Vrancken and G. A. E. Vandenbosch, “Hybrid dyadic-mixed potential integral equation analysis of 3D planar circuits and antennas,” IEE Proc., Microw. Antennas Propag. 149(5-6), 265–270 (2002).
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    [CrossRef] [PubMed]

2011 (1)

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[CrossRef] [PubMed]

2010 (8)

Y. Sheng, A. Best, H.-J. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Cerenkov-type second harmonic generation,” Opt. Express 18(16), 16539–16545 (2010).
[CrossRef] [PubMed]

Y. Tang and A. E. Cohen, “Optical chirality and its interaction with matter,” Phys. Rev. Lett. 104(16), 163901 (2010).
[CrossRef] [PubMed]

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium,” Nano Lett. 10(5), 1717–1721 (2010).
[CrossRef] [PubMed]

J. Butet, G. Bachelier, J. Duboisset, F. Bertorelle, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Three-dimensional mapping of single gold nanoparticles embedded in a homogeneous transparent matrix using optical second-harmonic generation,” Opt. Express 18(21), 22314–22323 (2010).
[CrossRef] [PubMed]

V. K. Valev, A. V. Silhanek, N. Verellen, W. Gillijns, P. Van Dorpe, O. A. Aktsipetrov, G. A. E. Vandenbosch, V. V. Moshchalkov, and T. Verbiest, “Asymmetric optical second-harmonic generation from chiral G-shaped gold nanostructures,” Phys. Rev. Lett. 104(12), 127401 (2010).
[CrossRef] [PubMed]

J. Butet, G. Bachelier, I. Russier-Antoine, C. Jonin, E. Benichou, and P.-F. Brevet, “Interference between selected dipoles and octupoles in the optical second-harmonic generation from spherical gold nanoparticles,” Phys. Rev. Lett. 105(7), 077401 (2010).
[CrossRef] [PubMed]

C. G. Biris and N. C. Panoiu, “Second harmonic generation in metamaterials based on homogeneous centrosymmetric nanowires,” Phys. Rev. B 81(19), 195102 (2010).
[CrossRef]

V. K. Valev, A. V. Silhanek, N. Smisdom, B. De Clercq, W. Gillijns, O. A. Aktsipetrov, M. Ameloot, V. V. Moshchalkov, and T. Verbiest, “Linearly polarized second harmonic generation microscopy reveals chirality,” Opt. Express 18(8), 8286–8293 (2010).
[CrossRef] [PubMed]

2009 (6)

V. K. Valev, N. Smisdom, A. V. Silhanek, B. De Clercq, W. Gillijns, M. Ameloot, V. V. Moshchalkov, and T. Verbiest, “Plasmonic ratchet wheels: switching circular dichroism by arranging chiral nanostructures,” Nano Lett. 9(11), 3945–3948 (2009).
[CrossRef] [PubMed]

Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, and J. V. Moloney, “Classical theory for second-harmonic generation from metallic nanoparticles,” Phys. Rev. B 79(23), 235109 (2009).
[CrossRef]

F. X. Wang, F. J. Rodríguez, W. M. Albers, R. Ahorinta, J. E. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80(23), 233402 (2009).
[CrossRef]

N. J. Borys, M. J. Walter, and J. M. Lupton, “Intermittency in second-harmonic radiation from plasmonic hot spots on rough silver films,” Phys. Rev. B 80(16), 161407(R) (2009).
[CrossRef]

A. Belardini, M. C. Larciprete, M. Centini, E. Fazio, C. Sibilia, M. Bertolotti, A. Toma, D. Chiappe, and F. Buatier de Mongeot, “Tailored second harmonic generation from self-organized metal nano-wires arrays,” Opt. Express 17(5), 3603–3609 (2009).
[CrossRef] [PubMed]

S. Foerier, I. A. Kolmychek, O. A. Aktsipetrov, T. Verbiest, and V. K. Valev, “Optical second harmonic generation chiral spectroscopy,” ChemPhysChem 10(9-10), 1431–1434 (2009).
[CrossRef] [PubMed]

2008 (1)

A. Lesuffleur, P. Gogol, P. Beauvillain, B. Guizal, D. Van Labeke, and P. Georges, “Nonlinear optical properties of interconnected gold nanoparticles on silicon,” J. Appl. Phys. 104(12), 124310 (2008).
[CrossRef]

2007 (4)

C. Hubert, L. Billot, P.-M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90(18), 181105 (2007).
[CrossRef]

V. K. Valev, A. Kirilyuk, F. Dalla Longa, J. Kohlhepp, B. Koopmans, and Th. Rasing, “Observation of periodic oscillations in magnetization-induced second harmonic generation at the Mn∕Co interface,” Phys. Rev. B 75(1), 012401 (2007).
[CrossRef]

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “Multipole interference in the second-harmonic optical radiation from gold nanoparticles,” Phys. Rev. Lett. 98(16), 167403 (2007).
[CrossRef] [PubMed]

Y. Schols and G. A. E. Vandenbosch, “Separation of horizontal and vertical dependencies in a surface/volume integral equation approach to model quasi 3-D structures in multilayered media,” IEEE Trans. Antenn. Propag. 55(4), 1086–1094 (2007).
[CrossRef]

2006 (2)

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006).
[CrossRef] [PubMed]

W. Fan, S. Zhang, N. C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood, K. J. Malloy, and S. R. J. Brueck, “Second harmonic generation from a nanopatterned isotropic nonlinear material,” Nano Lett. 6(5), 1027–1030 (2006).
[CrossRef]

2005 (3)

2004 (1)

N. I. Zheludev and V. I. Emel’yanov, “Phase matched second harmonic generation from nanostructured metallic surfaces,” J. Opt. A, Pure Appl. Opt. 6(1), 26–28 (2004).
[CrossRef]

2003 (2)

C. Anceau, S. Brasselet, J. Zyss, and P. Gadenne, “Local second-harmonic generation enhancement on gold nanostructures probed by two-photon microscopy,” Opt. Lett. 28(9), 713–715 (2003).
[CrossRef] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light-linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917–1926 (2003).

2002 (1)

M. Vrancken and G. A. E. Vandenbosch, “Hybrid dyadic-mixed potential integral equation analysis of 3D planar circuits and antennas,” IEE Proc., Microw. Antennas Propag. 149(5-6), 265–270 (2002).
[CrossRef]

2001 (1)

V. V. Pavlov, J. Ferré, P. Meyer, G. Tessier, P. Georges, A. Brun, P. Beauvillain, and V. Mathet, “Linear and non-linear magneto-optical studies of Pt/Co/Pt thin films,” J. Phys. Condens. Matter 13(44), 9867–9878 (2001).
[CrossRef]

1999 (2)

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

J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic Rayleigh scattering from a sphere of centrosymmetric material,” Phys. Rev. Lett. 83(20), 4045–4048 (1999).
[CrossRef]

1998 (2)

T. Verbiest, S. V. Elshocht, M. Kauranen, L. Hellemans, J. Snauwaert, C. Nuckolls, T. J. Katz, and A. Persoons, “Strong enhancement of nonlinear optical properties through supramolecular chirality,” Science 282(5390), 913–915 (1998).
[CrossRef] [PubMed]

A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998).
[CrossRef] [PubMed]

1995 (1)

J. J. Maki, M. Kauranen, and A. Persoons, “Surface second-harmonic generation from chiral materials,” Phys. Rev. B Condens. Matter 51(3), 1425–1434 (1995).
[CrossRef] [PubMed]

1994 (1)

J. D. Byers, H. I. Yee, and J. M. Hicks, “A second harmonic generation analog of optical rotatory dispersion for the study of chiral monolayers,” J. Chem. Phys. 101(7), 6233–6241 (1994).
[CrossRef]

1993 (1)

T. Petralli-Mallow, T. M. Wong, J. D. Byers, H. I. Yee, and J. M. Hicks, “Circular dichroism spectroscopy at interfaces: a surface second harmonic generation study,” J. Phys. Chem. 97(7), 1383–1388 (1993).
[CrossRef]

1984 (1)

O. A. Aktsipetrov, I. M. Baranova, E. D. Mishina, and A. V. Petukhov, “Lightning rod effect in surface-enhanced second-harmonic generation,” JETP Lett. 40, 1012–1015 (1984).

1983 (1)

H. W. K. Tom, T. F. Heinz, and Y. R. Shen, “Second-harmonic reflection from silicon surfaces and its relation to structural symmetry,” Phys. Rev. Lett. 51(21), 1983–1986 (1983).
[CrossRef]

1981 (1)

C. K. Chen, A. R. B. de Castro, and Y. R. Shen, “Surface-enhanced second-harmonic generation,” Phys. Rev. Lett. 46(2), 145–148 (1981).
[CrossRef]

1968 (1)

N. Bloembergen, R. K. Chang, S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174(3), 813–822 (1968).
[CrossRef]

1967 (1)

C. H. Lee, R. K. Chang, and N. Bloembergen, “Nonlinear electroreflectance in silicon and silver,” Phys. Rev. Lett. 18(5), 167–170 (1967).
[CrossRef]

Abdenour, A.

W. Fan, S. Zhang, N. C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood, K. J. Malloy, and S. R. J. Brueck, “Second harmonic generation from a nanopatterned isotropic nonlinear material,” Nano Lett. 6(5), 1027–1030 (2006).
[CrossRef]

Adam, P.-M.

C. Hubert, L. Billot, P.-M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90(18), 181105 (2007).
[CrossRef]

Ahorinta, R.

F. X. Wang, F. J. Rodríguez, W. M. Albers, R. Ahorinta, J. E. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80(23), 233402 (2009).
[CrossRef]

Aktsipetrov, O. A.

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[CrossRef] [PubMed]

V. K. Valev, A. V. Silhanek, N. Smisdom, B. De Clercq, W. Gillijns, O. A. Aktsipetrov, M. Ameloot, V. V. Moshchalkov, and T. Verbiest, “Linearly polarized second harmonic generation microscopy reveals chirality,” Opt. Express 18(8), 8286–8293 (2010).
[CrossRef] [PubMed]

V. K. Valev, A. V. Silhanek, N. Verellen, W. Gillijns, P. Van Dorpe, O. A. Aktsipetrov, G. A. E. Vandenbosch, V. V. Moshchalkov, and T. Verbiest, “Asymmetric optical second-harmonic generation from chiral G-shaped gold nanostructures,” Phys. Rev. Lett. 104(12), 127401 (2010).
[CrossRef] [PubMed]

S. Foerier, I. A. Kolmychek, O. A. Aktsipetrov, T. Verbiest, and V. K. Valev, “Optical second harmonic generation chiral spectroscopy,” ChemPhysChem 10(9-10), 1431–1434 (2009).
[CrossRef] [PubMed]

O. A. Aktsipetrov, T. V. Murzina, E. M. Kim, R. V. Kapra, A. A. Fedyanin, M. Inoue, A. F. Kravets, S. V. Kuznetsova, M. V. Ivanchenko, and V. G. Lifshits, “Magnetization-induced second- and third-harmonic generation in magnetic thin films and nanoparticles,” J. Opt. Soc. Am. B 22(1), 138–147 (2005).
[CrossRef]

O. A. Aktsipetrov, I. M. Baranova, E. D. Mishina, and A. V. Petukhov, “Lightning rod effect in surface-enhanced second-harmonic generation,” JETP Lett. 40, 1012–1015 (1984).

Albers, W. M.

F. X. Wang, F. J. Rodríguez, W. M. Albers, R. Ahorinta, J. E. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80(23), 233402 (2009).
[CrossRef]

Ameloot, M.

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[CrossRef] [PubMed]

V. K. Valev, A. V. Silhanek, N. Smisdom, B. De Clercq, W. Gillijns, O. A. Aktsipetrov, M. Ameloot, V. V. Moshchalkov, and T. Verbiest, “Linearly polarized second harmonic generation microscopy reveals chirality,” Opt. Express 18(8), 8286–8293 (2010).
[CrossRef] [PubMed]

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W. Fan, S. Zhang, N. C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood, K. J. Malloy, and S. R. J. Brueck, “Second harmonic generation from a nanopatterned isotropic nonlinear material,” Nano Lett. 6(5), 1027–1030 (2006).
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V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
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V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
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Rasing, Th.

V. K. Valev, A. Kirilyuk, F. Dalla Longa, J. Kohlhepp, B. Koopmans, and Th. Rasing, “Observation of periodic oscillations in magnetization-induced second harmonic generation at the Mn∕Co interface,” Phys. Rev. B 75(1), 012401 (2007).
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V. K. Valev, A. V. Silhanek, N. Smisdom, B. De Clercq, W. Gillijns, O. A. Aktsipetrov, M. Ameloot, V. V. Moshchalkov, and T. Verbiest, “Linearly polarized second harmonic generation microscopy reveals chirality,” Opt. Express 18(8), 8286–8293 (2010).
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V. K. Valev, A. V. Silhanek, N. Verellen, W. Gillijns, P. Van Dorpe, O. A. Aktsipetrov, G. A. E. Vandenbosch, V. V. Moshchalkov, and T. Verbiest, “Asymmetric optical second-harmonic generation from chiral G-shaped gold nanostructures,” Phys. Rev. Lett. 104(12), 127401 (2010).
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V. K. Valev, N. Smisdom, A. V. Silhanek, B. De Clercq, W. Gillijns, M. Ameloot, V. V. Moshchalkov, and T. Verbiest, “Plasmonic ratchet wheels: switching circular dichroism by arranging chiral nanostructures,” Nano Lett. 9(11), 3945–3948 (2009).
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V. K. Valev, A. V. Silhanek, N. Smisdom, B. De Clercq, W. Gillijns, O. A. Aktsipetrov, M. Ameloot, V. V. Moshchalkov, and T. Verbiest, “Linearly polarized second harmonic generation microscopy reveals chirality,” Opt. Express 18(8), 8286–8293 (2010).
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V. K. Valev, N. Smisdom, A. V. Silhanek, B. De Clercq, W. Gillijns, M. Ameloot, V. V. Moshchalkov, and T. Verbiest, “Plasmonic ratchet wheels: switching circular dichroism by arranging chiral nanostructures,” Nano Lett. 9(11), 3945–3948 (2009).
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T. Verbiest, S. V. Elshocht, M. Kauranen, L. Hellemans, J. Snauwaert, C. Nuckolls, T. J. Katz, and A. Persoons, “Strong enhancement of nonlinear optical properties through supramolecular chirality,” Science 282(5390), 913–915 (1998).
[CrossRef] [PubMed]

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J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomen,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
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V. V. Pavlov, J. Ferré, P. Meyer, G. Tessier, P. Georges, A. Brun, P. Beauvillain, and V. Mathet, “Linear and non-linear magneto-optical studies of Pt/Co/Pt thin films,” J. Phys. Condens. Matter 13(44), 9867–9878 (2001).
[CrossRef]

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H. W. K. Tom, T. F. Heinz, and Y. R. Shen, “Second-harmonic reflection from silicon surfaces and its relation to structural symmetry,” Phys. Rev. Lett. 51(21), 1983–1986 (1983).
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[CrossRef] [PubMed]

V. K. Valev, A. V. Silhanek, N. Smisdom, B. De Clercq, W. Gillijns, O. A. Aktsipetrov, M. Ameloot, V. V. Moshchalkov, and T. Verbiest, “Linearly polarized second harmonic generation microscopy reveals chirality,” Opt. Express 18(8), 8286–8293 (2010).
[CrossRef] [PubMed]

V. K. Valev, A. V. Silhanek, N. Verellen, W. Gillijns, P. Van Dorpe, O. A. Aktsipetrov, G. A. E. Vandenbosch, V. V. Moshchalkov, and T. Verbiest, “Asymmetric optical second-harmonic generation from chiral G-shaped gold nanostructures,” Phys. Rev. Lett. 104(12), 127401 (2010).
[CrossRef] [PubMed]

S. Foerier, I. A. Kolmychek, O. A. Aktsipetrov, T. Verbiest, and V. K. Valev, “Optical second harmonic generation chiral spectroscopy,” ChemPhysChem 10(9-10), 1431–1434 (2009).
[CrossRef] [PubMed]

V. K. Valev, N. Smisdom, A. V. Silhanek, B. De Clercq, W. Gillijns, M. Ameloot, V. V. Moshchalkov, and T. Verbiest, “Plasmonic ratchet wheels: switching circular dichroism by arranging chiral nanostructures,” Nano Lett. 9(11), 3945–3948 (2009).
[CrossRef] [PubMed]

V. K. Valev, A. Kirilyuk, F. Dalla Longa, J. Kohlhepp, B. Koopmans, and Th. Rasing, “Observation of periodic oscillations in magnetization-induced second harmonic generation at the Mn∕Co interface,” Phys. Rev. B 75(1), 012401 (2007).
[CrossRef]

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V. K. Valev, A. V. Silhanek, N. Verellen, W. Gillijns, P. Van Dorpe, O. A. Aktsipetrov, G. A. E. Vandenbosch, V. V. Moshchalkov, and T. Verbiest, “Asymmetric optical second-harmonic generation from chiral G-shaped gold nanostructures,” Phys. Rev. Lett. 104(12), 127401 (2010).
[CrossRef] [PubMed]

Van Labeke, D.

A. Lesuffleur, P. Gogol, P. Beauvillain, B. Guizal, D. Van Labeke, and P. Georges, “Nonlinear optical properties of interconnected gold nanoparticles on silicon,” J. Appl. Phys. 104(12), 124310 (2008).
[CrossRef]

Vandenbosch, G. A. E.

V. K. Valev, A. V. Silhanek, N. Verellen, W. Gillijns, P. Van Dorpe, O. A. Aktsipetrov, G. A. E. Vandenbosch, V. V. Moshchalkov, and T. Verbiest, “Asymmetric optical second-harmonic generation from chiral G-shaped gold nanostructures,” Phys. Rev. Lett. 104(12), 127401 (2010).
[CrossRef] [PubMed]

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[CrossRef]

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V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[CrossRef] [PubMed]

V. K. Valev, A. V. Silhanek, N. Smisdom, B. De Clercq, W. Gillijns, O. A. Aktsipetrov, M. Ameloot, V. V. Moshchalkov, and T. Verbiest, “Linearly polarized second harmonic generation microscopy reveals chirality,” Opt. Express 18(8), 8286–8293 (2010).
[CrossRef] [PubMed]

V. K. Valev, A. V. Silhanek, N. Verellen, W. Gillijns, P. Van Dorpe, O. A. Aktsipetrov, G. A. E. Vandenbosch, V. V. Moshchalkov, and T. Verbiest, “Asymmetric optical second-harmonic generation from chiral G-shaped gold nanostructures,” Phys. Rev. Lett. 104(12), 127401 (2010).
[CrossRef] [PubMed]

S. Foerier, I. A. Kolmychek, O. A. Aktsipetrov, T. Verbiest, and V. K. Valev, “Optical second harmonic generation chiral spectroscopy,” ChemPhysChem 10(9-10), 1431–1434 (2009).
[CrossRef] [PubMed]

V. K. Valev, N. Smisdom, A. V. Silhanek, B. De Clercq, W. Gillijns, M. Ameloot, V. V. Moshchalkov, and T. Verbiest, “Plasmonic ratchet wheels: switching circular dichroism by arranging chiral nanostructures,” Nano Lett. 9(11), 3945–3948 (2009).
[CrossRef] [PubMed]

T. Verbiest, S. V. Elshocht, M. Kauranen, L. Hellemans, J. Snauwaert, C. Nuckolls, T. J. Katz, and A. Persoons, “Strong enhancement of nonlinear optical properties through supramolecular chirality,” Science 282(5390), 913–915 (1998).
[CrossRef] [PubMed]

Verellen, N.

V. K. Valev, A. V. Silhanek, N. Verellen, W. Gillijns, P. Van Dorpe, O. A. Aktsipetrov, G. A. E. Vandenbosch, V. V. Moshchalkov, and T. Verbiest, “Asymmetric optical second-harmonic generation from chiral G-shaped gold nanostructures,” Phys. Rev. Lett. 104(12), 127401 (2010).
[CrossRef] [PubMed]

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V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[CrossRef] [PubMed]

Vrancken, M.

M. Vrancken and G. A. E. Vandenbosch, “Hybrid dyadic-mixed potential integral equation analysis of 3D planar circuits and antennas,” IEE Proc., Microw. Antennas Propag. 149(5-6), 265–270 (2002).
[CrossRef]

Walter, M. J.

N. J. Borys, M. J. Walter, and J. M. Lupton, “Intermittency in second-harmonic radiation from plasmonic hot spots on rough silver films,” Phys. Rev. B 80(16), 161407(R) (2009).
[CrossRef]

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F. X. Wang, F. J. Rodríguez, W. M. Albers, R. Ahorinta, J. E. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80(23), 233402 (2009).
[CrossRef]

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M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006).
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T. Petralli-Mallow, T. M. Wong, J. D. Byers, H. I. Yee, and J. M. Hicks, “Circular dichroism spectroscopy at interfaces: a surface second harmonic generation study,” J. Phys. Chem. 97(7), 1383–1388 (1993).
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Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, and J. V. Moloney, “Classical theory for second-harmonic generation from metallic nanoparticles,” Phys. Rev. B 79(23), 235109 (2009).
[CrossRef]

Zhang, S.

W. Fan, S. Zhang, N. C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood, K. J. Malloy, and S. R. J. Brueck, “Second harmonic generation from a nanopatterned isotropic nonlinear material,” Nano Lett. 6(5), 1027–1030 (2006).
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ACS Nano (1)

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

C. Hubert, L. Billot, P.-M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90(18), 181105 (2007).
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ChemPhysChem (1)

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Figures (4)

Fig. 1
Fig. 1

Second harmonic generation methods for studying chirality were developed in organic molecules before being applied to metamaterials. In (a), illustration of SHG from supramolecularly ordered chiral helicenes molecules. In (b), illustration of SHG from G-shaped nanostructures, arranged in a chiral unit cell. The incoming light is at 800 nm (near red color) and the detected signal is at 400 nm (near blue color).

Fig. 2
Fig. 2

Sample preparation. In (a), we start with a Si wafer. In (b), a double resist layer is spin-coated on the wafer. In (c), exposure: the nanostructures’ pattern is drawn on the resist with electron beam lithography. In (d), development: a solvent removes the resist within the pattern. In (e), drying of the resist produces a mask. In (f), the mask is subjected to metal evaporation. In (g), lift-off: all the resist is removed in a solvent bath. In (h), the sample is ready.

Fig. 3
Fig. 3

Mapping of the SHG sources matches the mapping of surface field enhancements at the fundamental frequency. In (a) and (b), the geometry of the two sample configurations that were used for the gold nanostructures. Experiments and calculations were performed for linearly, right-hand and left-hand circularly polarized light as indicated on the left side. The images are organized columnwise according to the sample. The images (c), (i), (o), (e), (k), (q), (g), (m), (s) and (d), (j), (p), (f), (l), (r), (h), (n), (t) refer to G-shaped and mirror-G, respectively. The first two columns of the images are obtained with SHG microscopy. The third and fourth columns are calculated with the MAGMAS software. The fifth and sixth columns are obtained with the DiffractMOD software.

Fig. 4
Fig. 4

Magnetic fields at the surface of the gold nanostructures also match the distribution of SHG sources. In (a), (c) and (e), magnetic field intensity in G-shaped nanostructures, for linearly, right-hand circularly and left-hand circularly polarized light, respectively. In (b), (d) and (f), magnetic field intensity in mirror-G-shaped nanostructures, for linearly, right-hand circularly and left-hand circularly polarized light, respectively. The white lines are guides to the eye, highlighting the correspondence to the SHG microscopy patterns.

Equations (7)

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P i ( 2 ω ) P i D ( 2 ω ) + P i Q ( 2 ω ) = χ i j k ( 2 ) : Ε j ( ω ) Ε k ( ω ) + χ i j k l ( 3 ) Ε j ( ω ) k Ε l ( ω ) ,
P Q ( 2 ω ) = ( χ X X X X χ X Y Y X χ X X Y Y χ X Y X Y ) i e ^ i E i ( ω ) i E i ( ω )               + χ X Y X Y 2 [ E ( ω ) E ( ω ) ] + χ X Y Y X [ E ( ω ) ] E ( ω ) + χ X X Y Y E ( ω ) [ E ( ω ) ] .
P Q ( 2 ω ) χ X Y Y X [ E ( ω ) ] E ( ω ) + χ X X Y Y E ( ω ) [ E ( ω ) ] .
P i , l o c a l D ( 2 ω ) L ( 2 ω ) χ i j k ( 2 ) : Ε j , l o c a l ( ω ) Ε k , l o c a l ( ω )                 L ( 2 ω ) L 2 ( ω ) P i D ( 2 ω ) ,
P l o c a l Q ( 2 ω ) L ( 2 ω ) χ X Y Y X [ L ( ω ) E ( ω ) ] L ( ω ) E ( ω )                                             + L ( 2 ω ) χ X X Y Y L ( ω ) E ( ω ) [ L ( ω ) E ( ω ) ] .
P l o c a l ( 2 ω ) = L ( 2 ω ) L 2 ( ω ) P ( 2 ω ) .
I ( 2 ω ) | L ( 2 ω ) L 2 ( ω ) P ( 2 ω ) | 2 .

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