Abstract

Photonic metamaterials could provide optical nonlinearities far exceeding those of natural substances due to the combined action of (magnetic) resonances and local-field enhancements. Here, we present our experiments on second- and third-harmonic generation from magnetic metamaterials composed of nanoscale gold split-ring resonators and from control samples for excitation with 170-fs pulses centered at 1.5-μm wavelength. The strongest nonlinear signals are found for resonances with magnetic-dipole character.

© 2007 Optical Society of America

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Corrections

Matthias W. Klein, Martin Wegener, Nils-Agne Feth, and Stefan Linden, "Experiments on second- and third-harmonic generation from magnetic metamaterials: erratum," Opt. Express 16, 8055-8055 (2008)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-16-11-8055

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2007 (5)

V. M. Shalaev, "Optical negative-index metamaterials," Nat. Phot. 1, 41-48 (2007).
[CrossRef]

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refraction at optical wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

G. Dolling, M. Wegener, and S. Linden, "Realization of a three-functional-layer negative-index photonic metamaterial," Opt. Lett. 32, in press (2007).
[CrossRef] [PubMed]

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780nm wavelength," Opt. Lett. 32, 53-55 (2007).
[CrossRef]

N. Feth, C. Enkrich, M. Wegener, and S. Linden, "Large-area magnetic metamaterials via compact interference lithography," Opt. Express 15, 501-507 (2007).
[CrossRef] [PubMed]

2006 (9)

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Low-loss negative-index metamaterial at telecommunication wavelengths," Opt. Lett. 31, 1800-1802 (2006).
[CrossRef] [PubMed]

A. K. Popov and V. M. Shalaev, "Compensating losses in negative-index metamaterials by optical parametric amplification," Opt. Lett. 31, 2169-2171 (2006).
[CrossRef] [PubMed]

C. Rockstuhl, F. Lederer, C. Etrich, Th. Zentgraf, J. Kuhl, and H. Giessen, "On the reinterpretation of resonances in split-ring-resonators at normal incidence," Opt. Express 14, 8827-8836 (2006).
[CrossRef] [PubMed]

J. P. Huang, L. Dong, and K. W. Yu, "Giant enhancement of optical nonlinearity in multilayer metallic films," J. Appl. Phys. B 99, 053503 (2006).

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

A. K. Popov, V. V. Slabko, and V. M. Shalaev, "Second-harmonic generation in left-handed metamaterials," Las. Phys. Lett. 3, 293-297 (2006).
[CrossRef]

A. K. Popov and V. M. Shalaev, "Negative-index metamaterials: second-harmonic generation, Manley-Rowe relations and parametric amplifications," Appl. Phys. B 84, 131-137 (2006).
[CrossRef]

M. V. Gorkunov, I. V. Shadrivov, and Y. S. Kivshar, "Enhanced parametric processes in binary metamaterials," Appl. Phys. Lett. 88, 71912 (2006).
[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

2005 (6)

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Y. S. Kivshar, "Subwavelength imaging with opaque nonlinear left-handed lenses," Appl. Phys. Lett. 87, 091104 (2005).
[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C. M. Soukoulis, and S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett. 30, 3198-3200 (2005).
[CrossRef] [PubMed]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

2004 (3)

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, Th. Koschny, and C. M. Soukoulis "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101 (2004).
[CrossRef]

2003 (1)

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, "Nonlinear properties of left-handed metamaterials," Phys. Rev. Lett. 91, 037401 (2003).
[CrossRef] [PubMed]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

1999 (2)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

R. S. Bennink, Y.-K. Yoon, and R. W. Boyd, "Accessing the optical nonlinearity of metals with metal-dielectric photonic bandgap structures," Opt. Lett. 24, 1416-1418 (1999).
[CrossRef]

1998 (1)

V. M. Shalaev and A. K. Sarychev, "Nonlinear optics of random metal-dielectric films," Phys. Rev. B 57, 13265-13288 (1998).
[CrossRef]

1997 (1)

L. L. Beecroft and C. K. Ober, "Nanocomposite materials for optical applications," Chem. Mater. 9, 1302-1317 (1997).
[CrossRef]

1996 (2)

V. M. Shalaev, "Electromagnetic properties of small-particle composites," Phys. Rep. 272, 61-137 (1996).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

1995 (1)

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, "Enhanced nonlinear optical response from composite materials," Phys. Rev. Lett. 74, 1871-1874 (1995).
[CrossRef] [PubMed]

1992 (1)

J. E. Sipe and R. W. Boyd, "Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model," Phys. Rev. A 46, 1614-1629 (1992).
[CrossRef] [PubMed]

Basov, D. N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Beecroft, L. L.

L. L. Beecroft and C. K. Ober, "Nanocomposite materials for optical applications," Chem. Mater. 9, 1302-1317 (1997).
[CrossRef]

Bennink, R. S.

Boyd, R. W.

R. S. Bennink, Y.-K. Yoon, and R. W. Boyd, "Accessing the optical nonlinearity of metals with metal-dielectric photonic bandgap structures," Opt. Lett. 24, 1416-1418 (1999).
[CrossRef]

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, "Enhanced nonlinear optical response from composite materials," Phys. Rev. Lett. 74, 1871-1874 (1995).
[CrossRef] [PubMed]

J. E. Sipe and R. W. Boyd, "Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model," Phys. Rev. A 46, 1614-1629 (1992).
[CrossRef] [PubMed]

Brueck, S. R. J.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Burger, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Cai, W.

Chettiar, U. K.

Dolling, G.

Dong, L.

J. P. Huang, L. Dong, and K. W. Yu, "Giant enhancement of optical nonlinearity in multilayer metallic films," J. Appl. Phys. B 99, 053503 (2006).

Drachev, V. P.

Enkrich, C.

N. Feth, C. Enkrich, M. Wegener, and S. Linden, "Large-area magnetic metamaterials via compact interference lithography," Opt. Express 15, 501-507 (2007).
[CrossRef] [PubMed]

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

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Low-loss negative-index metamaterial at telecommunication wavelengths," Opt. Lett. 31, 1800-1802 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C. M. Soukoulis, and S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett. 30, 3198-3200 (2005).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, Th. Koschny, and C. M. Soukoulis "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Etrich, C.

Fan, W.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Fang, N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Feth, N.

Fischer, G. L.

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, "Enhanced nonlinear optical response from composite materials," Phys. Rev. Lett. 74, 1871-1874 (1995).
[CrossRef] [PubMed]

Frauenglass, A.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

Gehr, R. J.

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, "Enhanced nonlinear optical response from composite materials," Phys. Rev. Lett. 74, 1871-1874 (1995).
[CrossRef] [PubMed]

Giessen, H.

Gorkunov, M. V.

M. V. Gorkunov, I. V. Shadrivov, and Y. S. Kivshar, "Enhanced parametric processes in binary metamaterials," Appl. Phys. Lett. 88, 71912 (2006).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Huang, J. P.

J. P. Huang, L. Dong, and K. W. Yu, "Giant enhancement of optical nonlinearity in multilayer metallic films," J. Appl. Phys. B 99, 053503 (2006).

Jenekhe, S. A.

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, "Enhanced nonlinear optical response from composite materials," Phys. Rev. Lett. 74, 1871-1874 (1995).
[CrossRef] [PubMed]

Kildishev, A. V.

Kivshar, Y. S.

M. V. Gorkunov, I. V. Shadrivov, and Y. S. Kivshar, "Enhanced parametric processes in binary metamaterials," Appl. Phys. Lett. 88, 71912 (2006).
[CrossRef]

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Y. S. Kivshar, "Subwavelength imaging with opaque nonlinear left-handed lenses," Appl. Phys. Lett. 87, 091104 (2005).
[CrossRef]

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, "Nonlinear properties of left-handed metamaterials," Phys. Rev. Lett. 91, 037401 (2003).
[CrossRef] [PubMed]

Klein, M. W.

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

Koschny, Th.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, Th. Koschny, and C. M. Soukoulis "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Kuhl, J.

Lederer, F.

Linden, S.

N. Feth, C. Enkrich, M. Wegener, and S. Linden, "Large-area magnetic metamaterials via compact interference lithography," Opt. Express 15, 501-507 (2007).
[CrossRef] [PubMed]

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refraction at optical wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780nm wavelength," Opt. Lett. 32, 53-55 (2007).
[CrossRef]

G. Dolling, M. Wegener, and S. Linden, "Realization of a three-functional-layer negative-index photonic metamaterial," Opt. Lett. 32, in press (2007).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Low-loss negative-index metamaterial at telecommunication wavelengths," Opt. Lett. 31, 1800-1802 (2006).
[CrossRef] [PubMed]

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

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C. M. Soukoulis, and S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett. 30, 3198-3200 (2005).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, Th. Koschny, and C. M. Soukoulis "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Malloy, K. J.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

McPeake, D.

S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101 (2004).
[CrossRef]

Minhas, B. K.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

Ober, C. K.

L. L. Beecroft and C. K. Ober, "Nanocomposite materials for optical applications," Chem. Mater. 9, 1302-1317 (1997).
[CrossRef]

O'Brien, S.

S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101 (2004).
[CrossRef]

Osaheni, J. A.

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, "Enhanced nonlinear optical response from composite materials," Phys. Rev. Lett. 74, 1871-1874 (1995).
[CrossRef] [PubMed]

Osgood, R. M.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Padilla, W. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Panoiu, N. C.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Pendry, J. B.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101 (2004).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Popov, A. K.

A. K. Popov and V. M. Shalaev, "Negative-index metamaterials: second-harmonic generation, Manley-Rowe relations and parametric amplifications," Appl. Phys. B 84, 131-137 (2006).
[CrossRef]

A. K. Popov, V. V. Slabko, and V. M. Shalaev, "Second-harmonic generation in left-handed metamaterials," Las. Phys. Lett. 3, 293-297 (2006).
[CrossRef]

A. K. Popov and V. M. Shalaev, "Compensating losses in negative-index metamaterials by optical parametric amplification," Opt. Lett. 31, 2169-2171 (2006).
[CrossRef] [PubMed]

Ramakrishna, S. A.

S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101 (2004).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Rockstuhl, C.

Sarychev, A. K.

Schmidt, F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Shadrivov, I. V.

M. V. Gorkunov, I. V. Shadrivov, and Y. S. Kivshar, "Enhanced parametric processes in binary metamaterials," Appl. Phys. Lett. 88, 71912 (2006).
[CrossRef]

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Y. S. Kivshar, "Subwavelength imaging with opaque nonlinear left-handed lenses," Appl. Phys. Lett. 87, 091104 (2005).
[CrossRef]

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, "Nonlinear properties of left-handed metamaterials," Phys. Rev. Lett. 91, 037401 (2003).
[CrossRef] [PubMed]

Shalaev, V. M.

V. M. Shalaev, "Optical negative-index metamaterials," Nat. Phot. 1, 41-48 (2007).
[CrossRef]

A. K. Popov, V. V. Slabko, and V. M. Shalaev, "Second-harmonic generation in left-handed metamaterials," Las. Phys. Lett. 3, 293-297 (2006).
[CrossRef]

A. K. Popov and V. M. Shalaev, "Compensating losses in negative-index metamaterials by optical parametric amplification," Opt. Lett. 31, 2169-2171 (2006).
[CrossRef] [PubMed]

A. K. Popov and V. M. Shalaev, "Negative-index metamaterials: second-harmonic generation, Manley-Rowe relations and parametric amplifications," Appl. Phys. B 84, 131-137 (2006).
[CrossRef]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

V. M. Shalaev and A. K. Sarychev, "Nonlinear optics of random metal-dielectric films," Phys. Rev. B 57, 13265-13288 (1998).
[CrossRef]

V. M. Shalaev, "Electromagnetic properties of small-particle composites," Phys. Rep. 272, 61-137 (1996).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Sipe, J. E.

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, "Enhanced nonlinear optical response from composite materials," Phys. Rev. Lett. 74, 1871-1874 (1995).
[CrossRef] [PubMed]

J. E. Sipe and R. W. Boyd, "Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model," Phys. Rev. A 46, 1614-1629 (1992).
[CrossRef] [PubMed]

Slabko, V. V.

A. K. Popov, V. V. Slabko, and V. M. Shalaev, "Second-harmonic generation in left-handed metamaterials," Las. Phys. Lett. 3, 293-297 (2006).
[CrossRef]

Smith, D. R.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Soukoulis, C. M.

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refraction at optical wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780nm wavelength," Opt. Lett. 32, 53-55 (2007).
[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Low-loss negative-index metamaterial at telecommunication wavelengths," Opt. Lett. 31, 1800-1802 (2006).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C. M. Soukoulis, and S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett. 30, 3198-3200 (2005).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, Th. Koschny, and C. M. Soukoulis "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Vier, D. C.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Wegener, M.

G. Dolling, M. Wegener, and S. Linden, "Realization of a three-functional-layer negative-index photonic metamaterial," Opt. Lett. 32, in press (2007).
[CrossRef] [PubMed]

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780nm wavelength," Opt. Lett. 32, 53-55 (2007).
[CrossRef]

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refraction at optical wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

N. Feth, C. Enkrich, M. Wegener, and S. Linden, "Large-area magnetic metamaterials via compact interference lithography," Opt. Express 15, 501-507 (2007).
[CrossRef] [PubMed]

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

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Low-loss negative-index metamaterial at telecommunication wavelengths," Opt. Lett. 31, 1800-1802 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C. M. Soukoulis, and S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett. 30, 3198-3200 (2005).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, Th. Koschny, and C. M. Soukoulis "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Weller-Brophy, L. A.

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, "Enhanced nonlinear optical response from composite materials," Phys. Rev. Lett. 74, 1871-1874 (1995).
[CrossRef] [PubMed]

Yen, T. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Yoon, Y.-K.

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Yu, K. W.

J. P. Huang, L. Dong, and K. W. Yu, "Giant enhancement of optical nonlinearity in multilayer metallic films," J. Appl. Phys. B 99, 053503 (2006).

Yuan, H.-K.

Zentgraf, Th.

Zhang, S.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Zhang, X.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Zharov, A. A.

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Y. S. Kivshar, "Subwavelength imaging with opaque nonlinear left-handed lenses," Appl. Phys. Lett. 87, 091104 (2005).
[CrossRef]

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, "Nonlinear properties of left-handed metamaterials," Phys. Rev. Lett. 91, 037401 (2003).
[CrossRef] [PubMed]

Zharova, N. A.

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Y. S. Kivshar, "Subwavelength imaging with opaque nonlinear left-handed lenses," Appl. Phys. Lett. 87, 091104 (2005).
[CrossRef]

Zhou, J.

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C. M. Soukoulis, and S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett. 30, 3198-3200 (2005).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, Th. Koschny, and C. M. Soukoulis "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Zschiedrich, L.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Appl. Phys. B (1)

A. K. Popov and V. M. Shalaev, "Negative-index metamaterials: second-harmonic generation, Manley-Rowe relations and parametric amplifications," Appl. Phys. B 84, 131-137 (2006).
[CrossRef]

Appl. Phys. Lett. (2)

M. V. Gorkunov, I. V. Shadrivov, and Y. S. Kivshar, "Enhanced parametric processes in binary metamaterials," Appl. Phys. Lett. 88, 71912 (2006).
[CrossRef]

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Y. S. Kivshar, "Subwavelength imaging with opaque nonlinear left-handed lenses," Appl. Phys. Lett. 87, 091104 (2005).
[CrossRef]

Chem. Mater. (1)

L. L. Beecroft and C. K. Ober, "Nanocomposite materials for optical applications," Chem. Mater. 9, 1302-1317 (1997).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. Appl. Phys. B (1)

J. P. Huang, L. Dong, and K. W. Yu, "Giant enhancement of optical nonlinearity in multilayer metallic films," J. Appl. Phys. B 99, 053503 (2006).

Las. Phys. Lett. (1)

A. K. Popov, V. V. Slabko, and V. M. Shalaev, "Second-harmonic generation in left-handed metamaterials," Las. Phys. Lett. 3, 293-297 (2006).
[CrossRef]

Nat. Phot. (1)

V. M. Shalaev, "Optical negative-index metamaterials," Nat. Phot. 1, 41-48 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (7)

Phys. Rep. (1)

V. M. Shalaev, "Electromagnetic properties of small-particle composites," Phys. Rep. 272, 61-137 (1996).
[CrossRef]

Phys. Rev. A (1)

J. E. Sipe and R. W. Boyd, "Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model," Phys. Rev. A 46, 1614-1629 (1992).
[CrossRef] [PubMed]

Phys. Rev. B (2)

V. M. Shalaev and A. K. Sarychev, "Nonlinear optics of random metal-dielectric films," Phys. Rev. B 57, 13265-13288 (1998).
[CrossRef]

S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101 (2004).
[CrossRef]

Phys. Rev. Lett. (6)

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, "Enhanced nonlinear optical response from composite materials," Phys. Rev. Lett. 74, 1871-1874 (1995).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, "Nonlinear properties of left-handed metamaterials," Phys. Rev. Lett. 91, 037401 (2003).
[CrossRef] [PubMed]

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Science (6)

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refraction at optical wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, Th. Koschny, and C. M. Soukoulis "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

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

Other (1)

R. W. Boyd, Nonlinear Optics (Academic, New York, 1992).

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Figures (4)

Fig. 1.
Fig. 1.

Experiments on three different samples: (a) small SRRs with a fundamental magnetic resonance centered at 1.5μm wavelength, (b) a slightly detuned structure, and (c) large SRRs with a higher-order resonance around 1.5μm. For each case, the two linear polarizations are shown (horizontal on top, vertical at bottom). The different columns (from left to right) show electron micrographs, measured linear transmittance spectra, measured SHG signal strength for excitation centered at 1.5μm wavelength, and corresponding THG signal strength. The arrows indicate the incident linear polarization (black), the measured linear polarization of the SHG (red), and that of the THG (green) – if sufficiently large. For clarity, the nonlinear signals are normalized to (a), horizontal incident polarization.

Fig. 2.
Fig. 2.

Experiments on control samples: (a) similar (but not identical) to Fig. 1(a), (b) metamaterial composed of single cut wires, and (c) metamaterial composed of “T”-structures. The representation is as in Fig. 1.

Fig. 3.
Fig. 3.

Oblique-incidence transmittance spectra of two samples. Row (a) corresponds to the sample in Fig. 1(a), rows (b) and (c) to that in Fig. 1(c). The angle of incidence with respect to the surface normal is indicated by the color, positive angles (solid curves) and negative angles (dots) are depicted. The left column corresponds to p-polarization, the right column to s-polarization. The polarization geometries (for positive angles) are also illustrated by the insets.

Fig. 4.
Fig. 4.

SHG signal strength obtained from SRRs excited under oblique incidence as a function of the angle of incidence α with respect to the surface normal. The samples and geometries directly correspond to those shown in Fig. 3. For convenience, the excitation geometries are again illustrated here. All SHG signal strengths are normalized to that for normal incidence in Fig. 1(a), horizontal incident linear polarization. Note the different SHG signal scales.

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