DOI: 10.1126/science.1129198. Second-Harmonic Generation from Magnetic Metamaterials

Second-Harmonic Generation from Magnetic Metamaterials

10.1126/science.1129198

Crossref journal-article

American Association for the Advancement of Science (AAAS)

Science (221)

Abstract

We observe second-harmonic generation from metamaterials composed of split-ring resonators excited at 1.5-micrometer wavelength. Much larger signals are detected when magnetic-dipole resonances are excited, as compared with purely electric-dipole resonances. The experiments are consistent with calculations based on the magnetic component of the Lorentz force exerted on metal electrons—an intrinsic second-harmonic generation mechanism that plays no role in natural materials. This unusual mechanism becomes relevant in our work as a result of the enhancement and the orientation of the local magnetic fields associated with the magnetic-dipole resonances of the split-ring resonators.

Authors 4

Matthias W. Klein (first)
Christian Enkrich (additional)
Martin Wegener (additional)
Stefan Linden (additional)

References 24 Referenced 678

10.1109/22.798002
10.1103/PhysRevLett.85.3966
10.1126/science.1058847
10.1126/science.1094025
10.1126/science.1105371
C. Enkrich et al., Phys. Rev. Lett.95, 203901 (2005). (10.1103/PhysRevLett.95.203901) / Phys. Rev. Lett. (2005)
10.1038/nature04242
G. Dolling, M. Wegener, S. Linden, C. Hormann, Opt. Express14, 1842 (2006). (10.1364/OE.14.001842) / Opt. Express (2006)
10.1126/science.1126021
10.1126/science.1125907
10.1126/science.1126493
M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, S. Linden, Opt. Lett.31, 1259 (2006). (10.1364/OL.31.001259) / Opt. Lett. (2006)
W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, R. D. Averitt, Phys. Rev. Lett.96, 107401 (2006). (10.1103/PhysRevLett.96.107401) / Phys. Rev. Lett. (2006)
10.1103/PhysRevB.65.195104
S. O'Brien, D. McPeake, S. A. Ramakrishna, J. B. Pendry, Phys. Rev. B69, 241101 (2004). (10.1103/PhysRevB.69.241101) / Phys. Rev. B (2004)
J. Zhou et al., Phys. Rev. Lett.95, 223902 (2005). (10.1103/PhysRevLett.95.223902) / Phys. Rev. Lett. (2005)
A. K. Popov V. M. Shalaev available at http://arxiv.org/abs/physics/0601055 (2006).
10.1070/PU1968v010n04ABEH003699
M. Wegener Extreme Nonlinear Optics (Springer Berlin 2004). (10.1007/978-3-662-09115-9_8)
H. M. Barlow, Nature173, 41 (1954). (10.1038/173041a0) / Nature (1954)
S.-Y. Chen, M. Maksimchuk, D. Umstadter, Nature396, 653 (1998). (10.1038/25303) / Nature (1998)
Materials and Methods are available as supporting material on Science Online.
P. Guyot-Sionnest, W. Chen, Y. R. Shen, Phys. Rev. B33, 8254 (1986). (10.1103/PhysRevB.33.8254) / Phys. Rev. B (1986)
We thank the groups of S. W. Koch J. V. Moloney and C. M. Soukoulis for discussions. The research of M.W. is supported by the Leibniz award 2000 of the Deutsche Forschungsgemeinschaft (DFG) that of S.L. through a Helmholtz-Hochschul-Nachwuchsgruppe (VH-NG-232).

Dates

Type	When
Created	19 years ago (July 27, 2006, 5:08 p.m.)
Deposited	1 year, 7 months ago (Jan. 9, 2024, 9:19 p.m.)
Indexed	3 days, 17 hours ago (Aug. 23, 2025, 9:18 p.m.)
Issued	19 years ago (July 28, 2006)
Published	19 years ago (July 28, 2006)
Published Print	19 years ago (July 28, 2006)

Funders 0

None

BibTeX

@article{Klein_2006, title={Second-Harmonic Generation from Magnetic Metamaterials}, volume={313}, ISSN={1095-9203}, url={http://dx.doi.org/10.1126/science.1129198}, DOI={10.1126/science.1129198}, number={5786}, journal={Science}, publisher={American Association for the Advancement of Science (AAAS)}, author={Klein, Matthias W. and Enkrich, Christian and Wegener, Martin and Linden, Stefan}, year={2006}, month=jul, pages={502–504} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        24
      ]
    ],
    "date-time": "2025-08-24T01:18:47Z",
    "timestamp": 1755998327447
  },
  "reference-count": 24,
  "publisher": "American Association for the Advancement of Science (AAAS)",
  "issue": "5786",
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        2006,
        7,
        28
      ]
    ]
  },
  "abstract": "<jats:p>We observe second-harmonic generation from metamaterials composed of split-ring resonators excited at 1.5-micrometer wavelength. Much larger signals are detected when magnetic-dipole resonances are excited, as compared with purely electric-dipole resonances. The experiments are consistent with calculations based on the magnetic component of the Lorentz force exerted on metal electrons\u2014an intrinsic second-harmonic generation mechanism that plays no role in natural materials. This unusual mechanism becomes relevant in our work as a result of the enhancement and the orientation of the local magnetic fields associated with the magnetic-dipole resonances of the split-ring resonators.</jats:p>",
  "DOI": "10.1126/science.1129198",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2006,
        7,
        27
      ]
    ],
    "date-time": "2006-07-27T21:08:36Z",
    "timestamp": 1154034516000
  },
  "page": "502-504",
  "source": "Crossref",
  "is-referenced-by-count": 678,
  "title": "Second-Harmonic Generation from Magnetic Metamaterials",
  "prefix": "10.1126",
  "volume": "313",
  "author": [
    {
      "given": "Matthias W.",
      "family": "Klein",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Institut fu\u0308r Angewandte Physik, Universita\u0308t Karlsruhe (TH), Wolfgang-Gaede-Stra\u00dfe 1, D-76131 Karlsruhe, Germany."
        },
        {
          "name": "DFG-Center for Functional Nanostructures (CFN), Universita\u0308t Karlsruhe (TH), D-76128 Karlsruhe, Germany."
        },
        {
          "name": "Institut fu\u0308r Nanotechnologie, Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft, D-76021 Karlsruhe, Germany."
        }
      ]
    },
    {
      "given": "Christian",
      "family": "Enkrich",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Institut fu\u0308r Angewandte Physik, Universita\u0308t Karlsruhe (TH), Wolfgang-Gaede-Stra\u00dfe 1, D-76131 Karlsruhe, Germany."
        },
        {
          "name": "DFG-Center for Functional Nanostructures (CFN), Universita\u0308t Karlsruhe (TH), D-76128 Karlsruhe, Germany."
        },
        {
          "name": "Institut fu\u0308r Nanotechnologie, Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft, D-76021 Karlsruhe, Germany."
        }
      ]
    },
    {
      "given": "Martin",
      "family": "Wegener",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Institut fu\u0308r Angewandte Physik, Universita\u0308t Karlsruhe (TH), Wolfgang-Gaede-Stra\u00dfe 1, D-76131 Karlsruhe, Germany."
        },
        {
          "name": "DFG-Center for Functional Nanostructures (CFN), Universita\u0308t Karlsruhe (TH), D-76128 Karlsruhe, Germany."
        },
        {
          "name": "Institut fu\u0308r Nanotechnologie, Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft, D-76021 Karlsruhe, Germany."
        }
      ]
    },
    {
      "given": "Stefan",
      "family": "Linden",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Institut fu\u0308r Angewandte Physik, Universita\u0308t Karlsruhe (TH), Wolfgang-Gaede-Stra\u00dfe 1, D-76131 Karlsruhe, Germany."
        },
        {
          "name": "DFG-Center for Functional Nanostructures (CFN), Universita\u0308t Karlsruhe (TH), D-76128 Karlsruhe, Germany."
        },
        {
          "name": "Institut fu\u0308r Nanotechnologie, Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft, D-76021 Karlsruhe, Germany."
        }
      ]
    }
  ],
  "member": "221",
  "reference": [
    {
      "key": "e_1_3_1_2_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1109/22.798002"
    },
    {
      "key": "e_1_3_1_3_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.85.3966"
    },
    {
      "key": "e_1_3_1_4_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1126/science.1058847"
    },
    {
      "key": "e_1_3_1_5_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1126/science.1094025"
    },
    {
      "key": "e_1_3_1_6_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1126/science.1105371"
    },
    {
      "key": "e_1_3_1_7_2",
      "doi-asserted-by": "crossref",
      "first-page": "203901",
      "DOI": "10.1103/PhysRevLett.95.203901",
      "volume": "95",
      "year": "2005",
      "unstructured": "C. Enkrich et al., Phys. Rev. Lett.95, 203901 (2005).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "e_1_3_1_8_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1038/nature04242"
    },
    {
      "key": "e_1_3_1_9_2",
      "doi-asserted-by": "crossref",
      "first-page": "1842",
      "DOI": "10.1364/OE.14.001842",
      "volume": "14",
      "year": "2006",
      "unstructured": "G. Dolling, M. Wegener, S. Linden, C. Hormann, Opt. Express14, 1842 (2006).",
      "journal-title": "Opt. Express"
    },
    {
      "key": "e_1_3_1_10_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1126/science.1126021"
    },
    {
      "key": "e_1_3_1_11_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1126/science.1125907"
    },
    {
      "key": "e_1_3_1_12_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1126/science.1126493"
    },
    {
      "key": "e_1_3_1_13_2",
      "doi-asserted-by": "crossref",
      "first-page": "1259",
      "DOI": "10.1364/OL.31.001259",
      "volume": "31",
      "year": "2006",
      "unstructured": "M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, S. Linden, Opt. Lett.31, 1259 (2006).",
      "journal-title": "Opt. Lett."
    },
    {
      "key": "e_1_3_1_14_2",
      "doi-asserted-by": "crossref",
      "first-page": "107401",
      "DOI": "10.1103/PhysRevLett.96.107401",
      "volume": "96",
      "year": "2006",
      "unstructured": "W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, R. D. Averitt, Phys. Rev. Lett.96, 107401 (2006).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "e_1_3_1_15_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevB.65.195104"
    },
    {
      "key": "e_1_3_1_16_2",
      "doi-asserted-by": "crossref",
      "first-page": "241101",
      "DOI": "10.1103/PhysRevB.69.241101",
      "volume": "69",
      "year": "2004",
      "unstructured": "S. O'Brien, D. McPeake, S. A. Ramakrishna, J. B. Pendry, Phys. Rev. B69, 241101 (2004).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "e_1_3_1_17_2",
      "doi-asserted-by": "crossref",
      "first-page": "223902",
      "DOI": "10.1103/PhysRevLett.95.223902",
      "volume": "95",
      "year": "2005",
      "unstructured": "J. Zhou et al., Phys. Rev. Lett.95, 223902 (2005).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "e_1_3_1_18_2",
      "unstructured": "A. K. Popov V. M. Shalaev available at http://arxiv.org/abs/physics/0601055 (2006)."
    },
    {
      "key": "e_1_3_1_19_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1070/PU1968v010n04ABEH003699"
    },
    {
      "key": "e_1_3_1_20_2",
      "doi-asserted-by": "crossref",
      "unstructured": "M. Wegener Extreme Nonlinear Optics (Springer Berlin 2004).",
      "DOI": "10.1007/978-3-662-09115-9_8"
    },
    {
      "key": "e_1_3_1_21_2",
      "doi-asserted-by": "crossref",
      "first-page": "41",
      "DOI": "10.1038/173041a0",
      "volume": "173",
      "year": "1954",
      "unstructured": "H. M. Barlow, Nature173, 41 (1954).",
      "journal-title": "Nature"
    },
    {
      "key": "e_1_3_1_22_2",
      "doi-asserted-by": "crossref",
      "first-page": "653",
      "DOI": "10.1038/25303",
      "volume": "396",
      "year": "1998",
      "unstructured": "S.-Y. Chen, M. Maksimchuk, D. Umstadter, Nature396, 653 (1998).",
      "journal-title": "Nature"
    },
    {
      "key": "e_1_3_1_23_2",
      "unstructured": "Materials and Methods are available as supporting material on Science Online."
    },
    {
      "key": "e_1_3_1_24_2",
      "doi-asserted-by": "crossref",
      "first-page": "8254",
      "DOI": "10.1103/PhysRevB.33.8254",
      "volume": "33",
      "year": "1986",
      "unstructured": "P. Guyot-Sionnest, W. Chen, Y. R. Shen, Phys. Rev. B33, 8254 (1986).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "e_1_3_1_25_2",
      "unstructured": "We thank the groups of S. W. Koch J. V. Moloney and C. M. Soukoulis for discussions. The research of M.W. is supported by the Leibniz award 2000 of the Deutsche Forschungsgemeinschaft (DFG) that of S.L. through a Helmholtz-Hochschul-Nachwuchsgruppe (VH-NG-232)."
    }
  ],
  "container-title": "Science",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://www.science.org/doi/pdf/10.1126/science.1129198",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        1,
        10
      ]
    ],
    "date-time": "2024-01-10T02:19:01Z",
    "timestamp": 1704853141000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://www.science.org/doi/10.1126/science.1129198"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2006,
        7,
        28
      ]
    ]
  },
  "references-count": 24,
  "journal-issue": {
    "issue": "5786",
    "published-print": {
      "date-parts": [
        [
          2006,
          7,
          28
        ]
      ]
    }
  },
  "alternative-id": [
    "10.1126/science.1129198"
  ],
  "URL": "http://dx.doi.org/10.1126/science.1129198",
  "relation": {},
  "ISSN": [
    "0036-8075",
    "1095-9203"
  ],
  "subject": [],
  "container-title-short": "Science",
  "published": {
    "date-parts": [
      [
        2006,
        7,
        28
      ]
    ]
  }
}