Three-dimensional optical metamaterials as
model systems for longitudinal and transverse
magnetic coupling

doi:10.1364/OE.16.021233

Three-dimensional optical metamaterials as model systems for longitudinal and transverse magnetic coupling

Na Liu and Harald Giessen »View Author Affiliations

Optics Express, Vol. 16, Issue 26, pp. 21233-21238 (2008)
http://dx.doi.org/10.1364/OE.16.021233

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Abstract

In this paper, we demonstrate that metamaterials represent model systems for longitudinal and transverse magnetic coupling in the optical domain. In particular, such coupling can lead to fully parallel or antiparallel alignment of the magnetic dipoles at the lowest frequency resonance. Also, we present the design scheme for constructing three-dimensional metamaterials with solely magnetic interaction. Our concept could pave the way for achieving rather complicated magnetic materials with desired arrangements of magnetic dipoles at optical frequencies.

OCIS Codes
(160.4760) Materials : Optical properties
(260.5740) Physical optics : Resonance
(160.3918) Materials : Metamaterials

ToC Category:
Metamaterials

History
Original Manuscript: October 16, 2008
Revised Manuscript: December 5, 2008
Manuscript Accepted: December 5, 2008
Published: December 9, 2008

Citation
Na Liu and Harald Giessen, "Three-dimensional optical metamaterials as model systems for longitudinal and transverse magnetic coupling," Opt. Express 16, 21233-21238 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-26-21233

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References

N. Majlis, The quantum theory of magnetism (World Scientific, Singapore, 2000). [CrossRef]
K. Itoh, Molecular magnetism: new magnetic materials (Gordon and Breach, Amsterdam, 2000).
C. Stamm, F. Marty, A. Vaterlaus, V. Weich, S. Egger, U. Maier, U. Ramsperger, H. Fuhrmann, and D. Pescia, "Two-dimensional magnetic particles," Science 282, 449-451 (1998). [CrossRef] [PubMed]
C. Chappert, H. Bernas, J. Ferre, V. Kottler, J. P. Jamet, Y. Chen, E. Cambril, T. Devolder, F. Rousseaux, V. Mathet, and H. Launois, "Planar patterned magnetic media obtained by ion irradiation," Science 280, 1919-1922 (1998). [CrossRef] [PubMed]
D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004). [CrossRef] [PubMed]
S. Palit, T. Driscoll, T. Ren, J. Mock, S. Y. Cho, N. M. Jokerst, D. R. Smith, and D. Basov, "Towards artificial magnetism using terahertz split ring resonator metamaterials," Lasers and electro-optics society, LEOS 2006. 19th annual meeting of the IEEE. 248-249 (2006).
S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, "Photonic metamaterials: magnetism at optical frequencies," IEEE J. Sel. Top. Quantum Electron. 12, 1097-1105 (2006). [CrossRef]
N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nature Mater. 7, 31-37 (2008). [CrossRef]
N. Liu, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Plasmonic building blocks for magnetic molecules in three-dimensional metamaterials," Adv. Mater. 20, 3859-3865 (2008). [CrossRef]
W. J. Padilla, D. R. Smith, and D. N. Basov, "Spectrodcopy of metamaterials from infrared to optical frequencies," J. Opt. Soc. Am. B 23, 404-414 (2006). [CrossRef]
C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refractive index at optical frequencies," Science 315, 47-49 (2007). [CrossRef] [PubMed]
V. M. Shalaev, "Optical negative-index metamaterials," Nature Photon. 1, 41-48 (2007). [CrossRef]
S. Blundell, Magnetism in condensed matter (Oxford University Press, 2004).
All the numerical simulations were performed by using the software package CST Microwave Studio, Darmstadt, Germany. The permittivity of bulk gold in the infrared spectral regime is described by the Drude model with plasma frequency ωpl = 1.37 × 1016 s-1 and the damping constant ωc = 4.08 × 1013 s-1.
E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, "A hybridization model for the plasmon response of complex nanostructures," Science 302, 419-422 (2003). [CrossRef] [PubMed]
N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Plasmon hybridization in stacked cut-wire metamaterials," Adv. Mater. 19, 3628-3632 (2007). [CrossRef]
H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, "Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures," Phys. Rev. B. 76, 073101 (2007). [CrossRef]
S. Zhang, W. J. 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]
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]
S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Optical negative-index bulk metamaterials consisting of 2D perforated metal-dielectric stacks," Opt. Express 14, 6778-6787 (2006). [CrossRef] [PubMed]
G. Dolling, M. Wegener, and S. Linden, "Realization of a three-functional-layer negative-index photonic metamaterial," Opt. Lett. 32, 551-553 (2007). [CrossRef] [PubMed]
T. Li, H. Liu, F. M. Wang, Z. G. Dong, S. N. Zhu, and X. Zhang, "Coupling effect of magnetic polariton in perforated metal/dielectric layered metamaterials and its influence on negative refraction transmission," Opt. Express 14, 11155-11163 (2006). [CrossRef] [PubMed]
F. Falcone, T. Lopetegi, M. A. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, "Babinet principle applied to the design of metasurfaces and metamaterials," Phys. Rev. Lett. 93, 197401 (2004). [CrossRef] [PubMed]
T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, "Babinet’s principle for optical frequency metamaterials and nanoantennas," Phys. Rev. B. 76, 033407 (2007). [CrossRef]

Adv. Mater.

N. Liu, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Plasmonic building blocks for magnetic molecules in three-dimensional metamaterials," Adv. Mater. 20, 3859-3865 (2008). [CrossRef]
N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Plasmon hybridization in stacked cut-wire metamaterials," Adv. Mater. 19, 3628-3632 (2007). [CrossRef]

IEEE J. Sel. Top. Quantum Electron.

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, "Photonic metamaterials: magnetism at optical frequencies," IEEE J. Sel. Top. Quantum Electron. 12, 1097-1105 (2006). [CrossRef]

J. Opt. Soc. Am. B

W. J. Padilla, D. R. Smith, and D. N. Basov, "Spectrodcopy of metamaterials from infrared to optical frequencies," J. Opt. Soc. Am. B 23, 404-414 (2006). [CrossRef]

Nature Mater.

N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nature Mater. 7, 31-37 (2008). [CrossRef]

Nature Photon.

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

Opt. Express

Opt. Lett.

G. Dolling, M. Wegener, and S. Linden, "Realization of a three-functional-layer negative-index photonic metamaterial," Opt. Lett. 32, 551-553 (2007). [CrossRef] [PubMed]

Phys. Rev. B.

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, "Babinet’s principle for optical frequency metamaterials and nanoantennas," Phys. Rev. B. 76, 033407 (2007). [CrossRef]
H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, "Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures," Phys. Rev. B. 76, 073101 (2007). [CrossRef]

Phys. Rev. Lett.

S. Zhang, W. J. 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]
F. Falcone, T. Lopetegi, M. A. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, "Babinet principle applied to the design of metasurfaces and metamaterials," Phys. Rev. Lett. 93, 197401 (2004). [CrossRef] [PubMed]

Science

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, "A hybridization model for the plasmon response of complex nanostructures," Science 302, 419-422 (2003). [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]
C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refractive index at optical frequencies," Science 315, 47-49 (2007). [CrossRef] [PubMed]
C. Stamm, F. Marty, A. Vaterlaus, V. Weich, S. Egger, U. Maier, U. Ramsperger, H. Fuhrmann, and D. Pescia, "Two-dimensional magnetic particles," Science 282, 449-451 (1998). [CrossRef] [PubMed]
C. Chappert, H. Bernas, J. Ferre, V. Kottler, J. P. Jamet, Y. Chen, E. Cambril, T. Devolder, F. Rousseaux, V. Mathet, and H. Launois, "Planar patterned magnetic media obtained by ion irradiation," Science 280, 1919-1922 (1998). [CrossRef] [PubMed]
D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004). [CrossRef] [PubMed]

Other

S. Palit, T. Driscoll, T. Ren, J. Mock, S. Y. Cho, N. M. Jokerst, D. R. Smith, and D. Basov, "Towards artificial magnetism using terahertz split ring resonator metamaterials," Lasers and electro-optics society, LEOS 2006. 19th annual meeting of the IEEE. 248-249 (2006).
N. Majlis, The quantum theory of magnetism (World Scientific, Singapore, 2000). [CrossRef]
K. Itoh, Molecular magnetism: new magnetic materials (Gordon and Breach, Amsterdam, 2000).
S. Blundell, Magnetism in condensed matter (Oxford University Press, 2004).
All the numerical simulations were performed by using the software package CST Microwave Studio, Darmstadt, Germany. The permittivity of bulk gold in the infrared spectral regime is described by the Drude model with plasma frequency ωpl = 1.37 × 1016 s-1 and the damping constant ωc = 4.08 × 1013 s-1.

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[1] N. Majlis, The quantum theory of magnetism (World Scientific, Singapore, 2000). [CrossRef]

[2] K. Itoh, Molecular magnetism: new magnetic materials (Gordon and Breach, Amsterdam, 2000).

[3] C. Stamm, F. Marty, A. Vaterlaus, V. Weich, S. Egger, U. Maier, U. Ramsperger, H. Fuhrmann, and D. Pescia, "Two-dimensional magnetic particles," Science 282, 449-451 (1998). [CrossRef] [PubMed]

[4] C. Chappert, H. Bernas, J. Ferre, V. Kottler, J. P. Jamet, Y. Chen, E. Cambril, T. Devolder, F. Rousseaux, V. Mathet, and H. Launois, "Planar patterned magnetic media obtained by ion irradiation," Science 280, 1919-1922 (1998). [CrossRef] [PubMed]

[5] D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004). [CrossRef] [PubMed]

[6] S. Palit, T. Driscoll, T. Ren, J. Mock, S. Y. Cho, N. M. Jokerst, D. R. Smith, and D. Basov, "Towards artificial magnetism using terahertz split ring resonator metamaterials," Lasers and electro-optics society, LEOS 2006. 19th annual meeting of the IEEE. 248-249 (2006).

[7] S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, "Photonic metamaterials: magnetism at optical frequencies," IEEE J. Sel. Top. Quantum Electron. 12, 1097-1105 (2006). [CrossRef]

[8] N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nature Mater. 7, 31-37 (2008). [CrossRef]

[9] N. Liu, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Plasmonic building blocks for magnetic molecules in three-dimensional metamaterials," Adv. Mater. 20, 3859-3865 (2008). [CrossRef]

[10] W. J. Padilla, D. R. Smith, and D. N. Basov, "Spectrodcopy of metamaterials from infrared to optical frequencies," J. Opt. Soc. Am. B 23, 404-414 (2006). [CrossRef]

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

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

[13] S. Blundell, Magnetism in condensed matter (Oxford University Press, 2004).

[14] All the numerical simulations were performed by using the software package CST Microwave Studio, Darmstadt, Germany. The permittivity of bulk gold in the infrared spectral regime is described by the Drude model with plasma frequency ωpl = 1.37 × 1016 s-1 and the damping constant ωc = 4.08 × 1013 s-1.

[15] E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, "A hybridization model for the plasmon response of complex nanostructures," Science 302, 419-422 (2003). [CrossRef] [PubMed]

[16] N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Plasmon hybridization in stacked cut-wire metamaterials," Adv. Mater. 19, 3628-3632 (2007). [CrossRef]

[17] H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, "Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures," Phys. Rev. B. 76, 073101 (2007). [CrossRef]

[18] S. Zhang, W. J. 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]

[19] 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]

[20] S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Optical negative-index bulk metamaterials consisting of 2D perforated metal-dielectric stacks," Opt. Express 14, 6778-6787 (2006). [CrossRef] [PubMed]

[21] G. Dolling, M. Wegener, and S. Linden, "Realization of a three-functional-layer negative-index photonic metamaterial," Opt. Lett. 32, 551-553 (2007). [CrossRef] [PubMed]

[22] T. Li, H. Liu, F. M. Wang, Z. G. Dong, S. N. Zhu, and X. Zhang, "Coupling effect of magnetic polariton in perforated metal/dielectric layered metamaterials and its influence on negative refraction transmission," Opt. Express 14, 11155-11163 (2006). [CrossRef] [PubMed]

[23] F. Falcone, T. Lopetegi, M. A. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, "Babinet principle applied to the design of metasurfaces and metamaterials," Phys. Rev. Lett. 93, 197401 (2004). [CrossRef] [PubMed]

[24] T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, "Babinet’s principle for optical frequency metamaterials and nanoantennas," Phys. Rev. B. 76, 033407 (2007). [CrossRef]

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