Modeling high-order plasmon resonances of a U-shaped nanowire used to build a negative-index metamaterial

We apply the concept of slow surface-plasmon polariton standing-wave resonances to model the plasmon resonances which exist on split-ring resonators (U-shaped nanowires) forming the unit cell of a metamaterial at infrared frequencies. We compare the expected resonances predicted by the model with full electrodynamic three-dimensional simulations of the U-shaped nanowires for varying geometrical parameters and find a reasonably good agreement. We also consider how far-field dipolar coupling between unit-cells and near-field coupling between the U-shaped nanowire's arms should be taken into account. In addition, we study how the different resonances give rise to negative constitutive parameters for the metamaterial and adjust the geometrical parameters so that the second and third order slow-SPP standing-wave resonances of the U-shaped nanowires result in a double-negative behavior at far-infrared wavelengths without the need of further wires or particles. Finally, we study the effects of stacking $N$ layers of such metamaterial, where each resonant mode splits into $N$ normal mode resonances, showing different electric or magnetic responses. This simple stacked structure maintains the left-handed behavior, exhibiting backward wave propagation.

[1]  Harald Ditlbacher,et al.  Plasmon dispersion relation of Au and Ag nanowires , 2003 .

[2]  A. Morimoto,et al.  Guiding of a one-dimensional optical beam with nanometer diameter. , 1997, Optics letters.

[3]  R. Wood.  XLII. On a remarkable case of uneven distribution of light in a diffraction grating spectrum , 1902 .

[4]  Lechner,et al.  Metal nanoparticle gratings: influence of dipolar particle interaction on the plasmon resonance , 2000, Physical review letters.

[5]  S. Bozhevolnyi,et al.  Plasmon-polariton nano-strip resonators: from visible to infra-red. , 2008, Optics express.

[6]  J. Pendry,et al.  Negative refraction makes a perfect lens , 2000, Physical review letters.

[7]  Carsten Rockstuhl,et al.  On the reinterpretation of resonances in split-ring-resonators at normal incidence. , 2006, Optics express.

[8]  J. Pendry,et al.  Magnetism from conductors and enhanced nonlinear phenomena , 1999 .

[9]  F Schmidt,et al.  Magnetic metamaterials at telecommunication and visible frequencies. , 2005, Physical review letters.

[10]  V. Podolskiy,et al.  PLASMON MODES IN METAL NANOWIRES AND LEFT-HANDED MATERIALS , 2002 .

[11]  R. W. Christy,et al.  Optical Constants of the Noble Metals , 1972 .

[12]  V. Yannopapas.  Subwavelength imaging of light by arrays of metal-coated semiconductor nanoparticles: a theoretical study , 2007, 0711.4019.

[13]  E. N. Economou,et al.  Saturation of the magnetic response of split-ring resonators at optical frequencies. , 2005, Physical review letters.

[14]  Eleftherios N. Economou,et al.  Surface polaritons in a circularly cylindrical interface: Surface plasmons , 1974 .

[15]  Stewart,et al.  Extremely low frequency plasmons in metallic mesostructures. , 1996, Physical review letters.

[16]  Photoexcitation-induced magnetism in arrays of semiconductor nanoparticles with a strong excitonic oscillator strength , 2006 .

[17]  V. Veselago.  The Electrodynamics of Substances with Simultaneously Negative Values of ∊ and μ , 1968 .

[18]  D. Smith,et al.  Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients , 2001, physics/0111203.

[19]  Xiang Zhang,et al.  Contribution of electric quadrupole resonance in optical metamaterials , 2008, 2008 Conference on Lasers and Electro-Optics and 2008 Conference on Quantum Electronics and Laser Science.

[20]  David R. Smith,et al.  Electromagnetic parameter retrieval from inhomogeneous metamaterials. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Jin Au Kong,et al.  Robust method to retrieve the constitutive effective parameters of metamaterials. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  R. H. Ritchie.  Plasma Losses by Fast Electrons in Thin Films , 1957 .

[23]  D. Smith,et al.  Resonant and antiresonant frequency dependence of the effective parameters of metamaterials. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Carsten Rockstuhl,et al.  The origin of magnetic polarizability in metamaterials at optical frequencies - an electrodynamic approach. , 2007, Optics express.

[25]  C. Mirkin,et al.  Multipole plasmon resonances in gold nanorods. , 2006, The journal of physical chemistry. B.

[26]  Vassilios Yannopapas.  Negative refractive index in the near-UV from Au-coated CuCl nanoparticle superlattices , 2007 .

[27]  P. Berini,et al.  Plasmon polariton modes guided by a metal film of finite width. , 1999, Optics letters.

[28]  Thomas Søndergaard,et al.  General properties of slow-plasmon resonant nanostructures: nano-antennas and resonators. , 2007, Optics express.

[29]  Paul F. Liao,et al.  Enhanced fields on rough surfaces: dipolar interactions among particles of sizes exceeding the Rayleigh limit , 1985 .

[30]  F. Aussenegg,et al.  Electromagnetic energy transport via linear chains of silver nanoparticles. , 1998, Optics letters.

[31]  Thomas Søndergaard,et al.  Metal nano-strip optical resonators. , 2007, Optics express.

[32]  Willie J Padilla,et al.  Terahertz Magnetic Response from Artificial Materials , 2004, Science.

[33]  Toralf Scharf,et al.  Design of an artificial three-dimensional composite metamaterial with magnetic resonances in the visible range of the electromagnetic spectrum. , 2007, Physical review letters.

[34]  Jiunn-Woei Liaw,et al.  Dispersion relation of surface plasmon wave propagating along a curved metal-dielectric interface. , 2008, Optics express.

[35]  G. W. Ford,et al.  PROPAGATION OF OPTICAL EXCITATIONS BY DIPOLAR INTERACTIONS IN METAL NANOPARTICLE CHAINS , 2004 .

[36]  A. Hohenau,et al.  Silver nanowires as surface plasmon resonators. , 2005, Physical review letters.

[37]  J. C. Ashley,et al.  Dispersion relations for non-radiative surface plasmons on cylinders☆ , 1974 .

[38]  R. Shelby,et al.  Experimental Verification of a Negative Index of Refraction , 2001, Science.

[39]  S. Bozhevolnyi,et al.  Slow-plasmon resonant nanostructures: Scattering and field enhancements , 2007 .

[40]  Gennady Shvets,et al.  Magnetic plasmon resonance. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  R. W. Wood,et al.  Anomalous Diffraction Gratings , 1935 .