Abstract

By applying a homogenization method based on systematic full-electrodynamic complex-band-structure calculations, we deduce the effective permittivity tensor of a uniaxial photonic crystal consisting of consecutive hexagonal arrays of aligned metallic nanorods of finite length. The form of the obtained permittivity tensor over a relatively broad low-frequency region, where homogenization is applicable, suggests the occurrence of unconventional refractive behavior, namely, negative refraction and self-collimation. This behavior is corroborated by straightforward calculation of the relevant group velocities in the actual photonic crystal. Moreover, it is shown that, in the frequency region where negative refraction occurs, a finite slab of the crystal possesses eigenmodes that form flat bands outside the light cone, as many as the number of its constituent layers. These eigenmodes allow for transfer of the evanescent components of an incident wave field to the other side of the slab, thus enabling subwavelength imaging.

© 2010 Optical Society of America

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2010 (9)

S.-D. Liu and M.-T. Cheng, “Linear plasmon ruler with tunable measurement range and sensitivity,” J. Appl. Phys. 108, 034313 (2010).
[CrossRef]

M. Fleischer, D. Zhang, K. Braun, S. Jäger, R. Ehlich, M. Häffner, C. Stanciu, J. K. H. Hörber, A. J. Meixner, and D. P. Kern, “Tailoring gold nanostructures for near-field optical applications,” Nanotecnology 21, 065301 (2010).
[CrossRef]

D. J. Lipomi, M. A. Kats, P. Kim, S. H. Kang, J. Aizenberg, F. Capasso, and G. M. Whitesides, “Fabrication and replication of arrays of single- or multicomponent nanostructures by replica molding and mechanical sectioning,” ACS Nano 4, 4017-4026 (2010).
[CrossRef] [PubMed]

C. Tserkezis and N. Stefanou, “Retrieving local effective costitutive parameters for anisotropic photonic crystals,” Phys. Rev. B 81, 115112 (2010).
[CrossRef]

N. Stefanou, N. Papanikolaou, and C. Tserkezis, “Plasmonic nanostructures and optical metamaterials: studies by the layer-multiple-scattering method,” Physica B 405, 2967-2971 (2010).
[CrossRef]

C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, “Validity of effective material parameters for optical fishnet metamaterials,” Phys. Rev. B 81, 035320 (2010).
[CrossRef]

J. Kanungo and J. Schilling, “Experimental determination of the principal dielectric functions in silver nanowire metamaterials,” Appl. Phys. Lett. 97, 021903 (2010).
[CrossRef]

J. Shi, B. K. Juluri, S.-C. S. Lin, M. Lu, T. Gao, and T. J. Huang, “Photonic crystal composites-based wide-band optical collimator,” J. Appl. Phys. 108, 043514 (2010).
[CrossRef]

R. Kullock, S. Grafström, P. R. Evans, R. J. Pollard, and L. M. Eng, “Metallic nanorod arrays: negative refraction and optical properties explained by retarded dipolar interactions,” J. Opt. Soc. Am. B 27, 1819-1827 (2010).
[CrossRef]

2009 (5)

Y.-F. Chau, M. W. Chen, and D. P. Tsai, “Three-dimensional analysis of surface plasmon resonance modes on a gold nanorod,” Appl. Opt. 48, 617-622 (2009).
[CrossRef] [PubMed]

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterial for biosensing,” Nature Mater. 8, 867-871 (2009).
[CrossRef]

A. M. Funston, C. Novo, T. J. Davis, and P. Mulvaney, “Plasmon coupling of gold nanorods at short distances and in different geomteries,” Nano Lett. 9, 1651-1658 (2009).
[CrossRef] [PubMed]

C. Tserkezis, N. Papanikolaou, E. Almpanis, and N. Stefanou, “Tailoring plasmons with metallic nanorod arrays,” Phys. Rev. B 80, 125124 (2009).
[CrossRef]

G. Gantzounis, “Plasmon modes in axisymmetric metallic nanoparticles: a group theory analysis,” J. Phys. Chem. C 113, 21560-21565 (2009).
[CrossRef]

2008 (12)

W. Ni, X. Kou, and J. Wang, “Tailoring longitudinal surface plasmon wavelengths, scattering and absorption cross sections of gold nanorods,” ACS Nano 2, 677-686 (2008).
[CrossRef]

B. Willingham, D. W. Brandl, and P. Nordlander, “Plasmon hybridization in nanorod dimers,” Appl. Phys. B: Lasers Opt. 93, 209-216 (2008).
[CrossRef]

P. R. Evans, R. Kullock, W. R. Hendren, R. Atkinson, R. J. Pollard, and L. M. Eng, “Optical transmission properties and elecric field distribution of interacting 2D silver nanorod arrays,” Adv. Funct. Mater. 18, 1075-1079 (2008).
[CrossRef]

S. Kawata, A. Ono, and P. Verma, “Subwavelength colour imaging with a metallic nanolens,” Nat. Photonics 2, 438-442 (2008).
[CrossRef]

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77, 195328 (2008).
[CrossRef]

G. A. Wurtz, W. Dickson, D. O'Connor, R. Atkinson, W. Hendren, P. Evans, R. Pollard, and A. V. Zayats, “Guided plasmonic modes in nanorod assemblies: strong electromagnetic couping regime,” Opt. Express 16, 7460-7470 (2008).
[CrossRef] [PubMed]

Y. Liu, G. Bartal, and X. Zhang, “All-angle negative refraction and imaging in a bulk medium made of metallic nanowires in the visible region,” Opt. Express 16, 15439-15448 (2008).
[CrossRef] [PubMed]

R. Kullock, W. R. Hendren, A. Hille, S. Grafström, P. R. Evans, R. J. Pollard, R. Atkinson, and L. M. Eng, “Polarization conversion through collective surface plasmons in metallic nanorod arrays,” Opt. Express 16, 21671-21681 (2008).
[CrossRef] [PubMed]

E. R. Encina and E. A. Coronado, “Plasmonic nanoantennas: angular scattering properties of multipole resonances in noble metal nanorods,” J. Phys. Chem. C 112, 9586-9594 (2008).
[CrossRef]

D. P. Lyvers, J.-M. Moon, A. V. Kildishev, V. M. Shalaev, and A. Wei, “Gold nanorod arrays as plasmonic cavity resonators,” ACS Nano 2, 2569-2576 (2008).
[CrossRef]

W. T. Lu and S. Sridhar, “Superlens imaging theory for anisotropic nanostructured metamaterials with broadband all-angle negative refraction,” Phys. Rev. B 77, 233101 (2008).
[CrossRef]

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef] [PubMed]

2007 (5)

C. R. Simovski and S. A. Tretyakov, “Local constitutive parameters of metamaterials from an effective-medium perspective,” Phys. Rev. B 75, 195111 (2007).
[CrossRef]

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D: Appl. Phys. 40, 2635-2651 (2007).
[CrossRef]

E. J. Smythe, E. Cubukcu, and F. Capasso, “Optical properties of surface plasmon resonances of coupled metallic nanorods,” Opt. Express 15, 7439-7447 (2007).
[CrossRef] [PubMed]

W. Dickson, G. A. Wurtz, P. Evans, D. O'Connor, R. Atkinson, R. Pollard, and A. V. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: a metamaterial with tuneable optical properties,” Phys. Rev. B 76, 115411 (2007).
[CrossRef]

B. N. Khlebtsov and N. G. Khlebtsov, “Multipole plasmons on metal nanorods: scaling properties and dependence on particle size, shape, orientation, and dielectric environment,” J. Phys. Chem. C 111, 11516-11527 (2007).
[CrossRef]

2006 (7)

P. K. Jain, S. Eustis, and M. A. El-Sayed, “Plasmon coupling in nanorod assemblies: optical absorption, discrete dipole approximation simulation, and exciton-coupling model,” J. Phys. Chem. B 110, 18243-18253 (2006).
[CrossRef] [PubMed]

E. S. Kooij and B. Poelsema, “Shape and size effects in the optical properties of metallic nanorods,” Phys. Chem. Chem. Phys. 8, 3349-3357 (2006).
[CrossRef]

S. W. Prescott and P. Mulvaney, “Gold nanorod extinction spectra,” J. Appl. Phys. 99, 123504 (2006).
[CrossRef]

Y. Liu, J. Fan, Y.-P. Zhao, S. Shanmukh, and R. A. Dluhy, “Angle dependent surface enhanced Raman scattering obtained from an Ag nanorod array substrate,” Appl. Phys. Lett. 89, 173134 (2006).
[CrossRef]

R. Atkinson, W. R. Hendren, G. A. Wurtz, W. Dickson, A. V. Zayats, P. Evans, and R. J. Pollard, “Anisotropic optical properties of arrays of gold nanorods embedded in alumina,” Phys. Rev. B 73, 235402 (2006).
[CrossRef]

G. Gantzounis and N. Stefanou, “Layer-multiple-scattering method for photonic crystals of nonspherical particles,” Phys. Rev. B 73, 035115 (2006).
[CrossRef]

J. Schilling, “Uniaxial metallo-dielectric metamaterials with scalar positive permeability,” Phys. Rev. E 74, 046618 (2006).
[CrossRef]

2005 (5)

R. Iliew, C. Etrich, and F. Lederer, “Self-collimation of light in three-dimensional photonic crystals,” Opt. Express 13, 7076-7085 (2005).
[CrossRef] [PubMed]

A. Ono, J.-I. Kato, and S. Kawata, “Subwavelength optical imaging through a metallic nanorod array,” Phys. Rev. Lett. 95, 267407 (2005).
[CrossRef]

Th. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71, 245105 (2005).
[CrossRef]

G. Gantzounis and N. Stefanou, “Theoretical analysis of three-dimensional polaritonic photonic crystals,” Phys. Rev. B 72, 075107 (2005).
[CrossRef]

K.-S. Lee and M. A. El-Sayed, “Dependence of the enhanced optical scattering efficiency relative to that of absorption for gold metal nanorods on aspect ratio, size, end-cap shape, and medium refractive index,” J. Phys. Chem. B 109, 20331-20338 (2005).
[CrossRef]

2004 (1)

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, “Partial focusing of radiation by a slab of indefinite media,” Appl. Phys. Lett. 84, 2244-2246 (2004).
[CrossRef]

2003 (3)

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003).
[CrossRef]

D. N. Chigrin, S. Enoch, C. M. Sotomayor Torres, and G. Tayeb, “Self-guiding in two-dimesional photonic crystals,” Opt. Express 11, 1203-1211 (2003).
[CrossRef] [PubMed]

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef] [PubMed]

2002 (3)

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, 2002).

2001 (1)

I. V. Lindell, S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, “BW media--media with negative parameters, capable of supporting backward waves,” Microwave Opt. Technol. Lett. 31, 129-133 (2001).
[CrossRef]

2000 (1)

N. Stefanou, V. Yannopapas, and A. Modinos, “MULTEM2: a new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132, 189-196 (2000).
[CrossRef]

1999 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

1998 (1)

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49-77 (1998).
[CrossRef]

1991 (1)

N. Stefanou and A. Modinos, “Optical properties of thin discontinuous metal films,” J. Phys.: Condens. Matter 3, 8149-8157 (1991).
[CrossRef]

1984 (2)

F. Abelès, Y. Borensztein, and T. López-Rios, “Optical properties of discontinuous thin films and rough surfaces of silver,” Festkörperprobleme--Adv. Solid St. Phys. 24, 93-117 (1984).
[CrossRef]

J. F. Cornwell, Group Theory in Physics, Vol. 1 (Academic, 1984).

1983 (1)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

1976 (1)

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders, 1976).

1973 (1)

R. W. Cohen, G. D. Cody, M. D. Coutts, and B. Abeles, “Optical properties of granular silver and gild films,” Phys. Rev. B 8, 3689-3703 (1973).
[CrossRef]

1971 (1)

F. L. Galeener, “Submicroscopic-void resonance: the effect of internal roughness on optical absorption,” Phys. Rev. Lett. 27, 421-423 (1971).
[CrossRef]

1960 (1)

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1960).

Abeles, B.

R. W. Cohen, G. D. Cody, M. D. Coutts, and B. Abeles, “Optical properties of granular silver and gild films,” Phys. Rev. B 8, 3689-3703 (1973).
[CrossRef]

Abelès, F.

F. Abelès, Y. Borensztein, and T. López-Rios, “Optical properties of discontinuous thin films and rough surfaces of silver,” Festkörperprobleme--Adv. Solid St. Phys. 24, 93-117 (1984).
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Aizenberg, J.

D. J. Lipomi, M. A. Kats, P. Kim, S. H. Kang, J. Aizenberg, F. Capasso, and G. M. Whitesides, “Fabrication and replication of arrays of single- or multicomponent nanostructures by replica molding and mechanical sectioning,” ACS Nano 4, 4017-4026 (2010).
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C. Tserkezis, N. Papanikolaou, E. Almpanis, and N. Stefanou, “Tailoring plasmons with metallic nanorod arrays,” Phys. Rev. B 80, 125124 (2009).
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N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders, 1976).

Atkinson, R.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterial for biosensing,” Nature Mater. 8, 867-871 (2009).
[CrossRef]

R. Kullock, W. R. Hendren, A. Hille, S. Grafström, P. R. Evans, R. J. Pollard, R. Atkinson, and L. M. Eng, “Polarization conversion through collective surface plasmons in metallic nanorod arrays,” Opt. Express 16, 21671-21681 (2008).
[CrossRef] [PubMed]

P. R. Evans, R. Kullock, W. R. Hendren, R. Atkinson, R. J. Pollard, and L. M. Eng, “Optical transmission properties and elecric field distribution of interacting 2D silver nanorod arrays,” Adv. Funct. Mater. 18, 1075-1079 (2008).
[CrossRef]

G. A. Wurtz, W. Dickson, D. O'Connor, R. Atkinson, W. Hendren, P. Evans, R. Pollard, and A. V. Zayats, “Guided plasmonic modes in nanorod assemblies: strong electromagnetic couping regime,” Opt. Express 16, 7460-7470 (2008).
[CrossRef] [PubMed]

W. Dickson, G. A. Wurtz, P. Evans, D. O'Connor, R. Atkinson, R. Pollard, and A. V. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: a metamaterial with tuneable optical properties,” Phys. Rev. B 76, 115411 (2007).
[CrossRef]

R. Atkinson, W. R. Hendren, G. A. Wurtz, W. Dickson, A. V. Zayats, P. Evans, and R. J. Pollard, “Anisotropic optical properties of arrays of gold nanorods embedded in alumina,” Phys. Rev. B 73, 235402 (2006).
[CrossRef]

Bartal, G.

Y. Liu, G. Bartal, and X. Zhang, “All-angle negative refraction and imaging in a bulk medium made of metallic nanowires in the visible region,” Opt. Express 16, 15439-15448 (2008).
[CrossRef] [PubMed]

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef] [PubMed]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Borensztein, Y.

F. Abelès, Y. Borensztein, and T. López-Rios, “Optical properties of discontinuous thin films and rough surfaces of silver,” Festkörperprobleme--Adv. Solid St. Phys. 24, 93-117 (1984).
[CrossRef]

Brandl, D. W.

B. Willingham, D. W. Brandl, and P. Nordlander, “Plasmon hybridization in nanorod dimers,” Appl. Phys. B: Lasers Opt. 93, 209-216 (2008).
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M. Fleischer, D. Zhang, K. Braun, S. Jäger, R. Ehlich, M. Häffner, C. Stanciu, J. K. H. Hörber, A. J. Meixner, and D. P. Kern, “Tailoring gold nanostructures for near-field optical applications,” Nanotecnology 21, 065301 (2010).
[CrossRef]

Capasso, F.

D. J. Lipomi, M. A. Kats, P. Kim, S. H. Kang, J. Aizenberg, F. Capasso, and G. M. Whitesides, “Fabrication and replication of arrays of single- or multicomponent nanostructures by replica molding and mechanical sectioning,” ACS Nano 4, 4017-4026 (2010).
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E. J. Smythe, E. Cubukcu, and F. Capasso, “Optical properties of surface plasmon resonances of coupled metallic nanorods,” Opt. Express 15, 7439-7447 (2007).
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Chen, C.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D: Appl. Phys. 40, 2635-2651 (2007).
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Chen, M. W.

Cheng, M.-T.

S.-D. Liu and M.-T. Cheng, “Linear plasmon ruler with tunable measurement range and sensitivity,” J. Appl. Phys. 108, 034313 (2010).
[CrossRef]

Chigrin, D. N.

Cody, G. D.

R. W. Cohen, G. D. Cody, M. D. Coutts, and B. Abeles, “Optical properties of granular silver and gild films,” Phys. Rev. B 8, 3689-3703 (1973).
[CrossRef]

Cohen, R. W.

R. W. Cohen, G. D. Cody, M. D. Coutts, and B. Abeles, “Optical properties of granular silver and gild films,” Phys. Rev. B 8, 3689-3703 (1973).
[CrossRef]

Cornwell, J. F.

J. F. Cornwell, Group Theory in Physics, Vol. 1 (Academic, 1984).

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E. R. Encina and E. A. Coronado, “Plasmonic nanoantennas: angular scattering properties of multipole resonances in noble metal nanorods,” J. Phys. Chem. C 112, 9586-9594 (2008).
[CrossRef]

Coutts, M. D.

R. W. Cohen, G. D. Cody, M. D. Coutts, and B. Abeles, “Optical properties of granular silver and gild films,” Phys. Rev. B 8, 3689-3703 (1973).
[CrossRef]

Cubukcu, E.

Davis, T. J.

A. M. Funston, C. Novo, T. J. Davis, and P. Mulvaney, “Plasmon coupling of gold nanorods at short distances and in different geomteries,” Nano Lett. 9, 1651-1658 (2009).
[CrossRef] [PubMed]

Dickson, W.

G. A. Wurtz, W. Dickson, D. O'Connor, R. Atkinson, W. Hendren, P. Evans, R. Pollard, and A. V. Zayats, “Guided plasmonic modes in nanorod assemblies: strong electromagnetic couping regime,” Opt. Express 16, 7460-7470 (2008).
[CrossRef] [PubMed]

W. Dickson, G. A. Wurtz, P. Evans, D. O'Connor, R. Atkinson, R. Pollard, and A. V. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: a metamaterial with tuneable optical properties,” Phys. Rev. B 76, 115411 (2007).
[CrossRef]

R. Atkinson, W. R. Hendren, G. A. Wurtz, W. Dickson, A. V. Zayats, P. Evans, and R. J. Pollard, “Anisotropic optical properties of arrays of gold nanorods embedded in alumina,” Phys. Rev. B 73, 235402 (2006).
[CrossRef]

Dluhy, R. A.

Y. Liu, J. Fan, Y.-P. Zhao, S. Shanmukh, and R. A. Dluhy, “Angle dependent surface enhanced Raman scattering obtained from an Ag nanorod array substrate,” Appl. Phys. Lett. 89, 173134 (2006).
[CrossRef]

Economou, E. N.

Th. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71, 245105 (2005).
[CrossRef]

Ehlich, R.

M. Fleischer, D. Zhang, K. Braun, S. Jäger, R. Ehlich, M. Häffner, C. Stanciu, J. K. H. Hörber, A. J. Meixner, and D. P. Kern, “Tailoring gold nanostructures for near-field optical applications,” Nanotecnology 21, 065301 (2010).
[CrossRef]

El-Sayed, M. A.

P. K. Jain, S. Eustis, and M. A. El-Sayed, “Plasmon coupling in nanorod assemblies: optical absorption, discrete dipole approximation simulation, and exciton-coupling model,” J. Phys. Chem. B 110, 18243-18253 (2006).
[CrossRef] [PubMed]

K.-S. Lee and M. A. El-Sayed, “Dependence of the enhanced optical scattering efficiency relative to that of absorption for gold metal nanorods on aspect ratio, size, end-cap shape, and medium refractive index,” J. Phys. Chem. B 109, 20331-20338 (2005).
[CrossRef]

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E. R. Encina and E. A. Coronado, “Plasmonic nanoantennas: angular scattering properties of multipole resonances in noble metal nanorods,” J. Phys. Chem. C 112, 9586-9594 (2008).
[CrossRef]

Eng, L. M.

Enoch, S.

Etrich, C.

Eustis, S.

P. K. Jain, S. Eustis, and M. A. El-Sayed, “Plasmon coupling in nanorod assemblies: optical absorption, discrete dipole approximation simulation, and exciton-coupling model,” J. Phys. Chem. B 110, 18243-18253 (2006).
[CrossRef] [PubMed]

Evans, P.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterial for biosensing,” Nature Mater. 8, 867-871 (2009).
[CrossRef]

G. A. Wurtz, W. Dickson, D. O'Connor, R. Atkinson, W. Hendren, P. Evans, R. Pollard, and A. V. Zayats, “Guided plasmonic modes in nanorod assemblies: strong electromagnetic couping regime,” Opt. Express 16, 7460-7470 (2008).
[CrossRef] [PubMed]

W. Dickson, G. A. Wurtz, P. Evans, D. O'Connor, R. Atkinson, R. Pollard, and A. V. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: a metamaterial with tuneable optical properties,” Phys. Rev. B 76, 115411 (2007).
[CrossRef]

R. Atkinson, W. R. Hendren, G. A. Wurtz, W. Dickson, A. V. Zayats, P. Evans, and R. J. Pollard, “Anisotropic optical properties of arrays of gold nanorods embedded in alumina,” Phys. Rev. B 73, 235402 (2006).
[CrossRef]

Evans, P. R.

Fan, J.

Y. Liu, J. Fan, Y.-P. Zhao, S. Shanmukh, and R. A. Dluhy, “Angle dependent surface enhanced Raman scattering obtained from an Ag nanorod array substrate,” Appl. Phys. Lett. 89, 173134 (2006).
[CrossRef]

Fleischer, M.

M. Fleischer, D. Zhang, K. Braun, S. Jäger, R. Ehlich, M. Häffner, C. Stanciu, J. K. H. Hörber, A. J. Meixner, and D. P. Kern, “Tailoring gold nanostructures for near-field optical applications,” Nanotecnology 21, 065301 (2010).
[CrossRef]

Funston, A. M.

A. M. Funston, C. Novo, T. J. Davis, and P. Mulvaney, “Plasmon coupling of gold nanorods at short distances and in different geomteries,” Nano Lett. 9, 1651-1658 (2009).
[CrossRef] [PubMed]

Galeener, F. L.

F. L. Galeener, “Submicroscopic-void resonance: the effect of internal roughness on optical absorption,” Phys. Rev. Lett. 27, 421-423 (1971).
[CrossRef]

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G. Gantzounis, “Plasmon modes in axisymmetric metallic nanoparticles: a group theory analysis,” J. Phys. Chem. C 113, 21560-21565 (2009).
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G. Gantzounis and N. Stefanou, “Layer-multiple-scattering method for photonic crystals of nonspherical particles,” Phys. Rev. B 73, 035115 (2006).
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G. Gantzounis and N. Stefanou, “Theoretical analysis of three-dimensional polaritonic photonic crystals,” Phys. Rev. B 72, 075107 (2005).
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Gao, T.

J. Shi, B. K. Juluri, S.-C. S. Lin, M. Lu, T. Gao, and T. J. Huang, “Photonic crystal composites-based wide-band optical collimator,” J. Appl. Phys. 108, 043514 (2010).
[CrossRef]

Grafström, S.

Häffner, M.

M. Fleischer, D. Zhang, K. Braun, S. Jäger, R. Ehlich, M. Häffner, C. Stanciu, J. K. H. Hörber, A. J. Meixner, and D. P. Kern, “Tailoring gold nanostructures for near-field optical applications,” Nanotecnology 21, 065301 (2010).
[CrossRef]

Hendren, W.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterial for biosensing,” Nature Mater. 8, 867-871 (2009).
[CrossRef]

G. A. Wurtz, W. Dickson, D. O'Connor, R. Atkinson, W. Hendren, P. Evans, R. Pollard, and A. V. Zayats, “Guided plasmonic modes in nanorod assemblies: strong electromagnetic couping regime,” Opt. Express 16, 7460-7470 (2008).
[CrossRef] [PubMed]

Hendren, W. R.

R. Kullock, W. R. Hendren, A. Hille, S. Grafström, P. R. Evans, R. J. Pollard, R. Atkinson, and L. M. Eng, “Polarization conversion through collective surface plasmons in metallic nanorod arrays,” Opt. Express 16, 21671-21681 (2008).
[CrossRef] [PubMed]

P. R. Evans, R. Kullock, W. R. Hendren, R. Atkinson, R. J. Pollard, and L. M. Eng, “Optical transmission properties and elecric field distribution of interacting 2D silver nanorod arrays,” Adv. Funct. Mater. 18, 1075-1079 (2008).
[CrossRef]

R. Atkinson, W. R. Hendren, G. A. Wurtz, W. Dickson, A. V. Zayats, P. Evans, and R. J. Pollard, “Anisotropic optical properties of arrays of gold nanorods embedded in alumina,” Phys. Rev. B 73, 235402 (2006).
[CrossRef]

Hille, A.

Hörber, J. K. H.

M. Fleischer, D. Zhang, K. Braun, S. Jäger, R. Ehlich, M. Häffner, C. Stanciu, J. K. H. Hörber, A. J. Meixner, and D. P. Kern, “Tailoring gold nanostructures for near-field optical applications,” Nanotecnology 21, 065301 (2010).
[CrossRef]

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J. Shi, B. K. Juluri, S.-C. S. Lin, M. Lu, T. Gao, and T. J. Huang, “Photonic crystal composites-based wide-band optical collimator,” J. Appl. Phys. 108, 043514 (2010).
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C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

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I. V. Lindell, S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, “BW media--media with negative parameters, capable of supporting backward waves,” Microwave Opt. Technol. Lett. 31, 129-133 (2001).
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M. Fleischer, D. Zhang, K. Braun, S. Jäger, R. Ehlich, M. Häffner, C. Stanciu, J. K. H. Hörber, A. J. Meixner, and D. P. Kern, “Tailoring gold nanostructures for near-field optical applications,” Nanotecnology 21, 065301 (2010).
[CrossRef]

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P. K. Jain, S. Eustis, and M. A. El-Sayed, “Plasmon coupling in nanorod assemblies: optical absorption, discrete dipole approximation simulation, and exciton-coupling model,” J. Phys. Chem. B 110, 18243-18253 (2006).
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C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104(R) (2002).
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J. Shi, B. K. Juluri, S.-C. S. Lin, M. Lu, T. Gao, and T. J. Huang, “Photonic crystal composites-based wide-band optical collimator,” J. Appl. Phys. 108, 043514 (2010).
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A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterial for biosensing,” Nature Mater. 8, 867-871 (2009).
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D. J. Lipomi, M. A. Kats, P. Kim, S. H. Kang, J. Aizenberg, F. Capasso, and G. M. Whitesides, “Fabrication and replication of arrays of single- or multicomponent nanostructures by replica molding and mechanical sectioning,” ACS Nano 4, 4017-4026 (2010).
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D. J. Lipomi, M. A. Kats, P. Kim, S. H. Kang, J. Aizenberg, F. Capasso, and G. M. Whitesides, “Fabrication and replication of arrays of single- or multicomponent nanostructures by replica molding and mechanical sectioning,” ACS Nano 4, 4017-4026 (2010).
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M. Fleischer, D. Zhang, K. Braun, S. Jäger, R. Ehlich, M. Häffner, C. Stanciu, J. K. H. Hörber, A. J. Meixner, and D. P. Kern, “Tailoring gold nanostructures for near-field optical applications,” Nanotecnology 21, 065301 (2010).
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D. J. Lipomi, M. A. Kats, P. Kim, S. H. Kang, J. Aizenberg, F. Capasso, and G. M. Whitesides, “Fabrication and replication of arrays of single- or multicomponent nanostructures by replica molding and mechanical sectioning,” ACS Nano 4, 4017-4026 (2010).
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Th. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71, 245105 (2005).
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L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1960).

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C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, “Validity of effective material parameters for optical fishnet metamaterials,” Phys. Rev. B 81, 035320 (2010).
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K.-S. Lee and M. A. El-Sayed, “Dependence of the enhanced optical scattering efficiency relative to that of absorption for gold metal nanorods on aspect ratio, size, end-cap shape, and medium refractive index,” J. Phys. Chem. B 109, 20331-20338 (2005).
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L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1960).

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J. Shi, B. K. Juluri, S.-C. S. Lin, M. Lu, T. Gao, and T. J. Huang, “Photonic crystal composites-based wide-band optical collimator,” J. Appl. Phys. 108, 043514 (2010).
[CrossRef]

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I. V. Lindell, S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, “BW media--media with negative parameters, capable of supporting backward waves,” Microwave Opt. Technol. Lett. 31, 129-133 (2001).
[CrossRef]

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D. J. Lipomi, M. A. Kats, P. Kim, S. H. Kang, J. Aizenberg, F. Capasso, and G. M. Whitesides, “Fabrication and replication of arrays of single- or multicomponent nanostructures by replica molding and mechanical sectioning,” ACS Nano 4, 4017-4026 (2010).
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S.-D. Liu and M.-T. Cheng, “Linear plasmon ruler with tunable measurement range and sensitivity,” J. Appl. Phys. 108, 034313 (2010).
[CrossRef]

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Y. Liu, G. Bartal, and X. Zhang, “All-angle negative refraction and imaging in a bulk medium made of metallic nanowires in the visible region,” Opt. Express 16, 15439-15448 (2008).
[CrossRef] [PubMed]

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef] [PubMed]

Y. Liu, J. Fan, Y.-P. Zhao, S. Shanmukh, and R. A. Dluhy, “Angle dependent surface enhanced Raman scattering obtained from an Ag nanorod array substrate,” Appl. Phys. Lett. 89, 173134 (2006).
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J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
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Figures (8)

Fig. 1
Fig. 1

Schematic view of the photonic crystal of metallic nanorods under consideration.

Fig. 2
Fig. 2

Complex photonic band structure of the crystal shown in Fig. 1 for k = ( 0.2 π a , 0 ) , neglecting absorptive losses. Solid (dashed) curves correspond to bands of Q 1 ( Q 2 ) symmetry. The segments of the Q 1 complex bands with the smallest-in-magnitude imaginary part over the gap region are shown in gray-shaded areas. Next to the band diagram we display the reflectance for TM-polarized light impinging with q = ( 0.2 π a , 0 ) on a slab consisting of eight (001) layers of the given crystal (light curve) together with the reflectance of the corresponding semi-infinite crystal (heavy curve).

Fig. 3
Fig. 3

Effective permittivities ɛ z and ɛ 1 of the photonic crystal shown in Fig. 1 calculated by least-squares fits of dispersion data, obtained for many propagation directions, to Eqs. (4, 5) (solid curves). The standard deviation of the fitting procedure is shown by gray-shaded areas. Corresponding results of the effective-medium approximations of Eqs. (7, 8) are represented by dashed and dotted curves, respectively.

Fig. 4
Fig. 4

Isofrequency contours in the k x k z plane ( k y = 0 ) , associated with the Q 1 modes at different frequencies (in ω p units). The shaded rectangle shows the projection of the first Brillouin zone on this plane. Only the heavy segments of the contours correspond to propagating waves outside the crystal.

Fig. 5
Fig. 5

Calculated isofrequency surfaces of the photonic crystal of Fig. 1 at ω = 0.30 ω p associated with the TM-like (left-hand panel) and TE-like (right-hand panel) modes inside the first Brillouin zone.

Fig. 6
Fig. 6

Wave-vector diagrams in the k x k z plane ( k y = 0 ) corresponding to Q 1 (left-hand panel) and Q 2 (right-hand panel) modes at ω = 0.30 ω p for the crystal of Fig. 1. The light circles are the isofrequency curves in air, while the hyperbola (left-hand panel) and the heavy circle (right-hand panel) are the corresponding curves in the photonic crystal. The dashed vertical line is the construction line. Long arrows represent wave vectors in the different media, and short arrows normal to the isofrequency curves represent the group velocity of the transmitted wave. Thin black arrows in the negative k z plane indicate the wave vector and group velocity of a transmitted wave for which the k x component is conserved but causality is violated.

Fig. 7
Fig. 7

Same as in Fig. 6 at ω = 0.25 ω p .

Fig. 8
Fig. 8

Projection of the photonic band structure of the crystal of Fig. 1 on the SBZ of its (001) surface along the symmetry lines shown in the inset. With heavy curves we present the eigenmodes of an eight-layer-thick slab of the above crystal. The dotted lines show the light cone in air.

Equations (9)

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ε m ( ω ) = 1 ω p 2 ω ( ω + i τ 1 ) ,
ɛ = ( ɛ 1 0 0 0 ɛ 1 0 0 0 ɛ z ) ,
μ = ( μ 1 0 0 0 μ 1 0 0 0 μ z ) ,
q 2 + q ( TE ) z 2 = ɛ 1 ω 2 c 2 ,
ɛ 1 ɛ z q 2 + q ( TM ) z 2 = ɛ 1 ω 2 c 2 ,
L z = 1 e 2 e 2 [ 1 2 e ln ( 1 + e 1 e ) 1 ] ,
L x = L y = 1 L z 2 ,
ɛ eff ( i ) ɛ h ɛ eff ( i ) + 2 ɛ h = f 3 ɛ m ɛ h ɛ h + L i ( ɛ m ɛ h ) ,
ɛ eff ( i ) ɛ h ɛ h + L i ( ɛ eff ɛ h ) = f ɛ m ɛ h ɛ h + L i ( ɛ m ɛ h ) .

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