Abstract

Plasmonic nanostructures offer a great potential to enhance light-matter interaction at the nanometer scale. The response upon illumination at a given wavelength and polarization is governed by the characteristic lengths associated to the shape and size of the nanostructure. Here, we propose the use of engineered fractal plasmonic structures to extend the degrees of freedom and the parameters available for their design. In particular, we focus on a paradigmatic fractal geometry, namely the Sierpinski carpet. We explore the possibility of using it to achieve a controlled broadband spectral response by controlling the degree of its fractal complexity. Furthermore, we investigate some other arising properties, such as subdiffraction limited focusing and its potential use for optical trapping of nano-objects. An attractive advantage of the focusing over more standard geometries, such as gap antennas, is that it occurs away from the metal surface (≈ 80nm) at the center of the nanostructure, leaving an open space accessible to objects for enhanced light-matter interaction.

© 2011 Optical Society of America

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References

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  8. F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77, 045124 (2008).
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  22. A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional Emission of a Quantum Dot Coupled to a Nnanoantenna,” Science 329, 930–933 (2010).
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  26. S. L. Bozhevolnyi, V. A. Markel, V. Coello, W. Kim, and W. E. Shalaev, “Direct obesercation of localized dipolar excitations on rough nanostructured surfaces,” Phys. Rev. B. 58, 11441 (1998).
    [Crossref]
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    [Crossref]
  31. J. S. Huang, V. Callegari, P. Geisler, C. Bruning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagoini, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures for plasmonic nanocircuitry,” Nature Commun. 1, 150 (2010).
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  35. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited Optical Imaging with a Silver Superlens,” Science 308534–537 (2005).
    [Crossref] [PubMed]
  36. G. Volpe, S. Cherukulappurath, R. Juanola Parramon, G. Molina-Terriza, and R. Quidant, “Controlling the optical near field of nanoantennas with spatial phase-shaped beams,” Nano Lett. 9, 3608–3611 (2009).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2010 (6)

X. Huang, S. Xiao, J. Huangfu, Z. Wang, L. Ran, and L. Zhou, “Fractal plasmonic metamaterials for subwavelength imaging,” Opt. Express 18, 10377–10387 (2010).
[Crossref] [PubMed]

S. Jia and J. W. Fleischer, “Nonlinear light propagation in fractal waveguide arrays,” Opt. Express 18, 14409–14415 (2010).
[Crossref] [PubMed]

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional Emission of a Quantum Dot Coupled to a Nnanoantenna,” Science 329, 930–933 (2010).
[Crossref] [PubMed]

V. Krachmalnicoff, E. Castani, Y. De Wilde, and R. Carminati, “Fluctuations of the Local Density of States Probe Licalized Surface Plasmons on Disordered Metal Films,” Phys. Rev. Lett. 105, 183901 (2010).
[Crossref]

J. S. Huang, V. Callegari, P. Geisler, C. Bruning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagoini, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures for plasmonic nanocircuitry,” Nature Commun. 1, 150 (2010).
[Crossref]

H. A. Atwater and A. Polmari, “Plasmonics for improved photovoltaic devices,” Nat. Materials 9, 205–213 (2010).
[Crossref]

2009 (4)

G. Volpe, S. Cherukulappurath, R. Juanola Parramon, G. Molina-Terriza, and R. Quidant, “Controlling the optical near field of nanoantennas with spatial phase-shaped beams,” Nano Lett. 9, 3608–3611 (2009).
[Crossref] [PubMed]

S. S. Acimovic, M. P. Kreuzer, M. U. Gonzalez, and R. Quidant, “Plasmon near-field coupling in metal dimers as a step toward single-molecule sensing,” ACSNano 3, 1231–1237 (2009).

P. Zijilstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459, 410–413 (2009).
[Crossref]

T. Yano, P. Verma, Y. Saito, T. Ichimura, and S. Kawata, “Pressure-assisted tip-enhanced Raman imaging at a resolution of a few nanometers,” Nature Photon. 3, 473–477 (2009).
[Crossref]

2008 (3)

K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16, 21793–21800 (2008).
[Crossref] [PubMed]

F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77, 045124 (2008).
[Crossref]

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, “Surface Plasmon Optical Tweezers: Tunable Optical Manipulation in the Femtonewton Range,” Phys. Rev. Lett. 100, 186804 (2008).
[Crossref] [PubMed]

2007 (4)

P. K. Jain, W. Huang, and M. A. El-Sayed, “On the Universal Scaling Behaviour of the Distance Decay of Plasmon Coupling in Metal Nanoparticle Pairs: A Plasmon Ruler Equation,” Nano Lett. 7, 2080–2088 (2007).
[Crossref]

M. Righini, A.S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nature Phys. 3, 477–480 (2007).
[Crossref]

L. Novotny, “Effective Wavelength Scaling for Optical Antennas,” Phys. Rev. Lett. 98, 266802 (2007).
[Crossref] [PubMed]

Y.J. Bao, B. Zhang, Z. Wu, J. W. Si, M. Wang, R. W. Peng, X. Lu, Z. F. Li, X. P. Hao, and N. B. Ming, “Surface-plasmon-enhanced transmission through metallic film perforated with fractal-featured aperture array,” Appl. Phys. Lett. 90, 251914 (2007).
[Crossref]

2006 (1)

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, “Surface Plasmon Radiation Forces,” Phys. Rev. Lett. 96, 238101 (2006).
[Crossref] [PubMed]

2005 (5)

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant Optical Antennas,” Science 308, 1607–1609 (2005).
[Crossref] [PubMed]

C. Girard, “Near fields in nanostructures,” Rep. Prog. Phys. 68, 1883–1933 (2005)
[Crossref]

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the Mismatch between Light and Nanoscale Objects with Gold Bowtie Nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
[Crossref] [PubMed]

R. Quidant, D. Petrov, and G. Badenes, “Radiation forces on a Rayleigh dielectric sphere in a patterned optical near field,” Opt. Lett. 30, 1009–1011 (2005).
[Crossref] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited Optical Imaging with a Silver Superlens,” Science 308534–537 (2005).
[Crossref] [PubMed]

2004 (1)

A. Grbic and G. V. Eleftheriades, “Overcoming the Diffraction Limit with a Planar Left-Handed Transmission-Line Lens,” Phys. Rev. Lett. 92, 117403 (2004).
[Crossref] [PubMed]

2003 (3)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

D. H. Werner and S. Ganguly, “An overview of fractal antenna engineering research,” IEEE Ant. Propag. Mag. 45, 38–57 (2003).
[Crossref]

W. Wen, L. Zhou, J. Li, W. Ge, C. T. Chan, and P. Sheng, “Subwavelength Photonic Band Gaps from Planar Fractals,” Phys. Rev. Lett. 82, 223901 (2003).

2002 (1)

L. Zhou, W. Wen, C. T. Chan, and P. Sheng, “Reflectivity of planar metallic fractal patterns,” Appl. Phys. Lett. 89, 1012–1014 (2002).

1998 (1)

S. L. Bozhevolnyi, V. A. Markel, V. Coello, W. Kim, and W. E. Shalaev, “Direct obesercation of localized dipolar excitations on rough nanostructured surfaces,” Phys. Rev. B. 58, 11441 (1998).
[Crossref]

1994 (1)

D. P. Tsai, J. Kovacs, Z. Wang, M. Moskovits, V. M. Shalaev, J. S. Suh, and R. Botet, “Photon Scanning Tunneling Micrscopy Images of Optical Excitations of Fractal Metal Colloid Clusters,” Phys. Rev. Lett. 72, 4149 (1994).
[Crossref] [PubMed]

1988 (1)

V. M. Shalaev and M. I. Stockman, “Fracatals: optical suscebtibility and giant Raman scattering,” Z. Phys. D 10, 71–79 (1988).
[Crossref]

1916 (1)

W. Sierpinski, “Sur une courbe cantorienne qui contient une image biunivoque et continue de toute courbe donnée,” C. r. hebd. Seanc. Acad. Sci., Paris 162, 629–632 (1916).

Acimovic, S. S.

S. S. Acimovic, M. P. Kreuzer, M. U. Gonzalez, and R. Quidant, “Plasmon near-field coupling in metal dimers as a step toward single-molecule sensing,” ACSNano 3, 1231–1237 (2009).

Atwater, H. A.

H. A. Atwater and A. Polmari, “Plasmonics for improved photovoltaic devices,” Nat. Materials 9, 205–213 (2010).
[Crossref]

Badenes, G.

Bao, Y.J.

Y.J. Bao, B. Zhang, Z. Wu, J. W. Si, M. Wang, R. W. Peng, X. Lu, Z. F. Li, X. P. Hao, and N. B. Ming, “Surface-plasmon-enhanced transmission through metallic film perforated with fractal-featured aperture array,” Appl. Phys. Lett. 90, 251914 (2007).
[Crossref]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

Biagoini, P.

J. S. Huang, V. Callegari, P. Geisler, C. Bruning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagoini, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures for plasmonic nanocircuitry,” Nature Commun. 1, 150 (2010).
[Crossref]

Botet, R.

D. P. Tsai, J. Kovacs, Z. Wang, M. Moskovits, V. M. Shalaev, J. S. Suh, and R. Botet, “Photon Scanning Tunneling Micrscopy Images of Optical Excitations of Fractal Metal Colloid Clusters,” Phys. Rev. Lett. 72, 4149 (1994).
[Crossref] [PubMed]

Bozhevolnyi, S. L.

S. L. Bozhevolnyi, V. A. Markel, V. Coello, W. Kim, and W. E. Shalaev, “Direct obesercation of localized dipolar excitations on rough nanostructured surfaces,” Phys. Rev. B. 58, 11441 (1998).
[Crossref]

Bruning, C.

J. S. Huang, V. Callegari, P. Geisler, C. Bruning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagoini, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures for plasmonic nanocircuitry,” Nature Commun. 1, 150 (2010).
[Crossref]

Callegari, V.

J. S. Huang, V. Callegari, P. Geisler, C. Bruning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagoini, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures for plasmonic nanocircuitry,” Nature Commun. 1, 150 (2010).
[Crossref]

Carminati, R.

V. Krachmalnicoff, E. Castani, Y. De Wilde, and R. Carminati, “Fluctuations of the Local Density of States Probe Licalized Surface Plasmons on Disordered Metal Films,” Phys. Rev. Lett. 105, 183901 (2010).
[Crossref]

Castani, E.

V. Krachmalnicoff, E. Castani, Y. De Wilde, and R. Carminati, “Fluctuations of the Local Density of States Probe Licalized Surface Plasmons on Disordered Metal Films,” Phys. Rev. Lett. 105, 183901 (2010).
[Crossref]

Catchpole, K. R.

Chan, C. T.

W. Wen, L. Zhou, J. Li, W. Ge, C. T. Chan, and P. Sheng, “Subwavelength Photonic Band Gaps from Planar Fractals,” Phys. Rev. Lett. 82, 223901 (2003).

L. Zhou, W. Wen, C. T. Chan, and P. Sheng, “Reflectivity of planar metallic fractal patterns,” Appl. Phys. Lett. 89, 1012–1014 (2002).

Cherukulappurath, S.

G. Volpe, S. Cherukulappurath, R. Juanola Parramon, G. Molina-Terriza, and R. Quidant, “Controlling the optical near field of nanoantennas with spatial phase-shaped beams,” Nano Lett. 9, 3608–3611 (2009).
[Crossref] [PubMed]

Chon, J. W. M.

P. Zijilstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459, 410–413 (2009).
[Crossref]

Coello, V.

S. L. Bozhevolnyi, V. A. Markel, V. Coello, W. Kim, and W. E. Shalaev, “Direct obesercation of localized dipolar excitations on rough nanostructured surfaces,” Phys. Rev. B. 58, 11441 (1998).
[Crossref]

Curto, A. G.

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional Emission of a Quantum Dot Coupled to a Nnanoantenna,” Science 329, 930–933 (2010).
[Crossref] [PubMed]

De Wilde, Y.

V. Krachmalnicoff, E. Castani, Y. De Wilde, and R. Carminati, “Fluctuations of the Local Density of States Probe Licalized Surface Plasmons on Disordered Metal Films,” Phys. Rev. Lett. 105, 183901 (2010).
[Crossref]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

Eisler, H. J.

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant Optical Antennas,” Science 308, 1607–1609 (2005).
[Crossref] [PubMed]

Eleftheriades, G. V.

A. Grbic and G. V. Eleftheriades, “Overcoming the Diffraction Limit with a Planar Left-Handed Transmission-Line Lens,” Phys. Rev. Lett. 92, 117403 (2004).
[Crossref] [PubMed]

El-Sayed, M. A.

P. K. Jain, W. Huang, and M. A. El-Sayed, “On the Universal Scaling Behaviour of the Distance Decay of Plasmon Coupling in Metal Nanoparticle Pairs: A Plasmon Ruler Equation,” Nano Lett. 7, 2080–2088 (2007).
[Crossref]

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited Optical Imaging with a Silver Superlens,” Science 308534–537 (2005).
[Crossref] [PubMed]

Feichtner, T.

J. S. Huang, V. Callegari, P. Geisler, C. Bruning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagoini, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures for plasmonic nanocircuitry,” Nature Commun. 1, 150 (2010).
[Crossref]

Fleischer, J. W.

Forchel, A.

J. S. Huang, V. Callegari, P. Geisler, C. Bruning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagoini, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures for plasmonic nanocircuitry,” Nature Commun. 1, 150 (2010).
[Crossref]

Fromm, D. P.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the Mismatch between Light and Nanoscale Objects with Gold Bowtie Nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
[Crossref] [PubMed]

Ganguly, S.

D. H. Werner and S. Ganguly, “An overview of fractal antenna engineering research,” IEEE Ant. Propag. Mag. 45, 38–57 (2003).
[Crossref]

Ge, W.

W. Wen, L. Zhou, J. Li, W. Ge, C. T. Chan, and P. Sheng, “Subwavelength Photonic Band Gaps from Planar Fractals,” Phys. Rev. Lett. 82, 223901 (2003).

Geisler, P.

J. S. Huang, V. Callegari, P. Geisler, C. Bruning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagoini, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures for plasmonic nanocircuitry,” Nature Commun. 1, 150 (2010).
[Crossref]

Girard, C.

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, “Surface Plasmon Optical Tweezers: Tunable Optical Manipulation in the Femtonewton Range,” Phys. Rev. Lett. 100, 186804 (2008).
[Crossref] [PubMed]

M. Righini, A.S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nature Phys. 3, 477–480 (2007).
[Crossref]

C. Girard, “Near fields in nanostructures,” Rep. Prog. Phys. 68, 1883–1933 (2005)
[Crossref]

Gonzalez, M. U.

S. S. Acimovic, M. P. Kreuzer, M. U. Gonzalez, and R. Quidant, “Plasmon near-field coupling in metal dimers as a step toward single-molecule sensing,” ACSNano 3, 1231–1237 (2009).

Grbic, A.

A. Grbic and G. V. Eleftheriades, “Overcoming the Diffraction Limit with a Planar Left-Handed Transmission-Line Lens,” Phys. Rev. Lett. 92, 117403 (2004).
[Crossref] [PubMed]

Gu, M.

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Nature (2)

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Figures (4)

Fig. 1
Fig. 1

Construction of the Sierpinski carpet. (a) First, (b) second, and (c) fourth step of the construction process of the fractal.

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Fig. 2
Fig. 2

Broadeining of the resonance in a plasmonic Sierpinsky nanocarpet. (a) First three fractal orders of the nanostructure, respectively in red, blue and black, and (b) relative far-field scattering spectra upon plane-wave excitation polarized along the x-axis. In pink, far-field spectrum of the basic building block of the fractal, a 50 × 50 × 35nm3 gold pad. All the spectra are in a logarithmic scale and normalized to the volume of the gold of the respective substructure.

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Fig. 3
Fig. 3

Sub-diffraction focusing by a plasmonic Sierpinsky nanocarpet. (a) Normalized intensity of the electric near-field generated by the second fractal level of the Sierpinsky nanocarpet (blue structure in Fig. 2(a)) upon plane-wave illumination at 760 nm. (b) Intensity (arbitrary units) at the focus of a Gaussian beam (NA = 1.25, λ = 760nm. (c) Normalized intensity in a gap antenna geometry with the same separation as the open region in the fractal geometry. (d–e) Normalized intensities of the electric near-field of two symmetric non-fractal nanstructures obtained by removing elements from the structure in (a). The intensities presented in (a), (c), (d) and (e) are normalized to the intensity of the incident field (enhancement factor). The white scale bar represents 100nm and is in the direction of the polarization of the incident fields.

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Fig. 4
Fig. 4

Trapping forces in the subwavelength focus at the center of the Sierpinski nanocarpet (cf. Fig. 3(a)). (a) 3D distribution of the force field and (b) trapping potential for particles (ɛparticle = 2.5) of different radii R.

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