Abstract

In this paper we analyze optical properties and plasmonic field enhancements in large aperiodic nanostructures. We introduce extension of Generalized Ohm’s Law approach to estimate electromagnetic properties of Fibonacci, Rudin-Shapiro, cluster-cluster aggregate and random deterministic clusters. Our results suggest that deterministic aperiodic structures produce field enhancements comparable to random morphologies while offering better understanding of field localizations and improved substrate design controllability. Generalized Ohm’s law results for deterministic aperiodic structures are in good agreement with simulations obtained using discrete dipole method.

© 2010 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2010 (4)

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[CrossRef] [PubMed]

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

P. Y. Chung, T. H. Lin, G. Schultz, C. Batich, and P. Jiang, “Nanopyramid surface plasmon resonance sensors,” Appl. Phys. Lett. 96(26), 261108 (2010).
[CrossRef] [PubMed]

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

2009 (2)

2008 (3)

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[CrossRef] [PubMed]

R. J. Brown and M. J. Milton, “Nanostructures and nanostructured substrates for surface-enhanced Raman scattering (SERS),” J. Raman Spectrosc. 39(10), 1313–1326 (2008).
[CrossRef]

L. Dal Negro, N. N. Fen, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A, Pure Appl. Opt. 10(6), 064013 (2008).
[CrossRef]

2007 (2)

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317(5845), 1698–1702 (2007).
[CrossRef] [PubMed]

L. Cao, D. N. Barsic, A. R. Guichard, and M. L. Brongersma, “Plasmon-assisted local temperature control to pattern individual semiconductor nanowires and carbon nanotubes,” Nano Lett. 7(11), 3523–3527 (2007).
[CrossRef] [PubMed]

2005 (2)

D. A. Genov, V. M. Shalaev, and A. K. Sarychev, “Surface plasmon excitation and correlation-induced localization-delocalization transition in semicontinuous metal films,” Phys. Rev. B 72(11), 113102 (2005).
[CrossRef]

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71(23), 235408 (2005).
[CrossRef]

2004 (1)

D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, “Resonant Field Enhancements from Metal Nanoparticle Arrays,” Nano Lett. 4(1), 153–158 (2004).
[CrossRef]

2003 (1)

D. A. Genov, A. K. Sarychev, and V. M. Shalaev, “Plasmon localization and local field distribution in metal-dielectric films,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5), 056611 (2003).
[CrossRef] [PubMed]

2000 (3)

A. K. Sarychev and V. M. Shalaev, “Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites,” Phys. Rep. 335(6), 275–371 (2000).
[CrossRef]

V. A. Shubin, A. K. Sarychev, J. P. Clerc, and V. M. Shalaev, “Local electric and magnetic fields in semicontinuous metal films: Beyond the quasistatic approximation,” Phys. Rev. B 62(16), 11230–11244 (2000).
[CrossRef]

L. Zekri, R. Bouamrane, N. Zekri, and F. Brouers, “Localization and absorption of the local field in two-dimensional composite metal-dielectric films at the percolation threshold,” J. Phys. Condens. Matter 12(3), 283–291 (2000).
[CrossRef]

1998 (2)

1997 (1)

R. Levy-Nathanson and D. J. Bergman, “Studies of the Generalized Ohm’s law,” Physica A 241(1-2), 166–172 (1997).
[CrossRef]

1996 (1)

V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, and R. L. Armstrong, “Small-particle composites. I. Linear optical properties,” Phys. Rev. B Condens. Matter 53(5), 2425–2436 (1996).
[CrossRef] [PubMed]

1995 (1)

A. K. Sarychev, D. J. Bergman, and Y. Yagil, “Theory of the optical and microwave properties of metal-dielectric films,” Phys. Rev. B Condens. Matter 51(8), 5366–5385 (1995).
[CrossRef] [PubMed]

1994 (1)

V. M. Shalaev, R. Botet, D. P. Tsai, J. Kovacs, and M. Moskovits, “Fractals: Localization of dipole excitations and giant optical polarizabilities,” Physica A 207(1-3), 197–207 (1994).
[CrossRef]

1989 (1)

S. Alexander, “Vibration of fractals and scattering of light from aerogels,” Phys. Rev. B 40(11), 7953–7965 (1989).
[CrossRef]

1988 (1)

B. T. Draine, “The discrete dipole approximation and its application to interstellar graphite dust,” Astrophys. J. 333(2), 848–872 (1988).
[CrossRef]

1979 (1)

D. Weaire and B. Kramer, “Numerical methods in the study of the Anderson transition,” J. Non-Cryst. Solids 32(1–3), 131–140 (1979).
[CrossRef]

1964 (1)

R. E. Aitchison, “Resistance between adjacent points of Liebman mesh,” Am. J. Phys. 32(7), 566 (1964).
[CrossRef]

1958 (1)

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[CrossRef]

Aitchison, R. E.

R. E. Aitchison, “Resistance between adjacent points of Liebman mesh,” Am. J. Phys. 32(7), 566 (1964).
[CrossRef]

Alexander, S.

S. Alexander, “Vibration of fractals and scattering of light from aerogels,” Phys. Rev. B 40(11), 7953–7965 (1989).
[CrossRef]

Anderson, P. W.

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[CrossRef]

Anker, J. N.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[CrossRef] [PubMed]

Armstrong, R. L.

V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, and R. L. Armstrong, “Small-particle composites. I. Linear optical properties,” Phys. Rev. B Condens. Matter 53(5), 2425–2436 (1996).
[CrossRef] [PubMed]

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[CrossRef] [PubMed]

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71(23), 235408 (2005).
[CrossRef]

Bao, J.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Bao, K.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Bardhan, R.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Barnard, E. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

Barsic, D. N.

L. Cao, D. N. Barsic, A. R. Guichard, and M. L. Brongersma, “Plasmon-assisted local temperature control to pattern individual semiconductor nanowires and carbon nanotubes,” Nano Lett. 7(11), 3523–3527 (2007).
[CrossRef] [PubMed]

Batich, C.

P. Y. Chung, T. H. Lin, G. Schultz, C. Batich, and P. Jiang, “Nanopyramid surface plasmon resonance sensors,” Appl. Phys. Lett. 96(26), 261108 (2010).
[CrossRef] [PubMed]

Bergman, D. J.

R. Levy-Nathanson and D. J. Bergman, “Studies of the Generalized Ohm’s law,” Physica A 241(1-2), 166–172 (1997).
[CrossRef]

A. K. Sarychev, D. J. Bergman, and Y. Yagil, “Theory of the optical and microwave properties of metal-dielectric films,” Phys. Rev. B Condens. Matter 51(8), 5366–5385 (1995).
[CrossRef] [PubMed]

Boriskina, S. V.

Botet, R.

V. M. Shalaev, R. Botet, D. P. Tsai, J. Kovacs, and M. Moskovits, “Fractals: Localization of dipole excitations and giant optical polarizabilities,” Physica A 207(1-3), 197–207 (1994).
[CrossRef]

Bouamrane, R.

L. Zekri, R. Bouamrane, N. Zekri, and F. Brouers, “Localization and absorption of the local field in two-dimensional composite metal-dielectric films at the percolation threshold,” J. Phys. Condens. Matter 12(3), 283–291 (2000).
[CrossRef]

Brongersma, M. L.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

L. Cao, D. N. Barsic, A. R. Guichard, and M. L. Brongersma, “Plasmon-assisted local temperature control to pattern individual semiconductor nanowires and carbon nanotubes,” Nano Lett. 7(11), 3523–3527 (2007).
[CrossRef] [PubMed]

Brouers, F.

L. Zekri, R. Bouamrane, N. Zekri, and F. Brouers, “Localization and absorption of the local field in two-dimensional composite metal-dielectric films at the percolation threshold,” J. Phys. Condens. Matter 12(3), 283–291 (2000).
[CrossRef]

P. Gadenne, F. Brouers, V. M. Shalaev, and A. K. Sarychev, “Giant Stokes fields on semicontinuous metal films,” J. Opt. Soc. Am. B 15(1), 68–72 (1998).
[CrossRef]

Brown, R. J.

R. J. Brown and M. J. Milton, “Nanostructures and nanostructured substrates for surface-enhanced Raman scattering (SERS),” J. Raman Spectrosc. 39(10), 1313–1326 (2008).
[CrossRef]

Cai, W.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

Cao, L.

L. Cao, D. N. Barsic, A. R. Guichard, and M. L. Brongersma, “Plasmon-assisted local temperature control to pattern individual semiconductor nanowires and carbon nanotubes,” Nano Lett. 7(11), 3523–3527 (2007).
[CrossRef] [PubMed]

Capasso, F.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Chung, P. Y.

P. Y. Chung, T. H. Lin, G. Schultz, C. Batich, and P. Jiang, “Nanopyramid surface plasmon resonance sensors,” Appl. Phys. Lett. 96(26), 261108 (2010).
[CrossRef] [PubMed]

Clerc, J. P.

V. A. Shubin, A. K. Sarychev, J. P. Clerc, and V. M. Shalaev, “Local electric and magnetic fields in semicontinuous metal films: Beyond the quasistatic approximation,” Phys. Rev. B 62(16), 11230–11244 (2000).
[CrossRef]

Dal Negro, L.

C. Forestiere, G. Miano, S. V. Boriskina, and L. Dal Negro, “The role of nanoparticle shapes and deterministic aperiodicity for the design of nanoplasmonic arrays,” Opt. Express 17(12), 9648–9661 (2009).
[CrossRef] [PubMed]

L. Dal Negro, N. N. Fen, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A, Pure Appl. Opt. 10(6), 064013 (2008).
[CrossRef]

Draine, B. T.

B. T. Draine, “The discrete dipole approximation and its application to interstellar graphite dust,” Astrophys. J. 333(2), 848–872 (1988).
[CrossRef]

Engheta, N.

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317(5845), 1698–1702 (2007).
[CrossRef] [PubMed]

Fan, J. A.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Fen, N. N.

L. Dal Negro, N. N. Fen, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A, Pure Appl. Opt. 10(6), 064013 (2008).
[CrossRef]

Forestiere, C.

Gadenne, P.

Genov, D. A.

D. A. Genov, V. M. Shalaev, and A. K. Sarychev, “Surface plasmon excitation and correlation-induced localization-delocalization transition in semicontinuous metal films,” Phys. Rev. B 72(11), 113102 (2005).
[CrossRef]

D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, “Resonant Field Enhancements from Metal Nanoparticle Arrays,” Nano Lett. 4(1), 153–158 (2004).
[CrossRef]

D. A. Genov, A. K. Sarychev, and V. M. Shalaev, “Plasmon localization and local field distribution in metal-dielectric films,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5), 056611 (2003).
[CrossRef] [PubMed]

Gopinath, A.

L. Dal Negro, N. N. Fen, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A, Pure Appl. Opt. 10(6), 064013 (2008).
[CrossRef]

Gray, S. K.

Guichard, A. R.

L. Cao, D. N. Barsic, A. R. Guichard, and M. L. Brongersma, “Plasmon-assisted local temperature control to pattern individual semiconductor nanowires and carbon nanotubes,” Nano Lett. 7(11), 3523–3527 (2007).
[CrossRef] [PubMed]

Halas, N. J.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Hall, W. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[CrossRef] [PubMed]

Imre, A.

Jiang, P.

P. Y. Chung, T. H. Lin, G. Schultz, C. Batich, and P. Jiang, “Nanopyramid surface plasmon resonance sensors,” Appl. Phys. Lett. 96(26), 261108 (2010).
[CrossRef] [PubMed]

Jun, Y. C.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

Kim, W.

V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, and R. L. Armstrong, “Small-particle composites. I. Linear optical properties,” Phys. Rev. B Condens. Matter 53(5), 2425–2436 (1996).
[CrossRef] [PubMed]

Kovacs, J.

V. M. Shalaev, R. Botet, D. P. Tsai, J. Kovacs, and M. Moskovits, “Fractals: Localization of dipole excitations and giant optical polarizabilities,” Physica A 207(1-3), 197–207 (1994).
[CrossRef]

Kramer, B.

D. Weaire and B. Kramer, “Numerical methods in the study of the Anderson transition,” J. Non-Cryst. Solids 32(1–3), 131–140 (1979).
[CrossRef]

Levy-Nathanson, R.

R. Levy-Nathanson and D. J. Bergman, “Studies of the Generalized Ohm’s law,” Physica A 241(1-2), 166–172 (1997).
[CrossRef]

Lin, T. H.

P. Y. Chung, T. H. Lin, G. Schultz, C. Batich, and P. Jiang, “Nanopyramid surface plasmon resonance sensors,” Appl. Phys. Lett. 96(26), 261108 (2010).
[CrossRef] [PubMed]

Lyandres, O.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[CrossRef] [PubMed]

Maier, S. A.

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71(23), 235408 (2005).
[CrossRef]

Manoharan, V. N.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Markel, V. A.

V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, and R. L. Armstrong, “Small-particle composites. I. Linear optical properties,” Phys. Rev. B Condens. Matter 53(5), 2425–2436 (1996).
[CrossRef] [PubMed]

Miano, G.

Milton, M. J.

R. J. Brown and M. J. Milton, “Nanostructures and nanostructured substrates for surface-enhanced Raman scattering (SERS),” J. Raman Spectrosc. 39(10), 1313–1326 (2008).
[CrossRef]

Montgomery, J. M.

Moskovits, M.

V. M. Shalaev, R. Botet, D. P. Tsai, J. Kovacs, and M. Moskovits, “Fractals: Localization of dipole excitations and giant optical polarizabilities,” Physica A 207(1-3), 197–207 (1994).
[CrossRef]

Nordlander, P.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Penninkhof, J. J.

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71(23), 235408 (2005).
[CrossRef]

Polman, A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[CrossRef] [PubMed]

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71(23), 235408 (2005).
[CrossRef]

Sarychev, A. K.

D. A. Genov, V. M. Shalaev, and A. K. Sarychev, “Surface plasmon excitation and correlation-induced localization-delocalization transition in semicontinuous metal films,” Phys. Rev. B 72(11), 113102 (2005).
[CrossRef]

D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, “Resonant Field Enhancements from Metal Nanoparticle Arrays,” Nano Lett. 4(1), 153–158 (2004).
[CrossRef]

D. A. Genov, A. K. Sarychev, and V. M. Shalaev, “Plasmon localization and local field distribution in metal-dielectric films,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5), 056611 (2003).
[CrossRef] [PubMed]

V. A. Shubin, A. K. Sarychev, J. P. Clerc, and V. M. Shalaev, “Local electric and magnetic fields in semicontinuous metal films: Beyond the quasistatic approximation,” Phys. Rev. B 62(16), 11230–11244 (2000).
[CrossRef]

A. K. Sarychev and V. M. Shalaev, “Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites,” Phys. Rep. 335(6), 275–371 (2000).
[CrossRef]

P. Gadenne, F. Brouers, V. M. Shalaev, and A. K. Sarychev, “Giant Stokes fields on semicontinuous metal films,” J. Opt. Soc. Am. B 15(1), 68–72 (1998).
[CrossRef]

A. K. Sarychev, D. J. Bergman, and Y. Yagil, “Theory of the optical and microwave properties of metal-dielectric films,” Phys. Rev. B Condens. Matter 51(8), 5366–5385 (1995).
[CrossRef] [PubMed]

Schuller, J. A.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

Schultz, G.

P. Y. Chung, T. H. Lin, G. Schultz, C. Batich, and P. Jiang, “Nanopyramid surface plasmon resonance sensors,” Appl. Phys. Lett. 96(26), 261108 (2010).
[CrossRef] [PubMed]

Shah, N. C.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[CrossRef] [PubMed]

Shalaev, V. M.

D. A. Genov, V. M. Shalaev, and A. K. Sarychev, “Surface plasmon excitation and correlation-induced localization-delocalization transition in semicontinuous metal films,” Phys. Rev. B 72(11), 113102 (2005).
[CrossRef]

D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, “Resonant Field Enhancements from Metal Nanoparticle Arrays,” Nano Lett. 4(1), 153–158 (2004).
[CrossRef]

D. A. Genov, A. K. Sarychev, and V. M. Shalaev, “Plasmon localization and local field distribution in metal-dielectric films,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5), 056611 (2003).
[CrossRef] [PubMed]

V. A. Shubin, A. K. Sarychev, J. P. Clerc, and V. M. Shalaev, “Local electric and magnetic fields in semicontinuous metal films: Beyond the quasistatic approximation,” Phys. Rev. B 62(16), 11230–11244 (2000).
[CrossRef]

A. K. Sarychev and V. M. Shalaev, “Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites,” Phys. Rep. 335(6), 275–371 (2000).
[CrossRef]

P. Gadenne, F. Brouers, V. M. Shalaev, and A. K. Sarychev, “Giant Stokes fields on semicontinuous metal films,” J. Opt. Soc. Am. B 15(1), 68–72 (1998).
[CrossRef]

V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, and R. L. Armstrong, “Small-particle composites. I. Linear optical properties,” Phys. Rev. B Condens. Matter 53(5), 2425–2436 (1996).
[CrossRef] [PubMed]

V. M. Shalaev, R. Botet, D. P. Tsai, J. Kovacs, and M. Moskovits, “Fractals: Localization of dipole excitations and giant optical polarizabilities,” Physica A 207(1-3), 197–207 (1994).
[CrossRef]

Shubin, V. A.

V. A. Shubin, A. K. Sarychev, J. P. Clerc, and V. M. Shalaev, “Local electric and magnetic fields in semicontinuous metal films: Beyond the quasistatic approximation,” Phys. Rev. B 62(16), 11230–11244 (2000).
[CrossRef]

Shvets, G.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Stechel, E. B.

V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, and R. L. Armstrong, “Small-particle composites. I. Linear optical properties,” Phys. Rev. B Condens. Matter 53(5), 2425–2436 (1996).
[CrossRef] [PubMed]

Sweatlock, L. A.

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71(23), 235408 (2005).
[CrossRef]

Tsai, D. P.

V. M. Shalaev, R. Botet, D. P. Tsai, J. Kovacs, and M. Moskovits, “Fractals: Localization of dipole excitations and giant optical polarizabilities,” Physica A 207(1-3), 197–207 (1994).
[CrossRef]

Van Duyne, R. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[CrossRef] [PubMed]

Vlasko-Vlasov, V.

Weaire, D.

D. Weaire and B. Kramer, “Numerical methods in the study of the Anderson transition,” J. Non-Cryst. Solids 32(1–3), 131–140 (1979).
[CrossRef]

Wei, A.

D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, “Resonant Field Enhancements from Metal Nanoparticle Arrays,” Nano Lett. 4(1), 153–158 (2004).
[CrossRef]

Welp, U.

White, J. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

Wriedt, T.

T. Wriedt, “A review of elastic light scattering theories,” Part. Syst. Charact. 15(2), 67–74 (1998).
[CrossRef]

Wu, C.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Yagil, Y.

A. K. Sarychev, D. J. Bergman, and Y. Yagil, “Theory of the optical and microwave properties of metal-dielectric films,” Phys. Rev. B Condens. Matter 51(8), 5366–5385 (1995).
[CrossRef] [PubMed]

Zekri, L.

L. Zekri, R. Bouamrane, N. Zekri, and F. Brouers, “Localization and absorption of the local field in two-dimensional composite metal-dielectric films at the percolation threshold,” J. Phys. Condens. Matter 12(3), 283–291 (2000).
[CrossRef]

Zekri, N.

L. Zekri, R. Bouamrane, N. Zekri, and F. Brouers, “Localization and absorption of the local field in two-dimensional composite metal-dielectric films at the percolation threshold,” J. Phys. Condens. Matter 12(3), 283–291 (2000).
[CrossRef]

Zhao, J.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[CrossRef] [PubMed]

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[CrossRef]

Appl. Phys. Lett. (1)

P. Y. Chung, T. H. Lin, G. Schultz, C. Batich, and P. Jiang, “Nanopyramid surface plasmon resonance sensors,” Appl. Phys. Lett. 96(26), 261108 (2010).
[CrossRef] [PubMed]

Astrophys. J. (1)

B. T. Draine, “The discrete dipole approximation and its application to interstellar graphite dust,” Astrophys. J. 333(2), 848–872 (1988).
[CrossRef]

J. Non-Cryst. Solids (1)

D. Weaire and B. Kramer, “Numerical methods in the study of the Anderson transition,” J. Non-Cryst. Solids 32(1–3), 131–140 (1979).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

L. Dal Negro, N. N. Fen, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A, Pure Appl. Opt. 10(6), 064013 (2008).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. Condens. Matter (1)

L. Zekri, R. Bouamrane, N. Zekri, and F. Brouers, “Localization and absorption of the local field in two-dimensional composite metal-dielectric films at the percolation threshold,” J. Phys. Condens. Matter 12(3), 283–291 (2000).
[CrossRef]

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R. J. Brown and M. J. Milton, “Nanostructures and nanostructured substrates for surface-enhanced Raman scattering (SERS),” J. Raman Spectrosc. 39(10), 1313–1326 (2008).
[CrossRef]

Nano Lett. (2)

L. Cao, D. N. Barsic, A. R. Guichard, and M. L. Brongersma, “Plasmon-assisted local temperature control to pattern individual semiconductor nanowires and carbon nanotubes,” Nano Lett. 7(11), 3523–3527 (2007).
[CrossRef] [PubMed]

D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, “Resonant Field Enhancements from Metal Nanoparticle Arrays,” Nano Lett. 4(1), 153–158 (2004).
[CrossRef]

Nat. Mater. (3)

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[CrossRef] [PubMed]

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[CrossRef] [PubMed]

Opt. Express (2)

Part. Syst. Charact. (1)

T. Wriedt, “A review of elastic light scattering theories,” Part. Syst. Charact. 15(2), 67–74 (1998).
[CrossRef]

Phys. Rep. (1)

A. K. Sarychev and V. M. Shalaev, “Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites,” Phys. Rep. 335(6), 275–371 (2000).
[CrossRef]

Phys. Rev. (1)

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[CrossRef]

Phys. Rev. B (4)

V. A. Shubin, A. K. Sarychev, J. P. Clerc, and V. M. Shalaev, “Local electric and magnetic fields in semicontinuous metal films: Beyond the quasistatic approximation,” Phys. Rev. B 62(16), 11230–11244 (2000).
[CrossRef]

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71(23), 235408 (2005).
[CrossRef]

D. A. Genov, V. M. Shalaev, and A. K. Sarychev, “Surface plasmon excitation and correlation-induced localization-delocalization transition in semicontinuous metal films,” Phys. Rev. B 72(11), 113102 (2005).
[CrossRef]

S. Alexander, “Vibration of fractals and scattering of light from aerogels,” Phys. Rev. B 40(11), 7953–7965 (1989).
[CrossRef]

Phys. Rev. B Condens. Matter (2)

V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, and R. L. Armstrong, “Small-particle composites. I. Linear optical properties,” Phys. Rev. B Condens. Matter 53(5), 2425–2436 (1996).
[CrossRef] [PubMed]

A. K. Sarychev, D. J. Bergman, and Y. Yagil, “Theory of the optical and microwave properties of metal-dielectric films,” Phys. Rev. B Condens. Matter 51(8), 5366–5385 (1995).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

D. A. Genov, A. K. Sarychev, and V. M. Shalaev, “Plasmon localization and local field distribution in metal-dielectric films,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5), 056611 (2003).
[CrossRef] [PubMed]

Physica A (2)

R. Levy-Nathanson and D. J. Bergman, “Studies of the Generalized Ohm’s law,” Physica A 241(1-2), 166–172 (1997).
[CrossRef]

V. M. Shalaev, R. Botet, D. P. Tsai, J. Kovacs, and M. Moskovits, “Fractals: Localization of dipole excitations and giant optical polarizabilities,” Physica A 207(1-3), 197–207 (1994).
[CrossRef]

Science (2)

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317(5845), 1698–1702 (2007).
[CrossRef] [PubMed]

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R. Jullien, and R. Botet, Aggregation and Fractal Aggregates (World Scientific, Singapore, 1987)

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1985)

L. R. Hirsch, J. L. West, R. J. Stafford, J. A. Bankson, S. R. Sershen, R. E. Price, J. D. Hazle, and N. J. Halas, “Nanoshell-Mediated Photothermal Tumor Therapy,” Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (Institute of Electrical and Electronics Engineers, New York, 2003) Vol. 2, 1230–1231.

V. M. Shalaev, Nonlinear Optics of Random Media: Fractal Composites and Metal-Dielectric Films (Springer, New York, 2000), Vol. 158.

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Figures (9)

Fig. 1
Fig. 1

The scheme used by Generalized Ohm’s Law approach. Under deterministic GOL extension particles and voids are represented as single metallic and dielectric bonds. Potential lattice sites coincide with points of particle contact in y direction.

Fig. 2
Fig. 2

Deterministic structure pattern and corresponding Fourier transform (a) Fibonacci (b) Rudin-Shapiro (c) CCA Fractal (d) Random.

Fig. 3
Fig. 3

Maximum field enhancement versus wavelength for structures of variable size ( N = 44 black, N = 72 red, N = 98 blue) and variable morphologies (A) Fibonacci (B) Rudin-Shapiro (C) CCA Fractal (D) Random.

Fig. 4
Fig. 4

Rudin-Shapiro array pattern (a) and corresponding current density distribution (b) λ = 422 nm (c) λ = 432 nm (d) λ = 452 nm, N = 44 .

Fig. 5
Fig. 5

Spatial intensity distribution at maximum field enhancement wavelength (a) Fibonacci (b) Rudin-Shapiro (c) CCA Fractal (d) Random. N = 72 in all cases.

Fig. 6
Fig. 6

Inverse participation ratio versus structure size (a) Fibonacci (b) Rudin-Shapiro (c) CCA Fractal (d) Random at λ = 358 nm (black squares) and at maximum field enhancement wavelength (red circles).

Fig. 7
Fig. 7

Intensity distribution function versus logarithm of intensity computed at maximum field enhancement wavelength (a) Fibonacci (b) Rudin-Shapiro (c) CCA Fractal (d) Random. N = 72 in all cases.

Fig. 8
Fig. 8

Eigenstate localization length versus eigenstate eigenvalue (a) Fibonacci (b) Rudin-Shapiro (c) CCA Fractal (d) Random. N = 72 , λ = 358 nm.

Fig. 9
Fig. 9

Absorbance versus wavelength for arrays of variable size ( N = 44 black, N = 72 red, N = 98 blue) and variable morphologies (A) Fibonacci (B) Rudin-Shapiro (C) CCA Fractal (D) Random.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

j E ( r ) = 0 , j H ( r ) = 0 ,
j E ( r ) = u ( r ) E ( r ) , j H ( r ) = w ( r ) H ( r ) ,
u ( r ) = i c 2 π tan ( D k / 4 ) + n ( r ) tan ( d k n ( r ) / 2 ) 1 n ( r ) tan ( D k / 4 ) tan ( d k n ( r ) / 2 ) ,
w ( r ) = i c 2 π n ( r ) tan ( D k / 4 ) + tan ( d k n ( r ) / 2 ) n ( r ) tan ( D k / 4 ) tan ( d k n ( r ) / 2 ) ,
[ ε ˜ ( r ) φ ( r ) ] = F ,
ε ˜ ( r ) = i 4 π u ( r ) w d .
H Φ = I ,
E 1 ( r ) = E ( r ) + 2 π c [ n × j H ( r ) ] .
u e = < j E E 0 > | E 0 | 2 , w e = < j H H 0 > | H 0 | 2 .
R = | ( 2 π / c ) ( u e + w e ) ( 1 + ( 2 π / c ) u e ) ( 1 ( 2 π / c ) w e ) | 2 ,
T = | 1 + ( 2 π / c ) 2 u e w e ( 1 + ( 2 π / c ) u e ) ( 1 ( 2 π / c ) w e ) | 2 ,
A = 1 R T ,
H ' Ψ n = Λ n Ψ n ,
ε ( ω ) = ε b ( ω p / ω ) 2 / ( 1 + i ω τ / ω ) ,

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