Abstract

We investigate effective medium properties of nanoparticles (NPs) in surface plasmon (SP) resonance detection. Attention was paid to the effective medium characteristics with respect to the particle distribution in equally spaced, aggregated, and intermediate models, although effects of other parameters such as size, material, and concentration were also explored. The results suggest that the distribution may cause significant measurement deviation by as much as 20% for gold NPs and less than 5% for silica. Particle concentration showed complicated dependence in the effective medium. Different mechanisms were observed to govern effective medium properties of dielectric and metal NPs, SP mode transition and multiple scattering for silica NPs. In contrast, metal damping dominated resonance characteristics for gold NPs. The results are expected to provide fresh insights on how to apply an effective medium and interpret measured data in SP resonance sensors and beyond.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (1)

E. Nadal, N. Barros, H. Glénat, and H. Kachakachi, “Optical properties of complex plasmonic materials studied with extended effective medium theories combined with rigorous coupled wave analysis,” Materials 11(3), 351 (2018).
[Crossref] [PubMed]

2017 (2)

X. Bian, D. L. Gao, and L. Gao, “Tailoring optical pulling force on gain coated nanoparticles with nonlocal effective medium theory,” Opt. Express 25(20), 24566–24578 (2017).
[Crossref] [PubMed]

P. T. Bowen, A. Baron, and D. R. Smith, “Effective-medium description of a metasurface composed of a periodic array of nanoantennas coupled to a metallic film,” Phys. Rev. A 95(3), 033822 (2017).
[Crossref]

2016 (1)

2015 (1)

X. Zhang and Y. Wu, “Effective medium theory for anisotropic metamaterials,” Sci. Rep. 5(1), 7892 (2015).
[Crossref] [PubMed]

2014 (1)

M. H. Tyboroski, N. R. Anderson, and R. E. Camley, “An effective medium study of surface plasmon polaritons in nanostructured gratings using attenuated total reflection,” J. Appl. Phys. 115(1), 013104 (2014).
[Crossref]

2012 (5)

J. Toudert, L. Simonot, S. Camelio, and D. Babonneau, “Advanced optical effective medium modeling for a single layer of polydisperse ellipsoidal nanoparticles embedded in a homogeneous dielectric medium: surface plasmon resonances,” Phys. Rev. B 86(4), 045415 (2012).
[Crossref]

P. Zijlstra, P. M. Paulo, and M. Orrit, “Optical detection of single non-absorbing molecules using the surface plasmon resonance of a gold nanorod,” Nat. Nanotechnol. 7(6), 379–382 (2012).
[Crossref] [PubMed]

M. A. Green and S. Pillai, “Harnessing plasmonics for solar cells,” Nat. Photonics 6(3), 130–132 (2012).
[Crossref]

S. Moon, Y. Kim, Y. Oh, H. Lee, H. C. Kim, K. Lee, and D. Kim, “Grating-based surface plasmon resonance detection of core-shell nanoparticle mediated DNA hybridization,” Biosens. Bioelectron. 32(1), 141–147 (2012).
[Crossref] [PubMed]

M. Terakawa, S. Takeda, Y. Tanaka, G. Obara, T. Miyanishi, T. Sakai, T. Sumiyoshi, H. Sekita, M. Hasegawa, P. Viktorovitch, and M. Obara, “Enhanced localized near field and scattered far field for surface nanophotonics applications,” Prog. Quantum Electron. 36(1), 194–271 (2012).
[Crossref]

2011 (1)

N. C. Dyck, R. C. Denomme, and P. M. Nieva, “Effective medium properties of arbitrary nanoparticle shapes in a localized surface plasmon resonance sensing layer,” J. Phys. Chem. C 115(31), 15225–15233 (2011).
[Crossref]

2010 (1)

2009 (2)

J. Fu, B. Park, and Y. Zhao, “Nanorod-mediated surface plasmon resonance sensor based on effective medium theory,” Appl. Opt. 48(23), 4637–4649 (2009).
[Crossref] [PubMed]

R. Nishitani, H. W. Liu, and H. Iwasaki, “Calculation of plasmon enhanced molecular fluorescence in scanning tunnel microscopy using effective medium model for molecules on metal substrate,” J. Vac. Sci. Technol. B 27(2), 993–996 (2009).
[Crossref]

2007 (5)

2006 (1)

2005 (2)

R. S. Kshetrimayum, “A brief intro to metamaterials,” IEEE Potentials 23(5), 44–46 (2005).
[Crossref]

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[Crossref] [PubMed]

2004 (3)

S. Elhadj, G. Singh, and R. F. Saraf, “Optical properties of an immobilized DNA monolayer from 255 to 700 nm,” Langmuir 20(13), 5539–5543 (2004).
[Crossref] [PubMed]

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93(10), 107402 (2004).
[Crossref] [PubMed]

I. Pastoriza-Santos, D. Gomez, J. Perez-Juste, L. M. Liz-Marzán, and P. Mulvaney, “Optical properties of metal nanoparticle coated silica spheres: a simple effective medium approach,” Phys. Chem. Chem. Phys. 6(21), 5056–5060 (2004).
[Crossref]

2003 (2)

A. J. A. El-Haija, “Effective medium approximation for the effective optical constants of a bilayer and a multilayer structure based on the characteristic matrix technique,” J. Appl. Phys. 93(5), 2590–2594 (2003).
[Crossref]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[Crossref] [PubMed]

2002 (1)

Y. Lu, Y. Yin, Z. Y. Li, and Y. Xia, “Synthesis and self-assembly of Au@ SiO2 core− shell colloids,” Nano Lett. 2(7), 785–788 (2002).
[Crossref]

2000 (2)

R. Ruppin, “Evaluation of extended Maxwell-Garnett theories,” Opt. Commun. 182(4–6), 273–279 (2000).
[Crossref]

L. He, M. D. Musick, S. R. Nicewarner, F. G. Salinas, S. J. Benkovic, M. J. Natan, and C. D. Keating, “Colloidal Au-enhanced surface plasmon resonance for ultrasensitive detection of DNA hybridization,” J. Am. Chem. Soc. 122(38), 9071–9077 (2000).
[Crossref]

1999 (1)

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82(12), 2590–2593 (1999).
[Crossref]

1998 (1)

J. Belloni, M. Mostafavi, H. Remita, J.-L. Marignier, and M.-O. Delcourt, “Radiation-induced synthesis of mono- and multi-metallic clusters and nanocolloids,” New J. Chem. 22(11), 1239–1255 (1998).
[Crossref]

1997 (1)

F. J. García-Vidal, J. M. Pitarke, and J. B. Pendry, “Effective medium theory of the optical properties of aligned carbon nanotubes,” Phys. Rev. Lett. 78(22), 4289–4292 (1997).
[Crossref]

1996 (1)

N. C. Constantinou and F. G. Elmzughi, “Effective medium intrasubband surface plasmon-polaritons on semi-infinite GaAs/AlAs superlattices,” Solid State Commun. 97(11), 947–950 (1996).
[Crossref]

1993 (1)

1989 (1)

J. W. Haus, R. Inguva, and C. M. Bowden, “Effective-medium theory of nonlinear ellipsoidal composites,” Phys. Rev. A 40(10), 5729–5734 (1989).
[Crossref] [PubMed]

1986 (2)

M. Quinten and U. Kreibig, “Optical properties of aggregates of small metal particles,” Surf. Sci. 172(3), 557–577 (1986).
[Crossref]

P. Dimon, S. K. Sinha, D. A. Weitz, C. R. Safinya, G. S. Smith, W. A. Varady, and H. M. Lindsay, “Structure of aggregated gold colloids,” Phys. Rev. Lett. 57(5), 595–598 (1986).
[Crossref] [PubMed]

1982 (1)

D. E. Aspnes, “Local-field effects and effective-medium theory: a microscopic perspective,” Am. J. Phys. 50(8), 704–709 (1982).
[Crossref]

1981 (1)

U. Kreibig, A. Althoff, and H. Pressmann, “Veiling of optical single particle properties in many particle systems by effective medium and clustering effects,” Surf. Sci. 106(1–3), 308–317 (1981).
[Crossref]

1980 (1)

W. Lamb, D. M. Wood, and N. W. Ashcroft, “Long-wavelength electromagnetic propagation in heterogeneous media,” Phys. Rev. B 21(6), 2248–2266 (1980).
[Crossref]

1979 (1)

G. C. Papavassiliou, “Optical properties of small inorganic and organic metal particles,” Prog. Solid State Chem. 12(3–4), 185–271 (1979).
[Crossref]

1976 (1)

P. Clippe, R. Evrard, and A. A. Lucas, “Aggregation effect on the infrared absorption spectrum of small ionic crystals,” Phys. Rev. B 14(4), 1715–1721 (1976).
[Crossref]

1965 (1)

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

1904 (1)

J. C.M. Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. Lond. 203(359-371), 385–420 (1904).
[Crossref]

Althoff, A.

U. Kreibig, A. Althoff, and H. Pressmann, “Veiling of optical single particle properties in many particle systems by effective medium and clustering effects,” Surf. Sci. 106(1–3), 308–317 (1981).
[Crossref]

Anderson, N. R.

M. H. Tyboroski, N. R. Anderson, and R. E. Camley, “An effective medium study of surface plasmon polaritons in nanostructured gratings using attenuated total reflection,” J. Appl. Phys. 115(1), 013104 (2014).
[Crossref]

Ashcroft, N. W.

W. Lamb, D. M. Wood, and N. W. Ashcroft, “Long-wavelength electromagnetic propagation in heterogeneous media,” Phys. Rev. B 21(6), 2248–2266 (1980).
[Crossref]

Aspnes, D. E.

D. E. Aspnes, “Local-field effects and effective-medium theory: a microscopic perspective,” Am. J. Phys. 50(8), 704–709 (1982).
[Crossref]

Aussenegg, F. R.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82(12), 2590–2593 (1999).
[Crossref]

Babonneau, D.

J. Toudert, L. Simonot, S. Camelio, and D. Babonneau, “Advanced optical effective medium modeling for a single layer of polydisperse ellipsoidal nanoparticles embedded in a homogeneous dielectric medium: surface plasmon resonances,” Phys. Rev. B 86(4), 045415 (2012).
[Crossref]

Baron, A.

P. T. Bowen, A. Baron, and D. R. Smith, “Effective-medium description of a metasurface composed of a periodic array of nanoantennas coupled to a metallic film,” Phys. Rev. A 95(3), 033822 (2017).
[Crossref]

Barros, N.

E. Nadal, N. Barros, H. Glénat, and H. Kachakachi, “Optical properties of complex plasmonic materials studied with extended effective medium theories combined with rigorous coupled wave analysis,” Materials 11(3), 351 (2018).
[Crossref] [PubMed]

Belloni, J.

J. Belloni, M. Mostafavi, H. Remita, J.-L. Marignier, and M.-O. Delcourt, “Radiation-induced synthesis of mono- and multi-metallic clusters and nanocolloids,” New J. Chem. 22(11), 1239–1255 (1998).
[Crossref]

Benkovic, S. J.

L. He, M. D. Musick, S. R. Nicewarner, F. G. Salinas, S. J. Benkovic, M. J. Natan, and C. D. Keating, “Colloidal Au-enhanced surface plasmon resonance for ultrasensitive detection of DNA hybridization,” J. Am. Chem. Soc. 122(38), 9071–9077 (2000).
[Crossref]

Bian, X.

Bourillot, E.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82(12), 2590–2593 (1999).
[Crossref]

Bowden, C. M.

J. W. Haus, R. Inguva, and C. M. Bowden, “Effective-medium theory of nonlinear ellipsoidal composites,” Phys. Rev. A 40(10), 5729–5734 (1989).
[Crossref] [PubMed]

Bowen, P. T.

P. T. Bowen, A. Baron, and D. R. Smith, “Effective-medium description of a metasurface composed of a periodic array of nanoantennas coupled to a metallic film,” Phys. Rev. A 95(3), 033822 (2017).
[Crossref]

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[Crossref]

Camelio, S.

J. Toudert, L. Simonot, S. Camelio, and D. Babonneau, “Advanced optical effective medium modeling for a single layer of polydisperse ellipsoidal nanoparticles embedded in a homogeneous dielectric medium: surface plasmon resonances,” Phys. Rev. B 86(4), 045415 (2012).
[Crossref]

Camley, R. E.

M. H. Tyboroski, N. R. Anderson, and R. E. Camley, “An effective medium study of surface plasmon polaritons in nanostructured gratings using attenuated total reflection,” J. Appl. Phys. 115(1), 013104 (2014).
[Crossref]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[Crossref]

Clippe, P.

P. Clippe, R. Evrard, and A. A. Lucas, “Aggregation effect on the infrared absorption spectrum of small ionic crystals,” Phys. Rev. B 14(4), 1715–1721 (1976).
[Crossref]

Constantinou, N. C.

N. C. Constantinou and F. G. Elmzughi, “Effective medium intrasubband surface plasmon-polaritons on semi-infinite GaAs/AlAs superlattices,” Solid State Commun. 97(11), 947–950 (1996).
[Crossref]

Delcourt, M.-O.

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic illustration of the calculation models with a label number N = 4: scattering NLs are assumed to be aggregated (AG model) and equally spaced (ES model). Intermediate model distribution appears between AG and ES model. x denotes the label-to-label distance. For AG and ES model, x = ϕ and Λ/N. All the distribution models correspond to an identical effective medium on the right. (b) Histograms of nearest-neighbor distances between NLs (ϕ = 100 nm) corresponding to the AG and ES model distributions and intermediate models with x = 1.25, 2.50, and 3.75 μm at a concentration of CNL = 4/Λ (Λ = 20 μm is assumed with N = 4). Each distribution consists of two components except for the ES model. Arrows represent the transition from the AG to the ES model. (c) Effective medium approximation of SPR detection characteristics compared with exact results calculated by RCWA. NLs were assumed to form ES and AG model distribution with ϕ = 50, 100, 250, and 500 nm. Both silica and gold NLs were considered (top two vs. bottom two rows for silica and gold). Label concentration is fixed at CNL = 1/μm with Λ = 20 μm and N = 20. The standard deviation σ with respect to the exact results for various distributions of (d) silica and (e) gold NLs with ϕ = 10 nm ~-700 nm. CNL = 1/μm with Λ = 20 μm and N = 20. The data were lineated by Bezier interpolation.
Fig. 2
Fig. 2 Effective medium refractive index neff (a) for silica and (b) gold NLs and absorption constant κeff (c) for silica and (d) gold with ϕ = 10 nm ~ 700 nm. Effective permittivity is given by εeff = (neff + iκeff)2. Arrows in (a) and (b) represent the largest index difference Δneff. Label concentration is fixed at CNL = 1/μm with Λ = 20 μm and N = 20. The gray shade represents the difference in the effective medium refractive index and absorption constant Δneff and Δκeff between the maximum and the minimum of the various distribution models. The data in solid lines were Bezier interpolated.
Fig. 3
Fig. 3 Near-field intensity distribution (|E|2): (a) ϕ = 30 nm and (b) 100 nm in the ES model (magnified view of two NLs). (c) ϕ = 200 nm and (d) 700 nm in the AG model. For both models, Λ = 20 μm.
Fig. 4
Fig. 4 Resonance characteristics with silica NLs: (a) ES model, intermediate models with (b) x = ϕ + 100 nm and (c) x = ϕ + 50 nm, and (d) AG model. For gold NLs, (e) ES model, (f) x = ϕ + 100 nm, (g) x = ϕ + 50 nm, and (h) AG model. Label concentration fixed at CNL = 1/μm with Λ = 20 μm and N = 20. Black dotted lines show the evolution of modes with the label size. Arrows represent an increase in diameter (larger NLs) from ϕ = 10 to 700 nm.
Fig. 5
Fig. 5 Concentration dependence of effective medium properties with respect to NL size (ϕ) for CNL = 0.25 ~ 1/μm with Λ = 20 μm and N = 20: (a) neff and (b) κeff for silica NLs. For gold NLs, (c) neff and (d) κeff. The labels are assumed in the ES and the AG model (ES: filled and AG: open symbol).

Equations (4)

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ε eff ε amb ε eff +2 ε amb = f v ε np ε amb ε np +2 ε amb ,
1 ε eff = f v ε np + 1 f v ε amb
[ E 0,i E 0,r ]=( m=0 4 S m,m+1 ) [ E 5,i 0 ],
S m,m+1 = 1 t m,m+1 [ e j δ m+1 r m,m+1 e j δ m+1 r m,m+1 e j δ m+1 e j δ m+1 ]

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