Abstract

Fano resonances between plasmons and diffracted light offer tunable energies and locales, but attribution of Fano resonance features to geometry and physicochemistry of metal nanostructures and adjacent dielectrics has been confounded by complexity and computational expense. This work shows predictable modal shifts of Fano resonance in square lattices of plasmonic nanostructures can be attributed directly to changes in medium wavenumber, particle size, and lattice constant that alter plasmon polarizability and diffractive interference. For 45 to 80 nm radius particles, a window of lattice constants that support Fano resonances is identified in a range from 500 to 900 nm. Lattice constants that support high intensity resonances are determined by individual particle polarizability and medium wavenumber. Fano resonance wavelengths redshift from diffracted photon energies as local refractive index (RI) changes due to coupling with particle polarizability in the window. Redshift sensitivities for quadrupole, dipole, and Fano resonances are 150, 348, and 541 nm, respectively, per RI unit. Fano resonance intensity may be enhanced more than tenfold by selecting nanoparticle sizes and lattice constants. The quantitative effects of such parametric changes are rapidly and intuitively distinguished using a semi-analytic approach, consisting of an exact expression for particle polarizability, a trigonometric description of diffraction, and a semi-analytical coupled dipole approximation.

© 2014 Chinese Laser Press

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    [CrossRef]

2012

Y. Francescato, V. Giannini, and S. Maier, “Plasmonic systems unveiled by Fano resonances,” ACS Nano 6, 1830–1838 (2012).
[CrossRef]

S. H. Mousavi, A. B. Khanikaev, and G. Shvets, “Optical properties of Fano-resonant metallic metasurfaces on a substrate,” Phys. Rev. B 85, 155429 (2012).
[CrossRef]

R. D. Artuso and G. W. Bryant, “Hybrid quantum dot-metal nanoparticle systems: connecting the dots,” Acta Phys. Pol. A 122, 289–293 (2012).

S. Park, K. H. Jin, M. Yi, J. C. Ye, J. Ahn, and K. Jeong, “Enhancement of terahertz pulse emission by optical nanoantenna,” ACS Nano 6, 2026–2031 (2012).
[CrossRef]

R. B. Dunbar, H. C. Hessee, D. S. Lembke, and L. Schmidt-Mende, “Light-trapping plasmonic nanovoid arrays,” Phys. Rev. B 85, 035301 (2012).
[CrossRef]

C. P. Huang, X. G. Yin, Y. Zhang, S. B. Wang, Y. Y. Zhu, H. Liu, and C. T. Chan, “Deep subwavelength Fabry–Perot-like resonances in a sandwiched reflection grating,” Phys. Rev. B 85, 235410 (2012).
[CrossRef]

N. N. Lal, H. Zhou, M. Hawkeye, J. K. Sinha, P. N. Bartlett, G. A. J. Amaratunga, and J. J. Baumberg, “Using spacer layers to control metal and semiconductor absorption in ultrathin solar cells with plasmonic substrates,” Phys. Rev. B 85, 245318 (2012).
[CrossRef]

A. B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, “Collective resonances in metal nanoparticle arrays with dipole-quadrupole interactions,” Phys. Rev. B 85, 245411 (2012).
[CrossRef]

A. Gopalakrishnan, M. Malerba, S. Tuccio, S. Panaro, E. Miele, M. Chirumamilla, S. Santoriello, C. Dorigoni, A. Giugni, R. P. Zaccaria, C. Liberale, F. De Angelis, L. Razzari, R. Krahne, A. Toma, G. Das, and E. Di Fabrizio, “Nanoplasmonic structures for biophotonic applications: SERS overview,” Ann. Phys. 524, 620–636 (2012).
[CrossRef]

G. Konstantatos, M. Badioli, L. Gaudreau, J. Osmond, M. Bernechea, F. P. G. de Arquer, F. Gatti, and F. H. L. Koppens, “Hybrid graphene–quantum dot phototransistors with ultrahigh gain,” Nat. Nanotechnol. 7, 363–368 (2012).
[CrossRef]

Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander, and N. J. Halas, “Graphene-antenna sandwich photodetector,” Nano Lett. 12, 3808–3813 (2012).
[CrossRef]

A. Gutes, B. Hsia, A. Sussman, W. Mickelson, A. Zettl, C. Carraro, and R. Maboudian, “Graphene decoration with metal nanoparticles: towards easy integration for sensing applications,” Nanoscale 4, 438–440 (2012).
[CrossRef]

Z. Fang, Y. Wang, Z. Liu, A. Schlather, P. M. Ajayan, F. H. L. Koppens, P. Nordlander, and N. J. Halas, “Plasmon-induced doping of graphene,” ACS Nano 6, 10222–10228 (2012).
[CrossRef]

H. Chen, L. Shao, Y. C. Man, C. Zhao, J. Wang, and B. Yang, “Fano resonance in (gold core)–(dielectric shell) nanostructures without symmetry breaking,” Small 8, 1503–1509 (2012).
[CrossRef]

D. DeJarnette, J. Norman, and D. K. Roper, “Spectral patterns underlying polarization-enhanced diffractive interference are distinguishable by complex trigonometry,” Appl. Phys. Lett. 101, 183104 (2012).
[CrossRef]

D. DeJarnette, D. K. Roper, and B. Harbin, “Geometric effects on far-field coupling between multipoles of nanoparticles in square arrays,” J. Opt. Soc. Am. B 29, 88–100 (2012).
[CrossRef]

C. Y. Liu, K. Liang, C. C. Chang, and Y. Tzeng, “Effects of plasmonic coupling and electrical current on persistent photoconductivity of single-layer graphene on pristine and silver nanoparticle-coated SiO2/Si,” Opt. Express 20, 22934–22952 (2012).
[CrossRef]

2011

B. Gallinet and O. J. F. Martin, “Relation between near-field and far-field properties of plasmonic Fano resonances,” Opt. Express 19, 22167–22175 (2011).
[CrossRef]

H. Chen, L. Shao, T. Ming, K. C. Woo, Y. C. Man, J. Wang, and H. Q. Lin, “Observation of the Fano resonance in gold nanorods supported on high-dielectric-constant substrates,” ACS Nano 5, 6754–6763 (2011).
[CrossRef]

Y. Zhao and A. Alu, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
[CrossRef]

P. Blake, J. Obermann, B. Harbin, and D. K. Roper, “Enhanced nanoparticle response from coupled dipole excitation for plasmon sensors,” IEEE Sens. J. 11, 3332–3340 (2011).
[CrossRef]

A. Artar, A. A. Yanik, and H. Altug, “Directional double Fano resonances in plasmonic hetero-oligomers,” Nano Lett. 11, 3694–3700 (2011).
[CrossRef]

B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B 83, 235427 (2011).
[CrossRef]

P. Offermans, M. C. Schaafsma, S. R. K. Rodrigue, Y. Zhang, M. Crego-Calama, S. H. Brongersma, and J. Gomez Rivas, “Universal scaling of the figure of merit of plasmonic sensors,” ACS Nano 5, 5151–5157 (2011).
[CrossRef]

S. Mai, S. V. Syzranov, and K. B. Efetov, “Photocurrent in a visible-light graphene photodiode,” Phys. Rev. B 83, 033402 (2011).
[CrossRef]

Y. Liu, R. Cheng, L. Liao, H. Zhou, J. Bai, G. Liu, L. Liu, Y. Huang, and X. Duan, “Plasmon resonance enhanced multicolour photodetection by graphene,” Nat. Commun. 2, 579 (2011).
[CrossRef]

S. F. Shi, X. Xu, D. C. Ralph, and P. L. McEuen, “Plasmon resonance in individual nanogap electrodes studied using graphene nanoconstrictions as photodetectors,” Nano Lett. 11, 1814–1818 (2011).
[CrossRef]

B. Bai, X. Li, I. Vartiainen, A. Lehmuskero, G. Kang, J. Turunen, M. Kuittinen, and P. Vahimaa, “Anomalous complete opaqueness in a sparse array of gold nanoparticle chains,” Appl. Phys. Lett. 99, 081911 (2011).
[CrossRef]

T. J. Echtermeyer, L. Britnell, P. K. Jasnos, A. Lombardo, R. V. Gorbachev, A. N. Grigorenko, A. K. Geim, A. C. Ferrari, and K. S. Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
[CrossRef]

V. Giannini, Y. Francescato, H. Amrania, C. C. Phillips, and S. A. Maier, “Fano resonances in nanoscale plasmonic systems: a parameter-free modeling approach,” Nano Lett. 11, 2835–2840 (2011).
[CrossRef]

S. R. K. Rodriguez, A. Abass, B. Maes, O. T. A. Janssen, G. Vecchi, and J. Gómez Rivas, “Coupling bright and dark plasmonic lattice resonances,” Phys. Rev. X 1, 021019 (2011).

B. Gallinet and O. J. F. Martin, “Influence of electromagnetic interactions on the line shape of plasmonic Fano resonances,” ACS Nano 5, 8999–9008 (2011).
[CrossRef]

Z. K. Zhou, X. N. Peng, Z. J. Yang, Z. S. Zhang, M. Li, X. R. Su, Q. Zhang, X. Shan, Q. Q. Wang, and Z. Zhang, “Tuning gold nanorod-nanoparticle hybrids into plasmonic Fano resonance for dramatically enhanced light emission and transmission,” Nano Lett. 11, 49–55 (2011).
[CrossRef]

T. G. Habteyes, S. Dhuey, S. Cabrini, P. J. Schuck, and S. R. Leone, “Theta-shaped plasmonic nanostructures: bringing “dark” multipole plasmon resonances into action via conductive coupling,” Nano Lett. 11, 1819–1825 (2011).
[CrossRef]

2010

B. luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

C. X. Guo, H. B. Yang, Z. M. Sheng, Z. S. Lu, Q. L. Song, and C. M. Li, “Layered graphene/quantum dots for photovoltaic devices,” Angew. Chem., Int. Ed. 49, 3014–3017 (2010).
[CrossRef]

P. Blake, W. Ahn, and D. K. Roper, “Enhanced uniformity in arrays of electroless plated spherical gold nanoparticles using tin presensitization,” Langmuir 26, 1533–1538 (2010).
[CrossRef]

W. Ahn, P. Blake, J. Schulz, M. E. Ware, and D. K. Roper, “Fabrication of regular arrays of Au nanospheres by thermal transformation of electroless-plated films,” J. Vac. Sci. Technol. B 28, 638–642 (2010).
[CrossRef]

T. J. Davis, D. E. Gómez, and K. C. Vernon, “Interaction of molecules with localized surface plasmons in metallic nanoparticles,” Phys. Rev. B 81, 045432 (2010).
[CrossRef]

D. K. Roper, W. Ahn, B. Taylor, and Y. D’Asen, “Enhanced spectral sensing by electromagnetic coupling with localized surface plasmons on subwavelength structures,” IEEE Sens. J. 10, 531–540 (2010).
[CrossRef]

N. Papasimakis, Z. Luo, Z. X. Shen, F. De Angelis, E. Di Fabrizio, A. E. Nikolaenko, and N. I. Zheludev, “Graphene in a photonic metamaterial,” Opt. Express 18, 8353–8359 (2010).
[CrossRef]

2009

M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg dcattering in photonic crystals,” Phys. Rev. Lett. 103, 023901 (2009).
[CrossRef]

T. Mueller, F. Xia, M. Freitag, J. Tsang, and P. Avouris, “Role of contacts in graphene transistors: a scanning photocurrent study,” Phys. Rev. B 79, 245430 (2009).
[CrossRef]

F. Xia, T. Mueller, Y. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4, 839–843 (2009).
[CrossRef]

E. Simsek, “Effective refractive index approximation and surface plasmon resonance modes of metal nanoparticle chains and arrays,” PIERS Online 5, 629–632 (2009).

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009).
[CrossRef]

F. Hao, P. Nordlander, Y. Sonnefraud, P. V. Dorpe, and S. Maier, “Tunability of subradiant dipolar and Fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano 3, 643–652 (2009).
[CrossRef]

2008

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A. Christ, Y. Ekinci, H. H. Solak, N. Gippius, S. G. Tikhodeev, and O. J. F. Martin, “Controlling the Fano interference in a plasmonic lattice,” Phys. Rev. B 76, 201405 (2007).
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Figures (7)

Fig. 1.
Fig. 1.

Schematic of the square lattice of nanoparticles (hollow circles) identifying diffraction modes (solid lines) that constitute unique particle chains. Inset depicts wavelength contraction of a plane wave moving from a smaller to a larger index of refraction medium and its effects on nanoparticle polarizability. Incident energy that excites resonance at η1 must be reduced to excite resonance at η2>η1.

Fig. 2.
Fig. 2.

Phase overlap (dashed line) onto a center particle was calculated using Ref. [41] for a lattice constant of 600 nm and RI values of 1.00 (black; peak 600nm), 1.17 (blue; 700nm), and 1.33 (red; 800 and 575 nm). Extinction spectra (solid line) were calculated by rsa-CDA for corresponding infinite arrays of 70 nm radius Au particles with lattice constant 600 nm. The inset expands the 1.17 RI array to show that constructive interference from lattice scattering supports extinction peaks.

Fig. 3.
Fig. 3.

Imaginary component of particle polarizability [Eq. (1)] is shown as the color gradient for RI values of 1.00 and 1.33 over a range of particle sizes and incident vacuum wavelength values.

Fig. 4.
Fig. 4.

Comparison of single particle extinction spectra calculated for 70 nm radius spherical particles using the exact Mie theory (dotted) and the dynamic dipole polarizability (solid lines) with the quadrupole extension. The homogeneous RI surrounding each particle is shown in the legend.

Fig. 5.
Fig. 5.

Extinction spectra for a square lattice of 70 nm radius particles spaced at 600 nm with RI values of 1.00, 1.17, and 1.33 using the rsa-CDA. Inset shows spectral results for a 5×5 array of 70 nm Au particles with a lattice constant of 600 nm using the finite CDA. The value of extinction efficiency at the RI and wavelength shown appears as a color gradient.

Fig. 6.
Fig. 6.

Sensitivity shown by wavelength shift of Fano resonance peak wavelength per RI unit (RIU) for a given geometric combination of lattice constant and particle radius. RI change for the calculation was from 1.00 to 1.10.

Fig. 7.
Fig. 7.

Array geometries that yield extraordinary Fano resonance through constructive interference of scattered light. The color gradient shows the maximum extinction of the Fano resonance as a function of lattice constant and particle radius.

Tables (1)

Tables Icon

Table 1. Categorization of Select, Recent Studies of Fano Resonant Plasmonic Nanostructures According to Source and Type of Description

Equations (1)

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αd=4π(3iR32x3a1),andαq=4π(10iR33x3a2),

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