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Singular Representation of Plasmon Resonance Modes to Optimize the Near- and Far-Field Properties of Metal Nanoparticles

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Abstract

A singular representation of the complex-valued extinction coefficient of metal nanoparticles is developed to characterize the resonant behavior of plasmonic systems exhibiting an arbitrary number of resonances. This complex coefficient is analytically represented in form of a meromorphic function of the pulsation containing a singular (resonant) and a regular part, and an original algorithm based on a numerical derivation is proposed to find all resonant parameters of each excited mode. This approach, applied to silver nanoparticles, allows a characterization of the resonance red-shift and broadening when increasing the particle size or the local refractive index, as well as a particular sphere radius presenting a minimal bandwidth corresponding to minimal losses in the system. The optical cross sections of individual modes present an optimal particle size that maximizes the absorption cross section and from which the scattering process becomes predominant with respect to the absorption. Optical efficiencies can also be optimized regarding the particle size, and their variations are correlated to those of the maximum near-field intensity. The hybrid modes in silver dimers are also analyzed, and the hot spot intensity resulting from the longitudinal mode excitation can also be maximized by optimizing the particle size and the local refractive index.

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References

  1. Kreibig U, Vollmer M (1995) Optical properties of metal clusters. Springer

  2. Zhang J, Zhang L (2012) Nanostructures for surface plasmons. Adv Opt Photonics 4:157–321. doi:10.1364/AOP.4.000157

    Article  Google Scholar 

  3. Bakhti S, Destouches N, Tishchenko AV (2014) Analysis of plasmon resonances on a metal particle. J Quant Spectrosc Radiat Transfer 146:113–122. doi:10.1016/j.jqsrt.2014.01.014

    Article  CAS  Google Scholar 

  4. Mock JJ, Barbic M, Smith DR et al (2002) Shape effects in plasmon resonance of individual colloidal silver nanoparticles. J Chem Phys 116:6755–6759. doi:10.1063/1.1462610

    Article  CAS  Google Scholar 

  5. Noguez C (2007) Surface plasmons on metal nanoparticles: the influence of shape and physical environment. J Phys Chem C 111:3806–3819. doi:10.1021/jp066539m

    Article  CAS  Google Scholar 

  6. Mock JJ, Smith DR, Schultz S (2003) Local refractive index dependence of plasmon resonance spectra from individual nanoparticles. Nano Lett 3:485–491. doi:10.1021/nl0340475

    Article  CAS  Google Scholar 

  7. Lee YH, Chen H, Xu Q-H, Wang J (2011) Refractive index sensitivities of noble metal nanocrystals: the effects of multipolar plasmon resonances and the metal type. J Phys Chem C 115:7997–8004. doi:10.1021/jp202574r

    Article  CAS  Google Scholar 

  8. Anker JN, Hall WP, Lyandres O et al (2008) Biosensing with plasmonic nanosensors. Nat Mater 7:442–453. doi:10.1038/nmat2162

    Article  CAS  Google Scholar 

  9. Clavero C (2014) Plasmon-induced hot-electron generation at nanoparticle/metal-oxide interfaces for photovoltaic and photocatalytic devices. Nat Photonics 8:95–103. doi:10.1038/nphoton.2013.238

    Article  CAS  Google Scholar 

  10. Kneipp K, Moskovits M, Kneipp H (2006) Surface-enhanced Raman scattering: physics and applications. Springer

  11. Boisselier E, Astruc D (2009) Gold nanoparticles in nanomedicine: preparations, imaging, diagnostics, therapies and toxicity. Chem Soc Rev 38:1759–1782. doi:10.1039/B806051G

    Article  CAS  Google Scholar 

  12. Kahnert FM (2003) Numerical methods in electromagnetic scattering theory. J Quant Spectrosc Radiat Transfer 79–80:775–824. doi:10.1016/S0022-4073(02)00321-7

    Article  Google Scholar 

  13. Bohren CF, Huffman DR (1983) Absorption and scattering of light by small particles. Wiley

  14. Asano S, Yamamoto G (1975) Light scattering by a spheroidal particle. Appl Opt 14:29–49. doi:10.1364/AO.14.000029

    Article  CAS  Google Scholar 

  15. Doicu A, Wriedt T, Eremin YA (2006) Light scattering by systems of particles. Null-field method with discrete sources: theory and programs. Springer

  16. Taflove A (1995) Computational electrodynamics: the finite-difference time-domain method. Artech House, Incorporated

  17. Meunier G (2010) The finite element method for electromagnetic modeling. John Wiley & Sons

  18. Mayergoyz ID, Fredkin DR, Zhang Z (2005) Electrostatic (plasmon) resonances in nanoparticles. Phys Rev B 72:155412. doi:10.1103/PhysRevB.72.155412

    Article  Google Scholar 

  19. Draine BT, Flatau PJ (1994) Discrete-dipole approximation for scattering calculations. J Opt Soc Am 11:1491–1499. doi:10.1364/JOSAA.11.001491

    Article  Google Scholar 

  20. Joe YS, Satanin AM, Kim CS (2006) Classical analogy of Fano resonances. Phys Scr 74:259. doi:10.1088/0031-8949/74/2/020

    Article  CAS  Google Scholar 

  21. Novotny L (2010) Strong coupling, energy splitting, and level crossings: a classical perspective. Am J Phys 78:1199–1202. doi:10.1119/1.3471177

    Article  Google Scholar 

  22. Lovera A, Gallinet B, Nordlander P, Martin OJF (2013) Mechanisms of Fano resonances in coupled plasmonic systems. ACS Nano 7:4527–4536. doi:10.1021/nn401175j

    Article  CAS  Google Scholar 

  23. Lassiter JB, Sobhani H, Knight MW et al (2012) Designing and deconstructing the Fano lineshape in plasmonic nanoclusters. Nano Lett 12:1058–1062. doi:10.1021/nl204303d

    Article  CAS  Google Scholar 

  24. Kolwas K, Derkachova A (2010) Plasmonic abilities of gold and silver spherical nanoantennas in terms of size dependent multipolar resonance frequencies and plasmon damping rates. Opto-Electron Rev 18:429–437. doi:10.2478/s11772-010-0043-6

    Article  CAS  Google Scholar 

  25. Kolwas K, Derkachova A (2013) Damping rates of surface plasmons for particles of size from nano- to micrometers; reduction of the nonradiative decay. J Quant Spectrosc Radiat Transfer 114:45–55. doi:10.1016/j.jqsrt.2012.08.007

    Article  CAS  Google Scholar 

  26. Prodan E, Radloff C, Halas NJ, Nordlander P (2003) A hybridization model for the plasmon response of complex nanostructures. Science 302:419–422. doi:10.1126/science.1089171

    Article  CAS  Google Scholar 

  27. Grigoriev V, Tahri A, Varault S et al (2013) Optimization of resonant effects in nanostructures via Weierstrass factorization. Phys Rev 88:011803. doi:10.1103/PhysRevA.88.011803

    Article  Google Scholar 

  28. Grigoriev V, Varault S, Boudarham G et al (2013) Singular analysis of Fano resonances in plasmonic nanostructures. Phys Rev 88:063805. doi:10.1103/PhysRevA.88.063805

    Article  Google Scholar 

  29. Bakhti S, Destouches N, Tishchenko AV (2015) Coupled mode modeling to interpret hybrid modes and Fano resonances in plasmonic systems. ACS Photonics 2:246. doi:10.1021/ph500356n

  30. Golub GH, Van Loan CF (1996) Matrix computations (3rd Ed.). Johns Hopkins University Press, Baltimore, MD, USA

  31. Baker GA (1975) Essentials of Padé approximants, Academic Press

  32. Tishchenko AV, Hamdoun M, Parriaux O (2003) Two-dimensional coupled mode equation for grating waveguide excitation by a focused beam. Opt Quantum Electron 35:475–491. doi:10.1023/A:1022921706176

    Article  Google Scholar 

  33. Tretyakov S (2014) Maximizing absorption and scattering by dipole particles. Plasmonics 9:935–944. doi:10.1007/s11468-014-9699-y

    Article  CAS  Google Scholar 

  34. Grigoriev V, Bonod N, Wenger J, Stout B (2015) Optimizing nanoparticle designs for ideal absorption of light. ACS Photonics 2:263. doi:10.1021/ph500456w

  35. Nordlander P, Oubre C, Prodan E et al (2004) Plasmon hybridization in nanoparticle dimers. Nano Lett 4:899–903. doi:10.1021/nl049681c

    Article  CAS  Google Scholar 

  36. Mackowski DW (1991) Analysis of radiative scattering for multiple sphere configurations. Proc R Soc Lond Ser Math Phys Sci 433:599–614. doi:10.1098/rspa.1991.0066

    Article  Google Scholar 

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Acknowledgments

This work was supported by the LABEX MANUTECH-SISE (ANR-10-LABX-0075) of Université de Lyon, within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). The authors thank ANR for its financial support in the framework of project PHOTOFLEX n°12-NANO-0006.

Compliance with Ethical Standards

The authors declare no competing financial or non-financial interest. This work does not involve human participants or animals.

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Authors and Affiliations

  1. Université de Lyon, 42023, Saint-Etienne, France

    Saïd Bakhti, Nathalie Destouches & Alexandre V. Tishchenko

  2. CNRS, UMR5516, Laboratoire Hubert Curien, 42000, Saint-Etienne, France

    Saïd Bakhti, Nathalie Destouches & Alexandre V. Tishchenko

  3. Université de Saint-Etienne Jean Monnet, 42000, Saint-Etienne, France

    Saïd Bakhti, Nathalie Destouches & Alexandre V. Tishchenko

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  1. Saïd Bakhti
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  2. Nathalie Destouches
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  3. Alexandre V. Tishchenko
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Correspondence to Nathalie Destouches.

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Bakhti, S., Destouches, N. & Tishchenko, A.V. Singular Representation of Plasmon Resonance Modes to Optimize the Near- and Far-Field Properties of Metal Nanoparticles. Plasmonics 10, 1391–1399 (2015). https://doi.org/10.1007/s11468-015-9937-y

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  • DOI: https://doi.org/10.1007/s11468-015-9937-y

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