Skip to main content
Log in

Quantum Confinement Effects on the Near Field Enhancement in Metallic Nanoparticles

  • Published:
Plasmonics Aims and scope Submit manuscript

Abstract

In this work, we study the strong confinement effects on the electromagnetic response of metallic nanoparticles. We calculate the field enhancement factor for nanospheres of various radii by using optical constants obtained from both classical and quantum approaches, and compare their size dependent features. To evaluate the scattered near field, we solve the electromagnetic wave equation within a finite element framework. When quantization of electronic states is considered for the input optical functions, a significant blue-shift in the resonance of the enhanced field is observed, in contrast to the case in which functions obtained classically are used. Furthermore, a noticeable underestimation of the field amplification is found in the calculation based on a classical dielectric function. Our results are in good agreement with available experimental reports and provide relevant information on the cross-over between classical and quantum regime, useful in potentiating nanoplasmonics applications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Wei Q-H, Su K-H, Durant S, Zhang X (2004) Plasmon resonance of finite one-dimensional Au nanoparticle chains. Nano Lett 4:1067

    Article  CAS  Google Scholar 

  2. Murray WA, Barnes WL (2007) Plasmonic materials. Adv Mat 19:3771

    Article  CAS  Google Scholar 

  3. Jakab A, Rosman C, Khalavka Y, Becker J, Trügler A, Hohenester U, Sönnichsen C (2011) Highly sensitive plasmonic silver nanorods. ACS Nano 5:6880

    Article  CAS  Google Scholar 

  4. Rycenga M, Cobley CM, Zeng J, Li WY, Moran CH, Zhang Q, Qin D, Xia YN (2011) Controlling the synthesis and assembly of silver nanostructures for plasmonic applications. Chem Rev 111:3669

    Article  CAS  Google Scholar 

  5. Igarashi T, Kawai H, Yanagi K, Cuong NT, Okada S, Pichler T (2015) Tuning localized transverse surface plasmon resonance in electricity-selected single-wall carbon nanotubes by electrochemical doping. Phys Rev Lett 114:176807

    Article  Google Scholar 

  6. Lin L, Zapata M, Xiong M, Liu ZH, Wang SS, Xu H, Borisov AG, Gu HC, Nordlander P, Aizpurua J, Ye J (2015) Nanooptics of plasmonic nanomatryoshkas: shrinking the size of a core–shell junction to subnanometer. Opt Lett 15:6419

    CAS  Google Scholar 

  7. Lerme J, Palpant B, Prével B, Pellarin M, Treilleux M, Vialle JL, Perez A, Broyer M (1998) Quenching of the size effects in free and matrix-embedded silver clusters. Phys Rev Lett 80:5105

    Article  CAS  Google Scholar 

  8. Scholl J, Koh AL, Dionne J (2012) Quantum plasmon resonances of individual metallic nanoparticles. Nature 483:421

    Article  CAS  Google Scholar 

  9. Garcia, de Abajo FJ (2012) Microscopy: plasmons go quantum. Nature 483:417

  10. Zuloaga J, Prodan E, Nordlander P (2010) Quantum plasmonics: optical properties and tunability of metallic nanorods. ACS Nano 4:5269

    Article  CAS  Google Scholar 

  11. Marinica DC, Kazansky AK, Nordlander P, Aizpurua J, Borisov AG (2012) Quantum plasmonics: nonlinear effects in the field enhancement of a plasmonic nanoparticle dimer. Nano Lett 12:1333

    Article  CAS  Google Scholar 

  12. Raza S, Stenger N, Kadkhodazadeh S, Fischer SV, Kostesha N, Jauho AP, Burrows A, Wubs M, Mortensen NA (2013) Blueshift of the surface plasmon resonance in silver nanoparticles studied with EELS. Nanophotonics 2:131

    Article  CAS  Google Scholar 

  13. Monreal RC, Tomasz J Antosiewicz TJ, Apell SP (2013) Competition between surface screening and size quantization for surface plasmons in nanoparticles. New J Phys 15:083044

    Article  Google Scholar 

  14. Talley CE, Jackson JB, Oubre C, Grady NK, Hollars CW, Lane SM, Huser TM, Nordlander P, Halas NJ (2005) Surface-enhanced Raman scattering from individual Au nanoparticles and nanoparticle dimer substrates. Nano Lett 5:1569

    Article  CAS  Google Scholar 

  15. Davoyan AR, Popov VV, Nikitov SA (2012) Tailoring terahertz near-field enhancement via two-dimensional plasmons. Phys Rev Lett 108:127401

    Article  Google Scholar 

  16. Huang Y, Ma LW, Hou MJ, Xieb Z, Zhang ZJ (2016) Gradual plasmon evolution and huge infrared near-field enhancement of metallic bridged nanoparticle dimers. Phys Chem Chem Phys 18:2319

    Article  CAS  Google Scholar 

  17. Zhu J, Zhao SM (2016) A computational study of the giant local electric field enhancement in Al-Au-Ag trimetallic three-layered nanoshells. Plasmonics 11:659

    Article  CAS  Google Scholar 

  18. Fung CKM, Xi N, Lou JY, Zhou ZF, Shanker B, Lai KWC, Chen HZ (2010) Quantum effect in field enhancement using antenna for carbon nanotube based infrared sensors. Proc 10th IEEE Conference on Nanotech 1:458

    Article  Google Scholar 

  19. Singh MR, Schindel DG, Hatef A (2011) Dipole-dipole interaction in a quantum dot and metallic nanorod hybrid system. Appl Phys Lett 99:181106

    Article  Google Scholar 

  20. Hatef A, Sadeghi SM, Singh MR (2012) Coherent molecular resonances in quantum dot–metallic nanoparticle systems: coherent self-renormalization and structural effects. Nanotechnology 23:205203

    Article  Google Scholar 

  21. Antón MA, Carreño F, Melle S, Calderón OG, Cabrera-Granado E (2013) Optical pumping of a single hole spin in a p-doped quantum dot coupled to a metallic nanoparticle. Phys Rev B 87:195303

    Article  Google Scholar 

  22. Ciracì C, Hill RT, Mock JJ, Urzhumov Y, Fernández-Domínguez AI, Maier SA, Pendry JB, Chilkoti A, Smith DR (2012) Probing the ultimate limits of plasmonic enhancement. Science 337 :1072

    Article  Google Scholar 

  23. Zhu W, Crozier KB (2014) Quantum mechanical limit to plasmonic enhancement as observed by surface-enhanced Raman scattering. Nature Comm 5:5228

    Article  CAS  Google Scholar 

  24. Zapata M, Camacho AS, Borisov AG, Aizpurua J (2015) Quantum effects in the optical response of extended plasmonic gaps: validation of the quantum corrected model in core-shell nanomatryushkas. Opt Express 23:8134

    Article  CAS  Google Scholar 

  25. Chang HW, Mu SY (2013) Semi-analytical solutions of the 3D homogeneous Helmholtz equation by the method of connected local fields. Prog Electromagn Res 142:159

    Article  Google Scholar 

  26. Deraemaeker A, Babuška I, Bouillard P (1999) Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions. Int J Numer Meth Eng 46 :471

    Article  Google Scholar 

  27. Micic M, Klymyshyn N, Suh YD, Lu HP (2003) Finite element method simulation of the field distribution for AFM tip-enhanced surface-enhanced Raman scanning microscopy. J Phys Chem B 107:1574

    Article  CAS  Google Scholar 

  28. Ramírez HY, Santana A (2012) Two interacting electrons confined in a 3D parabolic cylindrically symmetric potential, in presence of axial magnetic field: a finite element approach. Comput Phys Comm 183:1654

    Article  Google Scholar 

  29. Forouzeshfard MR, Hosseini Farzad M (2015) Electromagnetic wave propagation through two coaxial transformation-based cylindrical media. Plasmonics 10:1345

    Article  Google Scholar 

  30. Kluczyk K, Jacak W (2016) Damping-induced size effect in surface plasmon resonance in metallic nano-particles: comparison of RPA microscopic model with numerical finite element simulation (COMSOL) and Mie approach. J Quant Spectrosc Rad 168:78

    Article  CAS  Google Scholar 

  31. Maier SA (2007) Plasmonics: Fundamentals and Applications. New York - USA; Springer. Chapter 1

  32. Kelly KL, Coronado E, Zhao LL, Schatz GC (2003) The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment. J Phys Chem B 107:668

    Article  CAS  Google Scholar 

  33. Grady NK, Halas NJ, Nordlander P (2004) Influence of dielectric function properties on the optical response of plasmon resonant metallic nanoparticles. Chem Phys Lett 399:167

    Article  CAS  Google Scholar 

  34. Noguez C (2007) Surface plasmons on metal nanoparticles: the influence of shape and physical environment. J Phys Chem C 111:3806

    Article  CAS  Google Scholar 

  35. Esteban R, Borisov AG, Nordlander P, Aizpurua J (2012) Bridging quantum and classical plasmonics with a quantum-corrected model. Nature Comm 3:825

    Article  Google Scholar 

  36. Muñetón Arboleda D, Santillán JMJ, Mendoza Herrera LJ, Muraca D, Schinca DC, Scaffardi LB (2016) Size-dependent complex dielectric function of Ni, Mo, W, Pb, Zn and Na nanoparticles. Application to sizing. J Phys D 49:075302

    Article  Google Scholar 

  37. Genzel L, Martin TP, Kreibig U (1975) Dielectric function and plasma resonances of small metal particles. Z Phys B 21:339

    Article  CAS  Google Scholar 

  38. Ramírez HY, Flórez J, Camacho AS (2015) Efficient control of coulomb enhanced second harmonic generation from excitonic transitions in quantum dot ensembles. Phys Chem Chem Phys 17:23938

    Article  Google Scholar 

  39. Arfken GB, Weber HJ (2001) Mathematical Methods for Physicists, 5th Ed. Harcourt/Academic Press

  40. Johnson, Christy (1972) Optical constants of the noble metals. Phys Rev B 6:4370

    Article  CAS  Google Scholar 

  41. Charlé KP, Schulze W, Winter B (1989) The size dependent shift of the surface plasmon absorption band of small spherical metal particles. Z Physik D 12:471

    Article  Google Scholar 

  42. Negre FA, Perassi EM, Coronado EA, Sánchez CG (2013) Quantum dynamical simulations of local field enhancement in metal nanoparticles. J Phys Condens Matter 25:125304

    Article  Google Scholar 

  43. Blaber MG, Arnold MD, Ford MJ (2009) Search for the ideal plasmonic nanoshell: the effects of surface scattering and alternatives to gold and silver. J Phys Chem C 113:3041

    Article  CAS  Google Scholar 

  44. Jacak WA (2015) Lorentz friction for surface plasmons in metallic nanospheres. J Phys Chem C 119:6749

    Article  CAS  Google Scholar 

  45. Liz-Marzán LM (2006) Tailoring surface plasmons through the morphology and assembly of metal nanoparticles. Langmuir 22:32

    Article  Google Scholar 

  46. Zhang SP, Bao K, Halas NJ, Xu HX, Nordlander P (2011) Substrate-induced Fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed. Nano Lett 11:1657

    Article  CAS  Google Scholar 

  47. Zhang Y, Jia TQ, Zhang SA, Feng DH, Xu ZZ (2012) Dipole, quadrupole and octupole plasmon resonance modes in non-concentric nanocrescent/nanodisk structure: local field enhancement in the visible and near infrared regions. Opt Express 20:2924

    Article  CAS  Google Scholar 

  48. de Heer WA (1993) The physics of simple metal clusters: experimental aspects and simple models. Rev Mod Phys 65:611

  49. Brack M (1993) The physics of simple metal clusters: self-consistent jellium model and semiclassical approaches. Rev Mod Phys 65:677

    Article  CAS  Google Scholar 

Download references

Acknowledgments

The authors acknowledge the Department of Physics of the Universidad de Los Andes, and the UPTC’s Research Division for financial support.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hanz Y. Ramírez.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zapata-Herrera, M., Flórez, J., Camacho, A.S. et al. Quantum Confinement Effects on the Near Field Enhancement in Metallic Nanoparticles. Plasmonics 13, 1–7 (2018). https://doi.org/10.1007/s11468-016-0476-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11468-016-0476-y

Keywords

Navigation