Mathematical model of fluorescence processes accounting for the quantum effect of non-local screening

Yu. A. Eremin ; A. G. Sveshnikov

Matematičeskoe modelirovanie, Tome 31 (2019) no. 5, pp. 85-102.

Résumé

On the basis of the Discrete Sources Method, a mathematical model has been developed that enables to consider the fluorescence process in the presence of a plasmonic structure accounting for the nonlocal screening effect. It has been shown that the fluorescence quantum yield can be represented analytically. The influence of the effect on the quantum yield and the enhancement factor of fluorescence were investigated depending on the geometry of the plasmonic structure. It has been demonstrated that accounting for the non-local screening effect leads to a blue shift in the position of the maximum and a decrease in the amplitude of a fluorescence enhancement factor.

Détail

Keywords: discrete sources method, light scattering, plasmon resonance, non-local screening effect, quantum yield, fluorescence enhancement factor.
Mots-clés : fluorescence

Bibliographie

[1] Maier S. A., Plasmonics: Fundametals and Applications, Springer Science +Business Media LLC, 2007

[2] Klimov V. V., Nanoplazmonika, Fizmatlit, M., 2009

[3] Novotny L., Hecht B., Principles of Nano-Optics, Cambridge University Press, 2006

[4] Duan H., Fernandez-Dominguez A. I., Bosman M., Maier S. A., Yang J. K. W., “Nanoplasmonics: classical down to the nanometer scale”, Nano Lett., 12 (2012), 1683–1689 | DOI

[5] Kern J., Großmann S., Tarakina N. V., Hacke T. et al., “Atomic-scale confinement of resonant optical fields”, Nano Lett., 12 (2012), 5504–5509 | DOI

[6] Zhu W., Esteban R., Borisov A. G., Baumberg J. J., et al., “Quantum mechanical effects in plasmonic structures with subnanometre gaps”, Review. Nature Commun., 7 (2016), 11495 | DOI

[7] Garcia de Abajo F. J. J., “Nonlocal effects in the plasmons of strongly interacting nanoparticles, dimers, and waveguides”, Phys. Chem. C, 112 (2008), 17983–17987 | DOI

[8] Toscano G., Raza S., Jauho A., Mortensen N. A., Wubs M., “Modified field enhancement and extinction by plasmonic nanowire dimers due to nonlocal response”, Opt. Express, 20 (2012), 4176–4188 | DOI

[9] Stella L., Zhang P., Garcia-Vidal F. J., Rubio A., Garcia-Gonzalez P., “Performance of nonlocal optics when applied to plasmonic nanostructures”, J. Phys. Chem. C, 117 (2013), 8941–8949 | DOI

[10] Ciraci C., Hill R. T., Mock J. J., Urzhumov Y. et al., “Probing the ultimate limits of plasmonic enhancement”, Science, 337 (2012), 1072–1074 | DOI

[11] Bochterle J., Neubrech F., Nagao T., Pucci A., “Angstrom-scale distance dependence of antenna-enhanced vibrational signals”, ACS Nano, 6 (2012), 10917–10923 | DOI

[12] Teperik T. V., Nordlander P., Aizpurua J., Borisov A. G., “Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response”, Phys. Rev. Lett., 110 (2013), 263901 | DOI

[13] Toscano G., Straubel J., Kwiatkowski A., Rockstuhl C. et al., “Resonance shifts and spillout effects in self-consistent hydrodynamic nanoplasmonics”, Nat. Commun., 6 (2015), 7132 | DOI

[14] Raza S., Bozhevolnyi S. I., Wubs M., Mortensen A. N., “Nonlocal optical response in metallic nanostructures”, J. Phys. Condens. Matter., 27 (2015), 183204 | DOI

[15] Sui N., Wang L., Yan T., et al., “Selective and sensitive biosensors based on metal-enhanced fluorescence”, Sensors and Actuators B, 202 (2014), 1148–1153 | DOI

[16] Novotny L., van Hulst N., “Antennas for light (Review article)”, Nature photonics, 5 (2011), 83–90 | DOI

[17] Liaw J.-W., Chen H.-C., Kuo M.-K., “Comparison of Au and Ag nanoshells' metal-enhanced fluorescence”, J. Quantitat. Spectr. Radiat. Trans., 146 (2014), 321–330 | DOI

[18] Liaw J.-W., Chen H.-C., Chen J.-H., “Enhancement or quenching effect of metallic nanodimer on spontaneous emission”, J. Quantitat. Spectr. Radiat. Trans., 111 (2010), 454–465 | DOI

[19] Le Ru E. C., Etchegoin P. G., “Single-molecule surface-enhanced Raman spectroscopy”, Annu. Rev. Phys. Chem., 63 (2012), 65–87 | DOI

[20] Taflove A., Hagness S. C., Computational Electrodynamics — The Finite-Difference Time-Domain Method, Third Edition, Artech House Publishers, 2005 | MR

[21] Jin J. M., The Finite Element Method in Electromagnetics, 3rd Edition, Wiley-IEEE Press, 2014 | MR | Zbl

[22] Busch K., Konig M., Niegemann J., “Discontinuous Galerkin methods in nanophotonics”, Laser Photonics Rev., 5:6 (2011), 773–809 | DOI

[23] Li L., Lanteri S., Perrussel R., “A hybridizable discontinuous Galerkin method combined to a Schwarz algorithm for the solution of 3d time-harmonic Maxwell's equation”, J. Comput. Phys., 256:1 (2014), 563–581 | MR | Zbl

[24] Kahnert M., “Numerical solutions of the macroscopic Maxwell equations for scattering by non-spherical particles: A tutorial review”, J. Quantitat. Spectr. Radiat. Trans., 178 (2016), 22–37 | DOI | MR

[25] Yurkin M. A., “Computational Approaches for Plasmonics”, Handbook of Molecular Plasmonics, Chapter 2, eds. Della Sala F., D'Agostino S., Pan Stanford Publishing, 2013, 83–135 | DOI

[26] Forestiere C., Ladarola G., Rubinacci G., et al., “Surface integral furmulations for the design of plasmonic nanostructures”, J. Opt. Soc. Am. A, 29 (2012), 2314–2327 | DOI

[27] Garcia de Abajo F. J., Howie A., “Retarded field calculation of electron energy loss in inhomogeneous dielectrics”, Phys. Rev. B, 65 (2002), 115418 | DOI

[28] Khlebtsov N. G., “T-matrix method in plasmonics: An overview”, J. Quantit. Spectr. Radiat. Trans., 123 (2013), 184–217 | DOI

[29] Hafner Ch., Smajic J., Agio M., “Numerical Methods for the Electrodynamic Analysis of Nanostructures”, Nanoclusters and Nanostructured Surfaces, ed. Ray A. K., American Scientifc Publishers, Valencia, California, USA, 2010, 207–274

[30] Eremin Yu. A., Sveshnikov A. G., “Mathematical models in nanooptics and biophotonics based on the discrete sources method”, Computational Mathematics and Mathematical Physic, 47:2 (2007), 262–279 | DOI | MR | Zbl

[31] Eremin Yu. A., Sveshnikov A. G., “Mathematical Model Taking into Account Nonlocal Effects of Plasmonic Structures on the Basis of the Discrete Source Method”, Computational Mathematics and Mathematical Physic, 58:4 (2018), 572–580 | DOI | DOI | MR | Zbl

[32] Eremin Iu. A., Sveshnikov A. G., “Influence of Non-Local Effect on the Scattering Properties of NonSpherical Plasmonic Nanoparticles on a Substrate”, Mathematical Models and Computer Simulations, 10:6 (2018), 730–740 | DOI | MR | Zbl

[33] Huang Y. Q., Li J. C., Yang W., “Theoretical and numerical analysis of a non-local dispersion model for light interaction with metallic nanostructures”, Comput. Math. Appl., 72 (2016), 921–932 | DOI | MR | Zbl

[34] Schmitt N., Scheid C., Lanteri S., Moreau A., Viquerat J., “A DGTD method for the numerical modeling of the interaction of light with nanometer scale metallic structures taking into account non-local dispersion effects”, J. Comput. Phys., 316:1 (2016), 396–415 | DOI | MR | Zbl

[35] Li L., Lanteri S., Mortensen N. A., Wubs M., “A hybridizable discontinuous Galerkin method for solving nonlocal optical response models”, Comput. Phys. Commun., 219 (2017), 99–107 | DOI | MR

[36] Grishina N. V., Eremin Iu. A., Sveshnikov A. G., “New Concept of the Discrete Sources Method in Electromagnetic Scattering Problems”, Mathematical Models and Computer Simulations, 8:2 (2016), 175–182 | DOI | MR

[37] Grishina N. V., Eremin Iu. A., Sveshnikov A. G., “Discrete source method for analysis of fluorescence enhancement in the presence of plasmonic structures”, Computational Mathematics and Mathematical Physic, 56:1 (2016), 140–147 | DOI | MR | Zbl

[38] Bakhvalov N. S., Chislennye metody, Nauka, M., 1975

[39] Voevodin V. V., Kuznetsov Iu. A., Matritsy i vychisleniia, Nauka, M., 1984

[40] http://www.refractiveindex.info

[41] Grishina N. V., Eremin Iu. A., Sveshnikov A. G., “Analysis of plasmon resonances of closely located particles by the discrete sources method”, Optics and spectroscopy, 113:4 (2012), 440–445 | DOI | MR