Numerical simulation of harmonic multiples generation by a group of plasmonic nanoparticles
DOI:
https://doi.org/10.7242/1999-6691/2014.7.2.13Keywords:
nonlinear plasmonics, metal nanoparticles, third harmonic generationAbstract
We propose a theoretical (mathematical) model of nonlinear plasmonic oscillations in metal nanoparticles. The governing equation of motion is deduced from the least action principle and supplemented by a continuity equation resulting from the variational and differential formulations of charge conservation. The presence of irreversible processes is taken into account by the use of a polynomial dissipation term embedded into the action functional. Analysis of the structure of the Euler-Lagrange equation shows that it is possible to derive an expression for the stress tensor of an “electron gas - ionic frame” system. The formulation of an initial boundary value problem for nonlinear integrodifferential equations constituting the model of electron gas dynamics is given. Based on the finite-difference approximation, we developed an iterative method, an algorithm and a solver code for treating the problem. This allowed us to investigate the phenomena of odd (third and fifth) harmonic generation by a group of metal nanoparticles subjected to monochromatic light illumination. It is shown that the presence of higher order terms in the dissipative force expansion is important for providing the stability of the electron gas motion. Estimates for the density function parameter responsible for stable generation were obtained. The estimates were compared versus the analogous ones resulting from the theory of electronic structure of metals as well as from the Drude theory.
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References
Serebrennikov A.M. On the nonlinear mechanoplasmonic theory of frequency scaling and mixing effects // Plasmonics. - 2013 - V. 8, no. 3. - P. 1299-1308.
2. Majer S.A. Plazmonika: teoria i prilozenia. - M.-Izevsk: NIC <>, 2011. - 296 s.
3. Hiremath K.R., Zschiedrich L., Schmidt F. Numerical solution of nonlocal hydrodynamic Drude model for arbitrary shaped nano-plasmonic structures using Nedelec finite elements // J. Comput. Phys. - 2012. - Vol. 231, no. 17. - P. 5890-5896. DOI
4. Toscano G., Raza S., Jauho A.P., Mortensen N.A., Wubs M. Modified field enhancement and extinction by plasmonic nanowire dimers due to nonlocal response // Opt. Express. - 2012. - Vol. 20, no. 4. - P. 4176-4188. DOI
5. Scalora M., Vincenti M.A., de Ceglia D., Roppo V., Centini M., Akozbek N., Bloemer M.J. Second- and third-harmonic generation in metal-based structures // Phys. Rev. A. - 2010. - Vol. 82. - 043828. DOI
6. Vincenti M.A., Campione S., de Ceglia D., Capolino F., Scalora M. Gain-assisted harmonic generation in near-zero permittivity metamaterials made of plasmonic nanoshells // New J. Phys. - 2012. - Vol. 14, no. 10. - 103016. DOI
7. Ahmediev N.N., Ankevic A. Solitony. Nelinejnye impul’sy i pucki. - M.: Fizmatlit, 2003. - 304 s.
8. Landau L.D., Livsic E.M. Teoreticeskaa fizika: Kvantovaa mehanika. - M.: Fizmatlit, 2001. - T. 3. - 808 s.
9. Kohn W. Nobel Lecture: Electronic structure of matter-wave functions and density functionals // Rev. Mod. Phys. - 1999. - Vol. 71, no. 5. - P. 1253-1266.
10. Sedov L.I. Mehanika splosnoj sredy. - M.: Nauka, 1970. - T. 1. - 492 s.
11. Baranov A.A., Kolpasikov V.L. Relativistskaa termomehanika splosnyh sred. - M.: Editorial URSS, 2003. - 152 s.
12. Pimenov U.V., Vol’man V.I., Muravcov A.D. Tehniceskaa elektrodinamika. - M.: Radio i svaz’, 2000. - 536 s.
13. Ol’hovskij I.I. Kurs teoreticeskoj mehaniki dla fizikov. - M.: Izd-vo Mosk. un-ta, 1978. - 575 s.
14. Landau L.D., Livsic E.M. Teoreticeskaa fizika: Teoria pola. - M.: Fizmatlit, 2003. - T. 2. - 536 s.
15. Pavlov P.V., Hohlov A.F. Fizika tverdogo tela. - M.: Vyssfz skola, 2000. - 494 s.
16. Schumacher T., Kratzer K., Molnar D., Hentschel M., Giessen H., Lippitz M. Nanoantenna-enhanced ultrafast nonlinear spectroscopy of a single gold nanoparticle // Nature Communications. - 2011. - Vol. 2. - Article number: 333. DOI
17. Lippitz M., van Dijk M.A., Orrit M. Third-harmonic generation from single gold nanoparticles // Nano Lett. - 2005. - Vol. 5, no. 4. - P. 799-802. DOI
18. Slablab A., Xuan L.L., Zielinski M., de Wilde Y., Jacques V., Chauvat D., Roch J.-F. Second-harmonic generation from coupled plasmon modes in a single dimer of gold nanospheres // Opt. Express. - 2012. - Vol. 20, no. 1. - P. 220-227. DOI
19. Thyagarajan K., Rivier S, Lovera A., Martin O.J.F. Enhanced second-harmonic generation from double resonant plasmonic antennae // Opt. Express. - 2012. - Vol. 20, no. 12. - P. 12860-12865. DOI
20. Melentiev P.N., Afanasiev A.E., Kuzin A.A., Baturin A.S., Balykin V.I. Giant optical nonlinearity of a single plasmonic nanostructure // Opt. Express. - 2013. - Vol. 21, no. 12. - P. 13896-13905. DOI
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