Analytical study of nonlinear dynamics of laser beam interaction with metallic nanoparticle linear array in parallel propagation

Document Type : Full length research Paper

Authors

1 Physics Department-Science Faculty-University of Mohaghegh Ardabili-Ardabil-Iran.

2 Physics Department-Science Faculty-University of Mohaghegh Ardabili-Ardabil-Iran

Abstract

In this article using a modified Drude model, which includes all dominant electron energy scattering mechanisms and interparticle interactions, the relativistic dynamics of a linear chain of spherical nanoparticle interacting with a laser beam propagating parallel to the orientation of nanoparticles array is investigated. In the point-dipole description of nanoparticles, taking into account interaction of two nearest neighbors, analytical solutions are obtained for the momentum equations of conducting electrons of nanoparticles related to the first, second and third harmonics of laser fields. Formulae are simplified for some asymptotic cases. Numerical analysis is carried out for a linear chain including 10 of 10nm radius Au nanoparticles. It is shown that the interparticle separation has a key role in the nonlinear dynamics of the system. Dipole-dipole interaction of nanoparticles causes a blueshift for the main and third harmonics plasmon resonance, whereas it leads to a redshift for the plasmon resonance of the second order longitudinal displacements of nanoparticles. Related to the different orders, linear and nonlinear polarization of each particle is obtained and permittivity, first and second order susceptibility, linear and nonlinear refractive index of each nanoparticle are analytically obtained which these findings can have direct application in nano-optics and nano-plasmonics.

Keywords

Main Subjects

References

[1] S.A. Maier, P.G. Kik, H.A. Atwater, S. Meltzer, E. Harel, B.E. Koel, A.A. Requicha, Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides, Nature Materials 2 (2003) 229-232. https://doi.org/10.1038/nmat852
[2] M. Quinten, A. Lietner, J.R. Krenn, F.R. Aussenegg, Electromagnetic energy transport via linear chains of silver nanoparticles, Optics Letters 23 (1998) 1331. https://doi.org/10.1364/OL.23.001331
[3] J.R. Krenn et. al., Squeezing the Optical Near-Field Zone by Plasmon Coupling of Metallic Nanoparticles, Physical Review B 82 (1999) 2590. https://doi.org/10.1103/PhysRevLett.82.2590
[4] J. Muller et. al., Electrically controlled light scattering with single metal nanoparticles, Applied Physics Letters 81 (2002) 171. https://doi.org/10.1063/1.1491003
[5] T. Zentgraf, A. Christ, J. Kuhl, H. Giessen, Tailoring the Ultrafast Dephasing of Quasiparticles in Metallic Photonic Crystals, Physical Review Letters 93 (2004) 243901. https://doi.org/10.1103/PhysRevLett.93.243901
[6] M.L. Brongersma, J.W. Hartman, H.A. Atwater, Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit, Physical Review B 62 (2000) R16356. https://doi.org/10.1103/PhysRevB.62.R16356
[7] K.L. Kelly, E. Coronado, L.L. Zhao, G.C. Schatz, The Optical Properties of Metal Nanoparticles:  The Influence of Size, Shape, and Dielectric Environment, Journal of Physical Chemistry B 107 (2003) 668-677. https://doi.org/10.1021/jp026731y
[8] K. Li, M.I. Stockman, D. Bergman, Self-Similar Chain of Metal Nanospheres as an Efficient Nanolens, Physical Review Letters 91 (2003) 227402. https://doi.org/10.1103/PhysRevLett.91.227402
[9] S.Y. Park, D. Stroud, Surface-plasmon dispersion relations in chains of metallic nanoparticles: An exact quasistatic calculation, Physical Review B 69 (2004) 125418. https://doi.org/10.1103/PhysRevB.69.125418
[10] D.S. Citrin, Plasmon Polaritons in Finite-Length Metal−Nanoparticle Chains:  The Role of Chain Length Unravelled, Nano Letters 5 (2005) 985. https://doi.org/10.1021/nl050513+
[11] D.S. Citrin, Coherent Excitation Transport in Metal−Nanoparticle Chains, Nano Letters 4 (2004) 1561. https://doi.org/10.1021/nl049679l
[12] G.C. des Francs, C. Girard, O.J.F. Martin, Fluorescence resonant energy transfer in the optical near field, Physical Review Letters 67 (2003) 053805. https://doi.org/10.1103/PhysRevA.67.053805
[13] E. Fort, S. Gresillon, Surface enhanced fluorescence, Journal of Physics D: Applied Physics 41 (2008) 013001.       https://doi.org/10.1088/0022-3727/41/1/013001
[14] P.L. Stiles, J.A. Dieringer, N.C. Shah, R.P. Van Duyne, Surface-enhanced Raman spectroscopy, Annual Review of Analytical Chemistry 1 (2008) 601–626. https://doi.org/10.1146/annurev.anchem.1.031207.112814
[15] C.K. Chen, T.F. Heinz, D. Ricard, Y.R. Shen, Surface-enhanced second-harmonic generation and Raman scattering, Physical Review B 27 (1983) 1965–1979. https://doi.org/10.1103/PhysRevB.27.1965
[16] G.T. Boyd, Z.H. Yu, Y.R. Shen, Photoinduced luminescence from the noble metals and its enhancement on roughened surfaces, Physical Review B Condens. Matter 33 (1986) 7923–7936. https://doi.org/10.1103/PhysRevB.33.7923
[17] W.L. Barnes, A. Dereux, T.W. Ebbesen, Surface plasmon subwavelength optics, Nature 424 (2003) 824–830. https://doi.org/10.1038/nature01937
[18] S.A. Maier, Plasmonics: fundamentals and applications, Springer, (2007).
[19] F. Hache, D. Ricard, C. Flytzanis, U. Kreibig, The optical Kerr effect in small metal particles and metal colloids: the case of gold,  Applied Physics A: Materials Science and Processing 47 (1988) 347–357. https://doi.org/10.1007/BF00615498
[20] C.K. Chen, A.R.B. de Castro, Y.R. Shen, Surface-enhanced second-harmonic generation, Physical Review Letters 46 (1981) 145–148. https://doi.org/10.1103/PhysRevLett.46.145
[21] R. El-Ganainy, D.N. Christodoulides, C. Rotschild, M. Segev, Soliton dynamics and self-induced transparency in nonlinear nanosuspensions, Optics Express 15 (2007) 10208. https://doi.org/10.1364/OE.15.010207
[22] F. Ye, D. Mihalache, B. Hu, N.C. Panoiu, Subwavelength Plasmonic Lattice Solitons in Arrays of Metallic Nanowires, Physical Review Letters 104 (2010) 106802. https://doi.org/10.1103/PhysRevLett.104.106802
[23] N. Sepehri Javan, Raman parametric excitation effect upon the third harmonic generation by a metallic nanoparticle lattice, Journal of Applied Physics 118 (2015) 073104. https://doi.org/10.1063/1.4928810
[24] N. Sepehri Javan, Self-focusing of an intense laser pulse interacting with a periodic lattice of metallic nanoparticle, Phys. Plasmas 22 (2015) 093116. https://doi.org/10.1063/1.4931172
[25] N. Sepehri Javan, N. Amjadi, H. Mohammadzadeh, Dielectric coats effect on the third harmonic generation by a metallic nanoparticle lattice exposed to intense laser radiation, Physics of plasmas 23 (2016) 123114. https://doi.org/10.1063/1.4972139
[26] N. Sepehri Javan, F. Rouhi Erdi, M. N. Najafi, Magnetic field effect on the self-focusing of an intense laser pulse interacting with a bulk medium of graphite nanoparticles, Physics of plasmas 24 (2017) 052301. https://doi.org/10.1063/1.4981386
[27] N.S. Javan, F.R. Erdi, Magnetic Field Effect on Fresnel Coefficients of the Thin Slab of Graphite Nanocomposite, Plasmonics 14 (2019) 219.          https://doi.org/10.1007/s11468-018-0795-2
[28] N. Sepehri Javan, R. Naderali, M. Hosseinpour Azad, M. Najafi, Theoretical study of artificial Kerr effect on the self-focusing of laser in a dissipative suspension of silver nanoparticles, Physics of Plasmas 25 (2018) 082310. https://doi.org/10.1063/1.5043277
[29] N.S. Javan, R. Naderali, M.H. Azad, M. Najafi, Semi-Analytical Solution for Solitary Waves in a Dissipative Suspension of Metallic Nanoparticles, Plasmonics 1 (2018) 579-593. https://doi.org/10.1007/s11468-018-0837-9
[30] S.A. Maier, M.L. Brongersma, P.G. Kik, H.A. Atwater, Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy, Physical Review B 65 (2002) 193408. https://doi.org/10.1103/PhysRevB.65.193408
[31] S.A. Maier, P.G. Kik, H.A. Atwater, Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss, Applied Physics Letters 81 (2002) 1714. https://doi.org/10.1063/1.1503870
[32] S.A. Maier, P.G. Kik, H.A. Atwater, Optical pulse propagation in metal nanoparticle chain waveguides, Physical Review B 67 (2003) 205402. https://doi.org/10.1103/PhysRevB.67.205402
[33] C.-T. Tai, Dyadic Green’s Functions in Electromagnetic Theory, Intext, Scranton, PA, (1971).
[34] A.D. Yaghjian, Electric dyadic Green’s functions in the source region, Proc. IEEE 68 (1980) 248–263. https://doi.org/10.1109/PROC.1980.11620
[35] J. Van Bladel, Some remarks on Green’s dyadic for infinite space, IRE Trans. Antennas Propagat 9 (1961) 563–566. https://doi.org/10.1109/TAP.1961.1145064
[36] L. Novotny, B. Hecht, D.W. Pohl, Interference of locally excited surface plasmons, Journal of Applied Physics 81 (1997) 1798–1806. https://doi.org/10.1063/1.364036
[37] A. Kheirandish, N. S.Javan, H. Mohammadzadeh, Polarization effect on the nonlinear dynamics of linear chain of interactional metallic nanoparticles exposed on a laser beam: an analytical approach, Physica Scripta 93 (2018) 095802.       https://doi.org/10.1088/1402-4896/aad2ea
[38] A. Kheirandish, N. S.Javan, H. Mohammadzadeh, Modified Drude model for small gold nanoparticles surface plasmon resonance based on the role of classical confinement. Scientific reports 10 (2020) 1-10. https://doi.org/10.1038/s41598-020-63066-9
[39] A. Kheirandish, N. S.Javan, H. Mohammadzadeh, Analytical approach to the surface plasmon resonance characteristic of metal nanoparticle dimer in dipole-dipole approximation, Plasmonics 15 (2020) 1807-1814. https://doi.org/10.1007/s11468-020-01198-4
[40] A. Kheirandish, N. S.Javan, H. Mohammadzadeh, Second harmonic generation from metal nanoparticle dimer: an analytical approach in dipole approximation, Physica Scripta 96 (2020) 025506. https://doi.org/10.1088/1402-4896/abd27d
[41] W.H. Weber, G.W. Ford, Propagation of optical excitations by dipolar interactions in metal nanoparticle chains, Physical Review B 70 (2004) 125429. https://doi.org/10.1103/PhysRevB.70.125429
[42] Y.-R. Zhen, K.H. Fung, C.T. Chan, Collective plasmonic modes in two-dimensional periodic arrays of metal nanoparticles, Physical Review B 78 (2008) 035419. https://doi.org/10.1103/PhysRevB.78.035419
[43] J.I. Dadap, J. Shan, K.B. Eisenthal, T.F. Heinz, Second-harmonic Rayleigh scattering from a sphere of centrosymmetric material, Physical Review Letters 83 (1999) 4045. https://doi.org/10.1103/PhysRevLett.83.4045
[44] W.E. Lawrence W.E. Electron-electron scattering in the low-temperature resistivity of the noble metals, Physical Review B 13 (1976) 5316–5319. https://doi.org/10.1103/PhysRevB.13.5316
[45] W.E. Lawrence, J.W. Wilkins, Electron-electron scattering in the transport coefficients of simple metals. Physical Review B 7 (1973) 2317–2332. https://doi.org/10.1103/PhysRevB.7.2317
[46] A. Alabastri et al., Modeling of plasmonic resonances in metallic nanostructures: Dependence of the non-linear permittivity on system size and temperature. Materials 6 (2013) 4879-4910. https://doi.org/10.3390/ma6114879
[47] T. Holstein, Optical and infrared volume absorptivity of metals. Physical Review 96 (1954) 535–536. https://doi.org/10.1103/PhysRev.96.535
[48] T. Holstein, Theory of transport phenomena in an electron-phonon gas. Annals of Physics 29 (1964) 410–535. https://doi.org/10.1016/0003-4916(64)90008-9
[49] J.A. McKay, A. Rayne, Temperature dependence of the infrared absorptivity of the noble metals. Physical Review B 13 (1976) 673-685. https://doi.org/10.1103/PhysRevB.13.673
[50] C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles. AWiley-International Publication, NewYork, USA, (1983).
[51] L. Genzel, T.P. Martin, U. Kreibig, Dielectric function and plasma resonances of small metal particles, Zeitschrift für Physik B 21 (1975) 339–346. https://doi.org/10.1007/BF01325393
[52] E.A. Coronado, G.C. Schatz, Surface plasmon broadening for arbitrary shape nanoparticles: A geometrical probability approach. Journal of Chemical Physics 119 (2003) 3926–3934. https://doi.org/10.1063/1.1587686
[53] M. Liu, P. Guyot-Sionnest, Synthesis and optical characterization of Au/Ag core/shell nanorods, Journal of Physical Chemistry B 108 (2004) 5882–5888.  https://doi.org/10.1021/jp037644o
[54] S. Berciaud, L. Cognet, P. Tamarat, B. Lounis, Observation of intrinsic size effects in the optical response of individual gold nanoparticles, Nano Letters 5 (2005) 515–518. https://doi.org/10.1021/nl050062t
[55] M. Dehghanipour, M. Khanzadeh, S, Abotalebi, Enhancement of nonlinear absorption and optical limiting properties of graphene oxide in mixed with Fe2O3 nanoparticles, Journal of Research on Many-body Systems 8 (2018) 79-87. https://dx.doi.org/10.22055/jrmbs.2018.13943
[56] K.H. Bennemann, Non-linear optics in metals, Oxford University Press, (1998).
Journal of Research on Many-body Systems
Volume 11, Issue 2 - Serial Number 29
September 2021
Pages 55-83

Files

History

  • Receive Date: 26 April 2020
  • Revise Date: 29 June 2021
  • Accept Date: 04 August 2021

Share

How to cite

Statistics