Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
research-article

Closed Form Resonance Solution in Metallic Nanoparticles With Cubic Nonlinearity

Published: 01 January 2020 Publication History

Abstract

Higher order intensity of light introduces third order nonlinear susceptibility in metallic nanostructures. Circuit theory is often used to represent complex phenomena and adequately models the frequency dependent linear resonance in metallic nanostructures with great accuracy. In this article, we use the linear circuit approach and propose a compact impedance model to represent resonance in metallic nanoparticle with cubic nonlinearity. The model uses full-wave dipole equation by employing all time-dependent fields and introduces the concept of nonlinear radiation impedances. Analytical expressions for the nonlinear radiation (internal and external) impedances are derived and used for the first time to get the close-form expression of nonlinear (NL) scattering cross-sectional area using voltages, currents and circuit elements. The effects of nanoparticle parameters i.e. radius, intensity and dielectric function of surrounding medium on cubic nonlinearity are analyzed using impedance model. The validated close-form impedance model preserves the macroscopic properties to give intuitive understanding of NL behavior necessary in facilitating next-generation nanophotonics applications.

References

[1]
G. D’Aguanno, D. L. Sounas, H. M. Saied, and A. Alù, “Nonlinearity-based circulator,” Appl. Phys. Lett., vol. 114, no. , 2019, Art. no. .
[2]
P. Kumar et al., “Study of tunable plasmonic, photoluminscence, and nonlinear optical behavior of Ag nanoclusters embedded in a glass matrix for multifunctional applications,” Physica Status Solidi (A), vol. 216, no. 4, 2019, Art. no. .
[3]
Z.-H. Zhang, K.-X. Guo, and J.-H. Yuan, “Influence of the position dependent effective mass on the nonlinear optical properties in semiparabolic and parabolic quantum well with applied magnetic field,” Physica E: Low-Dimensional Syst. Nanostruct., vol. 108, pp. 238–243, 2019.
[4]
V. Belyaev, D. Murzin, N. Perova, A. Grunin, A. Fedyanin, and V. Rodionova, “Permalloy-based magnetoplasmonic crystals for sensor applications,” J. Magnetism Magn. Mater., vol. 482, pp. 292–295, 2019.
[5]
B. Choi, H. Xu, G. Hajisalem, and R. Gordon, “Localized surface plasmon resonance enhanced magneto-optical kerr effect in Ni80Fe20 thin films coated with Au nanorods,” Appl. Phys. Lett., vol. 112, no. 2, 2018, Art. no. .
[6]
M. Alam and Y. Massoud, “A closed-form analytical model for single nanoshells,” IEEE Trans. Nanotechnol., vol. 5, no. 3, pp. 265–272, May 2006.
[7]
Z. Tang et al., “Tuning the magneto-optical Kerr effect by the nanograting cross section,” Opt. Lett., vol. 44, no. 7, pp. 1666–1669, 2019.
[8]
A. D. Poletayev, M. C. Hoffmann, S. W. Teitelbaum, M. Trigo, W. C. Chueh, and A. M. Lindenberg, “Terahertz kerr effect in $\beta$-alumina ion conductors,” in Proc. CLEO: Sci. Innovations. Optical Society of America, 2019, Paper JTh4F–4.
[9]
M. Alam, “Compact models for nanophotonic structures and on-chip interconnects,” Ph.D. dissertation, Rice University, 2007.
[10]
N. M. Litchinitser, “Nonlinear optics in metamaterials,” Adv. Phys.: X, vol. 3, no. 1, 2018, Art. no. .
[11]
M. Alam and Y. Massoud, “An RLC ladder model for the equivalent impedance of single metal nanoparticles in electromagnetic field,” in, 2006, pp. 1029–1032.
[12]
M. Alam, A. Hosseini, and Y. Massoud, “Impedance formulation of single oscillating nanospheres at optical frequencies,” in Proc. 50th Midwest Symp. Circuits Syst., 2007, pp. 1249–1252.
[13]
M. Alam and Y. Massoud, “An accurate closed-form analytical model of single nanoshells for cancer treatment,” in Proc. 48th Midwest Symp. Circuits Syst., 2005, pp. 1928–1931.
[14]
G. Mie, “Beiträge zur optik trüber medien, speziell kolloidaler metallösungen,” Annalen Der Physik, vol. 330, no. 3, pp. 377–445, 1908.
[15]
A. Mahmood, A. Ranif, M. Alam, and Y. Massoud, “Effect of dielectric constant on the energy shift in localized surface plasmons resonance,” in Proc. IEEE Canad. Conf. Electric. Comput. Eng., 2018, pp. 1–4.
[16]
N. Engheta, A. Salandrino, and A. Alu, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett., vol. 95, no. 9, 2005, Art. no. .
[17]
A. Mahmood, M. Alam, and Y. Massoud, “A dynamic approach to the lumped impedance representation of a nanoparticle,” IEEE Photon. J., vol. 10, no. 4, Aug. 2018, Art. no.
[18]
A. Hanif, A. Mahmood, M. Alam, and Y. Massoud, “A compact impedance model of plasmonic nanoshell for metamatrial application,” IEEE Trans. Nanotechnol., vol. 18, no. 1, pp. 955–962, Sep. 2019.
[19]
M. U. Khan, A. Kousar, M. Alam, and Y. Massoud, “Frequency selective light scattering and absorption for maximum energy harvesting,” in Proc. 31st Int. Conf. Microelectronics, 2019, pp. 82–85.
[20]
M. Alam, Y. Massoud, and G. V. Eleftheriades, “A time-varying approach to circuit modeling of plasmonic nanospheres using radial vector wave functions,” IEEE Trans. Microw. Theory Techniq., vol. 59, no. 10, pp. 2595–2611, Oct. 2011.
[21]
M. Alam and G. V. Eleftheriades, “Multimode impedance representation of scattering, absorption and extinction cross-sectional areas for plasmonic nanoparticles,” J. Lightw. Technol., vol. 29, no. 17, pp. 2512–2526, Sep. 2011.
[22]
M. Alam, A. Mahmood, S. Azam, M. S. Butt, A. U. Haq, and Y. Massoud, “Impedance model of cylindrical nanowires for metamaterial applications,” Nanomaterials, vol. 9, no. 8, 2019, Art. no. .
[23]
C. Saeidi and D. van der Weide, “Nanoscale nonlinear circuit elements at optical frequencies,” IEEE Trans. Nanotechnol., vol. 17, no. 3, pp. 611–613, May 2018.
[24]
P. B. Johnson and R.-W. Christy, “Optical constants of the noble metals,” Phys. Rev. B, vol. 6, no. 12, 1972, Art. no. .
[25]
E. D. Palik, Handbook of Optical Constants of Solids, vol. 3. New York, NY, USA: Academic, 1998.
[26]
A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M. L. de La Chapelle, “Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B, vol. 71, no. 8, 2005, Art. no. .
[27]
J. B. Monteiro-Filho and L. A. Gómez-Malagón, “Resonant third order nonlinear optical susceptibility of gold nanoparticles,” JOSA B, vol. 29, no. 7, pp. 1793–1798, 2012.
[28]
L. Gao and Z.-Y. Li, “Third-order nonlinear optical response of metal dielectric composites,” J. Appl. Phys., vol. 87, no. 4, pp. 1620–1625, 2000.
[29]
A. Vial and T. Laroche, “Description of dispersion properties of metals by means of the critical points model and application to the study of resonant structures using the FDTD method,” J. Phys. D: Appl. Phys., vol. 40, no. 22, 2007, Art. no. .
[30]
R. Del Coso and J. Solis, “Relation between nonlinear refractive index and third-order susceptibility in absorbing media,” JOSA B, vol. 21, no. 3, pp. 640–644, 2004.
[31]
S. Rautian, “Nonlinear saturation spectroscopy of the degenerate electron gas in spherical metallic particles,” vol. 85, no. 3, pp. 451–461, 1997.
[32]
C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles. Hoboken, NJ, USA: Wiley, 2008.
[33]
J. D. Jackson, Classical Electrodynamics, Hoboken, NJ, USA: Wiley, 1999.

Cited By

View all
  • (2023)All-Photonic Magnetic Resonance in Silicon NanoparticlesIEEE Transactions on Nanotechnology10.1109/TNANO.2023.325056022(149-156)Online publication date: 1-Jan-2023

Index Terms

  1. Closed Form Resonance Solution in Metallic Nanoparticles With Cubic Nonlinearity
        Index terms have been assigned to the content through auto-classification.

        Recommendations

        Comments

        Information & Contributors

        Information

        Published In

        cover image IEEE Transactions on Nanotechnology
        IEEE Transactions on Nanotechnology  Volume 19, Issue
        2020
        227 pages

        Publisher

        IEEE Press

        Publication History

        Published: 01 January 2020

        Qualifiers

        • Research-article

        Contributors

        Other Metrics

        Bibliometrics & Citations

        Bibliometrics

        Article Metrics

        • Downloads (Last 12 months)0
        • Downloads (Last 6 weeks)0
        Reflects downloads up to 06 Oct 2024

        Other Metrics

        Citations

        Cited By

        View all
        • (2023)All-Photonic Magnetic Resonance in Silicon NanoparticlesIEEE Transactions on Nanotechnology10.1109/TNANO.2023.325056022(149-156)Online publication date: 1-Jan-2023

        View Options

        View options

        Get Access

        Login options

        Media

        Figures

        Other

        Tables

        Share

        Share

        Share this Publication link

        Share on social media