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2016-10-26

Full Hydrodynamic Model of Nonlinear Electromagnetic Response in Metallic Metamaterials (Invited Paper)

By Ming Fang, Zhi-Xiang Huang, Wei E. I. Sha, Xiaoyan Y. Z. Xiong, and Xian-Liang Wu
Progress In Electromagnetics Research, Vol. 157, 63-78, 2016
doi:10.2528/PIER16100401

Abstract

Applications of metallic metamaterials have generated significant interest in recent years. Electromagnetic behavior of metamaterials in the optical range is usually characterized by a local-linear response. In this article, we develop a finite-difference time-domain (FDTD) solution of the hydrodynamic model that describes a free electron gas in metals. Extending beyond the local-linear response, the hydrodynamic model enables numerical investigation of nonlocal and nonlinear interactions between electromagnetic waves and metallic metamaterials. By explicitly imposing the current continuity constraint, the proposed model is solved in a self-consistent manner. Charge, energy and angular momentum conservation laws of high-order harmonic generation have been demonstrated for the first time by the Maxwell-hydrodynamic FDTD model. The model yields nonlinear optical responses for complex metallic metamaterials irradiated by a variety of waveforms. Consequently, the multiphysics model opens up unique opportunities for characterizing and designing nonlinear nano devices.

Citation


Ming Fang, Zhi-Xiang Huang, Wei E. I. Sha, Xiaoyan Y. Z. Xiong, and Xian-Liang Wu, "Full Hydrodynamic Model of Nonlinear Electromagnetic Response in Metallic Metamaterials (Invited Paper)," Progress In Electromagnetics Research, Vol. 157, 63-78, 2016.
doi:10.2528/PIER16100401
http://jpier.org/PIER/pier.php?paper=16100401

References


    1. Soukoulis, C. M. and M. Wegener, "Past achievements and future challenges in the development of three-dimensional photonic metamaterials," Nature Photonics, Vol. 5, No. 9, 523-530, Jul. 2011.

    2. Soukoulis, C. M. and M. Wegener, "Optical metamaterials-more bulky and less lossy," Science, Vol. 330, No. 6011, 1633-1634, Dec. 2010.
    doi:10.1126/science.1198858

    3. Hess, O., J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, "Active nanoplasmonic metamaterials," Nature Materials, Vol. 11, No. 7, 573-584, Jul. 2012.
    doi:10.1038/nmat3356

    4. Jarrahi, M., "Advanced photoconductive terahertz optoelectronics based on nano-antennas and nano-plasmonic light concentrators," IEEE Transactions on Terahertz Science and Technology, Vol. 5, No. 3, 391-397, May 2015.
    doi:10.1109/TTHZ.2015.2406117

    5. Campbell, S. D. and R. W. Ziolkowski, "Near-field directive beams from passive and active asymmetric optical nanoantennas," IEEE Journal of Selected Topics in Quantum Electronics, Vol. 21, No. 4, 4800112, Jul.–Aug. 2015.

    6. Palomba, S., L. Novotny, and R. E. Palmer, "Blue-shifted plasmon resonance of individual sizeselected gold nanoparticles," Optics Communications, Vol. 281, No. 3, 480-483, Feb. 2008.
    doi:10.1016/j.optcom.2007.09.056

    7. Anderegg, M., B. Feuerbacher, and B. Fitton, "Optically excited longitudinal plasmons in potassium," Physical Review Letters, Vol. 27, 1565, Dec. 1971.
    doi:10.1103/PhysRevLett.27.1565

    8. Kauranen, M. and A. V. Zayats, "Nonlinear plasmonics," Nature Photonics, Vol. 6, No. 11, 737-748, Nov. 2012.
    doi:10.1038/nphoton.2012.244

    9. Fan, W., S. Zhang, N. C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood, K. J. Malloy, and S. R. J. Brueck, "Second harmonic generation from a nanopatterned isotropic nonlinear material," Nano Letters, Vol. 6, No. 5, 1027-1030, May 2006.
    doi:10.1021/nl0604457

    10. Mingaleev, S. F. and Y. S. Kivshar, "Nonlinear transmission and light localization in photoniccrystal waveguides," Journal of the Optical Society of America B-Optical Physics, Vol. 19, No. 9, 2241-2249, Sep. 2002.
    doi:10.1364/JOSAB.19.002241

    11. Minovich, A. E., A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, "Functional and nonlinear optical metasurfaces," Laser & Photonics Reviews, Vol. 9, No. 2, 195-213, Mar. 2015.
    doi:10.1002/lpor.201400402

    12. Newell, A. C. and J. V. Moloney, Nonlinear Optics, Addison-Wesley, 1992.

    13. Quijada, M., A. G. Borisov, I. Nagy, R. D. Muino, and P. M. Echenique, "Time-dependent densityfunctional calculation of the stopping power for protons and antiprotons in metals," Physical Review A, Vol. 75, No. 4, 042902, Apr. 2007.
    doi:10.1103/PhysRevA.75.042902

    14. Makitalo, J., S. Suuriniemi, and M. Kauranen, "Boundary element method for surface nonlinear optics of nanoparticles," Optics Express, Vol. 19, No. 23, 23386-23399, Nov. 2011.
    doi:10.1364/OE.19.023386

    15. Butet, J., B. Gallinet, K. Thyagarajan, and O. J. F. Martin, "Second-harmonic generation from periodic arrays of arbitrary shape plasmonic nanostructures: A surface integral approach," Journal of the Optical Society of America B-Optical Physics, Vol. 30, No. 11, 2970-2979, Nov. 2013.
    doi:10.1364/JOSAB.30.002970

    16. Bachelier, G., J. Butet, I. Russier-Antoine, C. Jonin, E. Bencichou, and P. F. Brevet, "Origin of optical second-harmonic generation in spherical gold nanoparticles: Local surface and nonlocal bulk contribution bulk contributions," Physical Review B, Vol. 82, No. 23, 235403, 2010.
    doi:10.1103/PhysRevB.82.235403

    17. Xiong, X. Y. Z., L. J. Jiang, W. E. I. Sha, Y. H. Lo, and W. C. Chew, "Compact nonlinear Yagi-Uda nanoantennas," Scientific Reports, Vol. 6, 18872, 2016.
    doi:10.1038/srep18872

    18. Ginzburg, P., A. V. Krasavin, G. A. Wurtz, and A. V. Zayats, "Nonperturbative hydrodynamic model for multiple harmonics generation in metallic nanostructures," ACS Photonics, Vol. 2, No. 1, 8-13, Jan. 2015.
    doi:10.1021/ph500362y

    19. Hille, A., M. Moeferdt, C. Molff, C. Matssek, R. Rodriguez-Oliveros, C. Prohm, J. Niegemann, S. Grafstrom, L. M. Eng, and K. Busch, "Second harmonic generation from metal nano-particle resonators: Numerical analysis on the basis of the hydrodynamic drude model," The Journal of Physical Chemistry, Vol. 120, No. 2, 1163-1169, 2016.

    20. Capretti, A., C. Forestiere, L. D. Negro, and G. Miano, "Full-wave analytical solution of secondharmonic generation in metal nanospheres," Plasmonics, Vol. 9, 151-166, Sep. 2013.

    21. Sipe, J. E., V. C. Y. So, M. Fukui, and G. I. Stegeman, "Analysis of second-harmonic generation at metal surfaces," Physical Review B, Vol. 21, No. 10, 4389, May 1980.
    doi:10.1103/PhysRevB.21.4389

    22. Thomas, L. H., "The calculation of atomic fields," Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 23, No. 5, 542-548, 1927.
    doi:10.1017/S0305004100011683

    23. Huang, Z., T. Koschny, and C. M. Soukoulis, "Theory of pump-probe experiments of metallic metamaterials coupled to a gain medium," Physical Review Letters, Vol. 108, No. 18, 187402, May 2012.
    doi:10.1103/PhysRevLett.108.187402

    24. Fang, A., T. Koschny, M. Wegener, and C. M. Soukoulis, "Self-consistent calculation of metamaterials with gain," Physical Review B, Vol. 79, No. 24, 241104, Jun. 2009.
    doi:10.1103/PhysRevB.79.241104

    25. Ahmed, I., H. Chu, W. B. Ewe, E. Li, and Z. Chen, "Modeling and simulation of nano-interconnects for nanophotonics," Electronics Packaging Technology Conference, 436-440, 2007.

    26. Fang, M., Z. Huang, Th. Koschny, and C. M. Soukoulis, "Electrodynamic modeling of quantum dot luminescence in plasmonic metamaterials," ACS Photonics, Vol. 2, 558-563, 2016.
    doi:10.1021/acsphotonics.5b00499

    27. Okoniewski, M. and E. Okoniewska, "Drude dispersion in ADE FDTD revisited," Electronics Letters, Vol. 42, No. 9, 503-504, Apr. 2006.
    doi:10.1049/el:20060328

    28. Greenwood, A. D., "FDTD models for complex materials," The Open Plasma Journal, Vol. 3, 42-47, 2010.
    doi:10.2174/1876534301003020042

    29. Fang, M., Z. Huang, and X. Wu, "Quantum electrodynamic modeling of quantum dot luminescence in plasmonic metamaterials," IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization 2015, Ottawa, 2015.

    30. Taflove, A. and S. C. Hagness, "Computational Electrodynamics: The Finite-Difference Time- Domain Method," Artecb House, 2005.

    31. Tanaka, K., E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, "Multifold enhancement of quantum dot luminescence in plasmonic metamaterials," Physical Review Letters, Vol. 105, No. 22, 227403, Nov. 2010.
    doi:10.1103/PhysRevLett.105.227403

    32. Berenger, J., "A perfectly matched layer for the absorption of electromagnetic waves," Journal of Computational Physics, Vol. 114, No. 2, 185-200, 1994.
    doi:10.1006/jcph.1994.1159

    33. Konishi, K., T. Higuchi, J. Li, J. Larsson, S. Ishii, and M. K. Gonokami, "Polarization-controlled circular second-harmonic generation from metal hole arrays with threefold rotational symmetry," Physical Review Letters, Vol. 112, No. 13, 135502, Apr. 2014.
    doi:10.1103/PhysRevLett.112.135502

    34. Kelly, S. M., T. J. Jess, and N. C. Price, "How to study proteins by circular dichroism," Biochimica Et Biophysica Acta-Proteins and Proteomics, Vol. 1751, No. 2, 119-139, Aug. 2005.
    doi:10.1016/j.bbapap.2005.06.005

    35. Wang, Y. H. and N. Gedik, "Circular dichroism in angle-resolved photoemission spectroscopy of topological insulators," Physica Status Solidi-Rapid Research Letters, Vol. 7, No. 1–2, 64-71, Feb. 2013.
    doi:10.1002/pssr.201206458

    36. Toscano, G., J. Straubel, A. Kwiatkowski, C. Rockstuhl, F. Evers, H. X. Xu, N. A. Mortensen, and M. Wubs, "Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics," Nature Communications, Vol. 6, 7132, May 2015.
    doi:10.1038/ncomms8132