volume | PIER Journals

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.

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. Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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. Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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 Google Scholar

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 Google Scholar

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

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. Google Scholar

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

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

Dr. Ming Fang

Dr. Zhixiang Huang

Dr. Wei E. I. Sha

Dr. Xiaoyan Y. Z. Xiong

Dr. Xian-Liang Wu