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3 - Frequency-domain methods for modeling plasmonics

Published online by Cambridge University Press:  05 March 2014

Er-Ping Li  and
Hong-Son Chu
Er-Ping Li
Affiliation:
A*STAR Institute of High Performance Computing, Singapore
Hong-Son Chu
Affiliation:
A*STAR Institute of High Performance Computing, Singapore
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Summary

Introduction

The rapid development of research on plasmonics in recent years has led to numerous interesting applications, and many plasmonic nanostructures have been designed and fabricated to achieve novel functionalities and/or better performance. For example, optical antennas are used for biochemical sensing [1–4], plasmonic waveguides have been proposed for on-chip optical communications [5], and metamaterials are under consideration for subwavelength imaging [6]. Most of those plasmonic nanostructures are complicated, so we cannot find analytical solutions for them. Therefore numerical modeling methods are the only choice when it comes to device modeling and structural design. Many numerical methods for solving Maxwell's equations have been established. They can be generally categorized into two classes: frequency-domain methods and time-domain methods.

In frequency-domain methods we assume that the electromagnetic wave is a single-frequency harmonic wave with a time dependence term eiωt or e−iωt (most electrical engineers use eiωt, while e−iωtis more popular among physicists. They are essentially the same, except that, when a medium is lossy, the imaginary parts of its refractive index and permittivity take positive values for e−iωt and negative values for eiωt). Then the time dependence in Maxwell's equations can easily be eliminated and the fields are functions solely of space coordinates. The solutions obtained from frequency-domain methods are generally steady-state solutions. There are many frequency-domain methods available for plasmonic device modeling, among which the finite-element method (FEM) and the method of moments (MoM) are very popular.

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Plasmonic Nanoelectronics and Sensing , pp. 67 - 98
Publisher: Cambridge University Press
Print publication year: 2014

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References

[1] K. A., Willets and R. P., Van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Ann. Rev. Phys. Chem., vol. 58, pp. 267–297, 2007.Google Scholar
[2] M. E., Stewart, C. R., Anderton, L. B., Thompsonet al., “Nanostructured plasmonic sensors,” Chem. Rev., vol. 108, pp. 494–521, 2008.Google Scholar
[3] E., Petryayeva and U. J., Krull, “Localized surface plasmon resonance: Nanostructures, bioas-says and biosensing – A review,” Anal. Chim. Acta., vol. 706, pp. 8–24, 2011.Google Scholar
[4] C., Hoppener and L., Novotny, “Exploiting the light–metal interaction for biomolecular sensing and imaging,” Q. Rev. Biophys., vol. 45, pp. 209–255, 2012.Google Scholar
[5] J., Grandidier, G. C. D., Francs, S., Massenotet al., “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett., vol. 9, pp. 2935–2939, 2009.Google Scholar
[6] J. B., Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett., vol. 85, pp. 3966–3969, 2000.Google Scholar
[7] J., Jin, The Finite Element Method in Electromagnetics, 2nd ed. New York: Wiley-IEEE Press, 2002.
[8] A., Taflove and S. C., Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. New York: Artech House, 2005.
[9] C. B., Burckhardt, “Diffraction of a plane wave at a sinusoidally stratified dielectric grating,” J. Opt. Soc. Am., vol. 56, pp. 1502–1509, 1966.Google Scholar
[10] F. G., Kaspar, “Diffraction by thick, periodically stratified gratings with complex dielectric-constant,” J. Opt. Soc. Am., vol. 63, pp. 37–15, 1973.Google Scholar
[11] K., Knop, “Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves,” J. Opt. Soc. Am., vol. 68, pp. 1206–1210, 1978.Google Scholar
[12] M. G., Moharam and T. K., Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am., vol. 71, pp. 811–818, 1981.Google Scholar
[13] M. G., Moharam and T. K., Gaylord, “Rigorous coupled-wave analysis of grating diffraction – E-mode polarization and losses,” J. Opt. Soc. Am., vol. 73, pp. 451–155, 1983.Google Scholar
[14] P., Lalanne and G. M., Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A – Opt. Image Sci. Vision, vol. 13, pp. 779–784, 1996.Google Scholar
[15] G., Granet and B., Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A – Opt. Image Sci. Vision, vol. 13, pp. 1019–1023, 1996.Google Scholar
[16] L. F., Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A – Opt. Image Sci. Vision, vol. 13, pp. 1870–1876, 1996.Google Scholar
[17] L. F., Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A – Opt. Image Sci. Vision, vol. 13, pp. 1024–1035, 1996.Google Scholar
[18] L. F., Li, “Note on the S-matrix propagation algorithm,” J. Opt. Soc. Am. A – Opt. Image Sci. Vision, vol. 20, pp. 655–660, 2003.Google Scholar
[19] E., Noponen and J., Turunen, “Eigenmode method for electromagnetic synthesis of diffractive elements with 3-dimensional profiles,” J. Opt. Soc. Am. A – Opt. Image Sci. Vision, vol. 11, pp. 2494–2502, 1994.Google Scholar
[20] L. F., Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A – Opt. Image Sci. Vision, vol. 14, pp. 2758–2767, 1997.Google Scholar
[21] Z. T., Liu, K. P., Chen, X. J., Niet al., “Experimental verification of two-dimensional spatial harmonic analysis at oblique light incidence,” J. Opt. Soc. Am. B – Opt. Phy., vol. 27, pp. 2465–2470, 2010.Google Scholar
[22] P. B., Johnson and R. W., Christy, “Optical constants of noble metals,” Phys. Rev. B, vol. 6, pp. 4370–4379, 1972.Google Scholar
[23] V. P., Drachev, U. K., Chettiar, A. V., Kildishevet al., “The Ag dielectric function in plasmonic metamaterials,” Opt. Express, vol. 16, pp. 1186–1195, 2008.Google Scholar
[24] E. G., Loewen and E., Popov, Diffraction Gratings and Applications. New York: Marcel Dekker, Inc., 1997.
[25] K. P., Chen, V. P., Drachev, J. D., Borneman, A. V., Kildishev, and V. M., Shalaev, “Drude relaxation rate in grained gold nanoantennas,” Nano Lett., vol. 10, pp. 916–922, 2010.Google Scholar
[26] X., Ni, Z., Liu, F., Guet al., Photonics SHA-2D: Modeling of Single-Period Multilayer Optical Gratings and Metamaterials, 2009. Available from: https://nanohub.org/tools/sha2d/.
[27] Z., Liu, A., Boltasseva, R. H., Pedersenet al., “Plasmonic nanoantenna arrays for the visible,” Metamaterials, vol. 2, pp. 45–51, 2008.Google Scholar
[28] S., Zhang, W. J., Fan, N. C., Panoiuet al., “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett., vol. 95, 137404, 2005.Google Scholar
[29] J. P., Kottmann and O. J. F., Martin, “Plasmon resonant coupling in metallic nanowires,” Opt. Express, vol. 8, pp. 655–663, 2001.Google Scholar
[30] S. A., Maier, M. L., Brongersma, P. G., Kiket al., “Plasmonics – A route to nanoscale optical devices,” Adv. Mater., vol. 13, pp. 1501–1505, 2001.Google Scholar
[31] M., Moskovits, “Surface-enhanced Raman spectroscopy: A brief retrospective,” J. Raman Spectrosc., vol. 36, pp. 485–496, 2005.Google Scholar
[32] P., Muhlschlegel, H. J., Eisler, O. J. F., Martin, B., Hecht, and D. W., Pohl, “Resonant optical antennas,” Science, vol. 308, pp. 1607–1609, 2005.Google Scholar
[33] E. Y., Poliakov, V. M., Shalaev, V. A., Markel, and R., Botet, “Enhanced Raman scattering from self-affine thin films,” Opt. Lett., vol. 21, pp. 1628–1630, 1996.Google Scholar
[34] W., Rechberger, A., Hohenau, A., Leitneret al., “Optical properties of two interacting gold nanoparticles,” Opt. Commun., vol. 220, pp. 137–141, 2003.Google Scholar
[35] V. G., Veselago, “Electrodynamics of substances with simultaneously negative values of sigma and mu,” Sov. Phys. Usp., vol. 10, pp. 509–514, 1968.Google Scholar
[36] S. H., Jiang and R., Pike, “A full electromagnetic simulation study of near-field imaging using silver films,” New J. Phys., vol. 7, 169, 2005.Google Scholar
[37] S. A., Ramakrishna and J. B., Pendry, “The asymmetric lossy near-perfect lens,” J. Mod. Opt., vol. 49, pp. 1747–1762, 2002.Google Scholar
[38] S. A., Ramakrishna, J. B., Pendry, M. C. K., Wiltshire, and W. J., Stewart, “Imaging the near field,” J. Mod. Opt., vol. 50, pp. 1419–1430, 2003.Google Scholar
[39] Z. W., Liu, N., Fang, T. J., Yen, and X., Zhang, “Rapid growth of evanescent wave by a silver superlens,” Appl. Phys. Lett., vol. 83, pp. 5184–5186, 2003.Google Scholar
[40] R., Borghi, F., Gori, M., Santarsiero, F., Frezza, and G., Schettini, “Plane-wave scattering by a perfectly conducting circular cylinder near a plane surface: Cylindrical-wave approach,” J. Opt. Soc. Am. A – Opt. Image Sci. Vision, vol. 13, pp. 483–493, 1996.Google Scholar
[41] R., Borghi, M., Santarsiero, F., Frezza, and G., Schettini, “Plane-wave scattering by a dielectric circular cylinder parallel to a general reflecting flat surface,” J. Opt. Soc. Am. A – Opt. Image Sci. Vision, vol. 14, pp. 1500–1504, 1997.Google Scholar
[42] J. J., Bowman, T. B. A., Senior, and P. L. E., Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes, revised ed. Amsterdam: North-Holland, 1969.
[43] A., Madrazo and M., Nietovesperinas, “Scattering of electromagnetic-waves from a cylinder in front of a conducting plane,” J. Opt. Soc. Am. A – Opt. Image Sci. Vision, vol. 12, pp. 1298–1309, 1995.Google Scholar
[44] P. J., Valle, F., Gonzalez, and F., Moreno, “Electromagnetic-wave scattering from conducting cylindrical structures on flat substrates – Study by means of the extinction theorem,” Appl. Opt., vol. 33, pp. 512–523, 1994.Google Scholar
[45] P. J., Valle, F., Moreno, J. M., Saiz, and F., Gonzalez, “Near-field scattering from subwavelength metallic protuberances on conducting flat substrates,” Phys. Rev. B, vol. 51, pp. 13681–13690, 1995.Google Scholar
[46] Z. T., Liu, V. M., Shalaev, and A. V., Kildishev, “Coupling effect ina near-field object–superlens system,” Appl. Phys. A – Mater. Sci. Processing, vol. 107, pp. 83–88, 2012.Google Scholar
[47] C. F., Bohren and D. R., Huffman, Absorption and Scattering of Light by Small Particles. New York: John Wiley & Sons, 1983.
[48] P., Yeh, Optical Waves in Layered Media. New York: John Wiley & Sons, 1988.
[49] Z. T., Liu, M. D., Thoreson, A. V., Kildishev, and V. M., Shalaev, “Translation of nanoantenna hot spots by a metal–dielectric composite superlens,” Appl. Phys. Lett., vol. 95, 033114, 2009.Google Scholar
[50] M. D., Thoreson, R. B., Nielsen, P. R., Westet al., “Studies of plasmonic hot-spot translation by a metal-dielectric layered superlens,” in Metamaterials: Fundamentals and Applications IV, A. D., Boardman, N., Engheta, M. A., Noginov, and N. I., Zheludev, Eds. Bellingham, WA: SPIE – International Society for Optical Engineering, pp. 80931J1–80931J20, 2011.
[51] Z. T., Liu, E. P., Li, V. M., Shalaev, and A. V., Kildishev, “Near ield enhancement in silver nanoantenna-superlens systems,” Appl. Phys. Lett., vol. 101, pp. 021109–021111, 2012.Google Scholar

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