## Surface integral formulations for the design of plasmonic nanostructures |

JOSA A, Vol. 29, Issue 11, pp. 2314-2327 (2012)

http://dx.doi.org/10.1364/JOSAA.29.002314

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### Abstract

Numerical formulations based on surface integral equations (SIEs) provide an
accurate and efficient framework for the solution of the electromagnetic
scattering problem by three-dimensional plasmonic nanostructures in the
frequency domain. In this paper, we
present a unified description of SIE formulations with both singular and
nonsingular kernel and we study their accuracy in solving the scattering problem
by metallic nanoparticles with spherical and nonspherical shape. In fact, the
accuracy of the numerical solution, especially in the near zone, is of great
importance in the analysis and design of plasmonic nanostructures, whose
operation critically depends on the manipulation of electromagnetic hot spots.
Four formulation types are considered: the

© 2012 Optical Society of America

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(050.1755) Diffraction and gratings : Computational electromagnetic methods

(350.4238) Other areas of optics : Nanophotonics and photonic crystals

(250.5403) Optoelectronics : Plasmonics

(050.5745) Diffraction and gratings : Resonance domain

(050.6624) Diffraction and gratings : Subwavelength structures

**ToC Category:**

Optoelectronics

**History**

Original Manuscript: June 18, 2012

Manuscript Accepted: August 22, 2012

Published: October 16, 2012

**Citation**

Carlo Forestiere, Giovanni Iadarola, Guglielmo Rubinacci, Antonello Tamburrino, Luca Dal Negro, and Giovanni Miano, "Surface integral formulations for the design of plasmonic nanostructures," J. Opt. Soc. Am. A **29**, 2314-2327 (2012)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-11-2314

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### References

- S. Maier, Plasmonics: Fundamental and Applications (Springer, 2007).
- J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010). [CrossRef]
- C. Forestiere, M. Donelli, G. Walsh, E. Zeni, G. Miano, and L. Dal Negro, “Particle-swarm optimization of broadband nanoplasmonic arrays,” Opt. Lett. 35, 133–135 (2010). [CrossRef]
- P. Ginzburg, N. Berkovitch, A. Nevet, I. Shor, and M. Orenstein, “Resonances on-demand for plasmonic nano-particles,” Nano Lett. 11, 2329–2333 (2011). [CrossRef]
- C. Forestiere, A. J. Pasquale, A. Capretti, G. Miano, A. Tamburrino, S. Y. Lee, B. M. Reinhard, and L. Dal Negro, “Genetically engineered plasmonic nanoarrays,” Nano Lett. 12, 2037–2044 (2012). [CrossRef]
- C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
- S. Asano and G. Yamamoto, “Light scattering by a spheroidal particle,” Appl. Opt. 14, 29–49 (1975).
- E. Purcell and C. R. Pennypacker, “Scattering and absorption of light by non-spherical dielectric grains,” Astrophys. J. 186, 705–714 (1973). [CrossRef]
- B. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988). [CrossRef]
- A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
- K. Yee and J. Chen, “The finite-difference time-domain (FDTD) and the finite-volume time-domain (FVTD) methods in solving maxwell’s equations,” IEEE Trans. Antennas Propag. 45, 354–363 (1997). [CrossRef]
- L. Dal Negro, G. Miano, G. Rubinacci, A. Tamburrino, and S. Ventre, “A fast computation method for the analysis of an array of metallic nanoparticles,” IEEE Trans. Magn. 45, 1618–1621 (2009). [CrossRef]
- G. Miano, G. Rubinacci, and A. Tamburrino, “Numerical modeling for the analysis of plasmon oscillations in metallic nanoparticles,” IEEE Trans. Antennas Propag. 58, 2920–2933 (2010). [CrossRef]
- G. Miano, G. Rubinacci, and A. Tamburrino, “Numerical modeling for plasmonics nanoparticles,” Int. J. Appl. Electromag. Mech. 35, 79–91 (2011).
- J. Mautz and R. Harrington, “Electromagnetic scattering from a homogeneous material body of revolution,” Arch. Elektron. Uebertraeg. 33, 71–80 (1979).
- C. Muller, Foundations of the Mathematical Theory of Electromagnetic Waves (Springer, 1969).
- P. Yla-Oijala and M. Taskinen, “Well-conditioned Muller formulation for electromagnetic scattering by dielectric objects,” IEEE Trans. Antennas Propag. 53, 3316–3323 (2005). [CrossRef]
- P. Yla-Oijala and M. Taskinen, “Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects,” IEEE Trans. Antennas Propag. 53, 1168–1173 (2005). [CrossRef]
- J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. Garcia de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90, 057401 (2003). [CrossRef]
- G. W. Bryant, F. J. Garcia de Abajo, and J. Aizpurua, “Mapping the plasmon resonances of metallic nanoantennas,” Nano Lett. 8, 631–636 (2008). [CrossRef]
- A. M. Kern and O. J. F. Martin, “Surface integral formulation for 3D simulations of plasmonic and high permittivity nanostructures,” J. Opt. Soc. Am. A 26, 732–740 (2009). [CrossRef]
- B. Gallinet, A. M. Kern, and O. J. F. Martin, “Accurate and versatile modeling of electromagnetic scattering on periodic nanostructures with a surface integral approach,” J. Opt. Soc. Am. A 27, 2261–2271 (2010). [CrossRef]
- J. M. Taboada, J. Rivero, F. Obelleiro, M. G. Araújo, and L. Landesa, “Method-of-moments formulation for the analysis of plasmonic nano-optical antennas,” J. Opt. Soc. Am. A 28, 1341–1348 (2011). [CrossRef]
- J. Mäkitalo, S. Suuriniemi, and M. Kauranen, “Boundary element method for surface nonlinear optics of nanoparticles,” Opt. Express 19, 23386–23399 (2011). [CrossRef]
- M. G. Araújo, J. M. Taboada, D. M. Solís, J. Rivero, L. Landesa, and F. Obelleiro, “Comparison of surface integral equation formulations for electromagnetic analysis of plasmonic nanoscatterers,” Opt. Express 20, 9161–9171 (2012). [CrossRef]
- P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965). [CrossRef]
- P. C. Waterman, “Scattering by dielectric obstacles,” Alta Freq. 38, 348–352 (1969).
- A. Doicu and T. Wriedt, “Calculation of the T matrix in the null-field method with discrete sources,” J. Opt. Soc. Am. A 16, 2539–2544 (1999). [CrossRef]
- A. Doicu and T. Wriedt, “Near-field computation using the null-field method,” J. Quant. Spectrosc. Radiat. Transfer 111, 466–473 (2010). [CrossRef]
- C. Forestiere, G. Iadarola, L. Dal Negro, and G. Miano, “Near-field calculation based on the T-matrix method with discrete sources,” J. Quant. Spectrosc. Radiat. Transfer. 112, 2384–2394 (2011). [CrossRef]
- M. Karamehmedović, R. Schuh, V. Schmidt, T. Wriedt, C. Matyssek, W. Hergert, A. Stalmashonak, G. Seifert, and O. Stranik, “Comparison of numerical methods in near-field computation for metallic nanoparticles,” Opt. Express 19, 8939–8953 (2011). [CrossRef]
- S. Rao, D. Wilton, and A. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 30, 409–418 (1982). [CrossRef]
- A. E. H. Love, “The integration of equation of propagation of electric waves,” Proc. R. Soc. London 197, 1–45 (1901). [CrossRef]
- R. Harrington, “Boundary integral formulations for homogeneous material bodies,” J. Electromag. Waves Appl. 3, 1–15, (1969). [CrossRef]
- P. M. Taskinen, P. Ylä-Oijala, and S. Järvenpää, “Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods,” Radio Sci. 40, 1–19 (2005).
- A. Zhu, and S. Gedney, “Comparison of the Muller and PMWCHT surface integral formulations for the locally corrected Nystrom method,” in Proceedings of 2004 Antennas and Propagation Society International Symposium (IEEE, 2004), pp. 3871–3874.
- B. H. Jung, T. K. Sarkar, and Y.-S. Chung, “A survey of various frequency domain integral equations for the analysis of scattering from three-dimensional dielectric objects,” Prog. Electromagn. Res. 33, 193–245 (2002). [CrossRef]
- X. Sheng, J.-M. Jin, J. Song, W. Chew, and C.-C. Lu, “Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies,” IEEE Trans. Antennas Propag. 46, 1718–1726 (1998). [CrossRef]
- R. Harrington, Field Computation by Moment Methods(Macmillan, 1968).
- C. Leat, N. Shuley, and G. Stickley, “Triangular-patch model of bowtie antennas: validation against Brown and Woodward,” IEEE Proc. Microw. Antennas Propag. 145, 465–470 (1998). [CrossRef]
- L. Tsang, J. A. Kong, and K. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000).
- R. Graglia, “On the numerical integration of the linear shape functions times the 3-D Green’s function or its gradient on a plane triangle,” IEEE Trans. Antennas Propag. 41, 1448–1455 (1993). [CrossRef]
- A. Doicu, T. Wriedt, and Y. Eremin, Light Scattering by Systems of Particles (Springer-Verlag, 2006).
- M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge University, 2006).
- P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]
- C. Geuzaine and J. Remacle, “Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities,” Int. J. Numer. Methods Eng. 79, 1309–1331 (2009).
- D. Lindholm, “Automatic triangular mesh generation on surfaces of polyhedra,” IEEE Trans. Magn. 19, 2539–2542 (1983). [CrossRef]
- W. C. Chew, J. M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics.(Artech House, 2001).
- P. Yla-Oijala and M. Taskinen, “Electromagnetic scattering analysis with combined field integral equations,” in Proceedings of Antennas and Propagation Society International Symposium (IEEE, 2007), pp. 4869–4872.
- G. Iadarola, C. Forestiere, L. Dal Negro, F. Villone, and G. Miano, “GPU-accelerated T-matrix algorithm for light-scattering simulations,” J. Comput. Phys. 231, 5640–5652 (2012). [CrossRef]
- D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. E. Moerner, “Gap-dependent optical coupling of single “bowtie” nanoantennas resonant in the visible,” Nano Lett. 4, 957–961 (2004). [CrossRef]
- M. Mishchenko and L. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994). [CrossRef]
- B. Draine and P. Flatau, “User Guide for the Discrete Dipole Approximation Code DDSCAT 7.1” (2010).

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