Vol. 154
Latest Volume
All Volumes
PIER 180 [2024] PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2015-11-19
Squeezing Maxwell's Equations into the Nanoscale (Invited Paper)
By
Progress In Electromagnetics Research, Vol. 154, 35-50, 2015
Abstract
The plasmonic behavior of nanostructured materials has ignited intense research for the fundamental physics of plasmonic structures and their cutting edge applications concerning the fields of nanoscience and biosensing. The optical response of plasmonic metals is generally well-described by classical Maxwell's Equations (ME). Thus, the understanding of plasmons and the design of plasmonic nanostructures can therefore directly benefit from lastest advances achieved in classic research areas such as computational electromagnetics. In this context, this paper is devoted to review the most recent advances in nanoplasmonic modeling, related with the latest breakthroughs in surface integral equation (SIE) formulations derived from ME. These works have extended the scope of application of Maxwell's Equations, from microwave/milimeter waves to infrared and optical frequency bands, in the emerging fields of nanoscience and medical biosensing.
Citation
Diego M. Solis, Jose Taboada, Luis Landesa, Jose Luis Rodriguez, and Fernando Obelleiro, "Squeezing Maxwell's Equations into the Nanoscale (Invited Paper)," Progress In Electromagnetics Research, Vol. 154, 35-50, 2015.
doi:10.2528/PIER15110103
References

1. "Nature milestones: Photons supplement,", 2010, http://www.nature.com/milestones/photons.

2. O’Neal, D. P., L. R. Hirsch, N. J. Halas, J. D. Payne, and J. L. West, "Photo-thermal tumor ablation in mice using near infrared-absorbing nanoparticles," Cancer Lett., Vol. 209, 171-176, 2004.

3. Oulton, R. F., V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, "Plasmon lasers at deep subwavelength scale," Nature, Vol. 461, 629-632, 2009.

4. Alvarez-Puebla, R. A. and L. M. Liz-Marzn, "SERS-based diagnosis and biodetection," Small, Vol. 6, No. 5, 604-610, 2010.

5. Atwater, H. A. and A. Polman, "Plasmonics for improved photovoltaic devices," Nat. Mater., Vol. 9, 205-213, 2010.

6. Noginov, M. A., G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, "Demonstration of a spaser-based nanolaser," Nature, Vol. 460, 1110-1113, 2009.

7. Akimov, A. V., A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, "Generation of single optical plasmons in metallic nanowires coupled to quantum dots," Nature, Vol. 450, 402-406, 2007.

8. Alu, A. and N. Engheta, "Wireless at the nanoscale: Optical interconnects using matched nanoantennas," Phys. Rev. Lett., Vol. 104, 213902, 2010.

9. Atwater, H. A., "The promise of plasmonics," Scientific American, Vol. 296, No. 4, 56-62, 2007.

10. Maier, S. A., Plasmonics: Fundamentals and Applications, Springer, 2010.

11. Jackson, J. D., Classical Electrodynamics, Wiley, 1962.

12. Johnson, P. B. and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B, Vol. 6, No. 12, 4370-4379, 1972.

13. Palik, E. D., Handbook of Optical Constants of Solids, Academic Press, 1985.

14. García de Abajo, F. J., "Nonlocal effects in the plasmons of strongly interacting nanoparticles, dimers, and waveguides," J. Phys. Chem. C, Vol. 112, No. 46, 17983-17987, 2008.

15. Draine, B. T., "The discrete-dipole approximation and its application to interstellargraphite grains," Astrophys. J., Vol. 333, 848-872, 1988.

16. Taflove, A. and M. E. Brodwin, "Numerical solution of steadystate electromagnetic scattering problems using the timedependent Maxwell’s equations," IEEE Trans. Microwave Theory Tech., Vol. 23, 623-630, 1975.

17. Hao, F., C. L. Nehl, J. H. Hafner, and P. Nordlander, "Plasmon resonances of a gold nanostar," Nano Lett., Vol. 7, 729-732, 2007.

18. Jin, J., The Finite Element Method in Electromagnetics, Wiley, 2002.

19. Zhang, S., K. Bao, N. J. Halas, H. Xu, and P. Nordlander, "Substrate-induced fano resonances of a plasmonic nanocube: A route to increased-sensitivity localized surface plasmon resonance sensors revealed," Nano Lett., Vol. 11, 1657-1663, 2011.

20. Harrington, R. F., Field Computation by Moment Method, IEEE Press, 1993.

21. Taboada, J. M., 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, Vol. 28, 1341-1348, 2011.

22. Solís, D. M., J. M. Taboada, F. Obelleiro, L. M. Liz-Marzán, and F. J. García de Abajo, "Toward ultimate nanoplasmonics modeling," ACS Nano, Vol. 8, 7559-7570, 2014.

23. Hamon, C., S. M. Novikov, L. Scarabelli, D. M. Solís, T. Altantzis, S. Bals, J. M. Taboada, F. Obelleiro, and L. M. Liz-Marzán, "Collective plasmonic properties in few-layer gold nanorod supercrystals," ACS Photonics, Vol. 2, No. 10, 1482-1488, 2015.

24. Araújo, M. G., 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," Optics Express, Vol. 20, No. 8, 9161-9171, 2012.

25. Solís, D. M., J. M. Taboada, and F. Obelleiro, "Surface integral equation method of moments with multiregion basis functions applied to plasmonics," IEEE Trans. Antennas Propag., Vol. 63, No. 5, 2141-2152, 2015.

26. Solís, D. M., J. M. Taboada, O. Rubiños-López, and F. Obelleiro, "Improved combined tangential formulation for electromagnetic analysis of penetrable bodies," JOSA B, Vol. 32, No. 9, 1780-1787, 2015.

27. Song, J. M., C. C. Lu, and W. C. Chew, "Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects," IEEE Trans. Antennas Propag., Vol. 45, 1488-1493, 1997.

28. Donepudi, K. C., J.-M. Jin, and W. C. Chew, "A higher order multilevel fast multipole algorithm for scattering from mixed conducting/dielectric bodies," IEEE Trans. Antennas Propag., Vol. 51, No. 10, 2814-2821, 2003.

29. Araújo, M. G., D. M. Solís, J. Rivero, J. M. Taboada, and F. Obelleiro, "Solution of large-scale plasmonic problems with the multilevel fast multipole algorithm," Optics Letters, Vol. 37, No. 3, 416-418, 2012.

30. Taboada, J. M., M. G. Ara´ujo, J. M. B´ertolo, L. Landesa, F. Obelleiro, and J. L. Rodrguez, "MLFMA-FFT parallel algorithm for the solution of large-scale problems in electromagnetics (Invited Paper)," Progress In Electromagnetics Research, Vol. 105, 15-30, 2010.

31. Araújo, M. G., J. M. Taboada, F. Obelleiro, J. M. Bértolo, L. Landesa, J. Rivero, and J. L. Rodrguez, "Supercomputer aware approach for the solution of challenging electromagnetic problems," Progress In Electromagnetics Research, Vol. 101, 241-256, 2010.

32. Taboada, J. M., M. G. Araújo, F. Obelleiro, J. L. Rodríguez, and L. Landesa, "MLFMA-FFT parallel algorithm for the solution of extremely large problems in electromagnetics," Proceedings of the IEEE, Special issue on Large Scale Electromagnetic Computation for Modeling and Applications, Vol. 101, No. 2, 350-363, 2013.

33. Solís, D. M., J. M. Taboada, M. G. Araújo, F. Obelleiro, and J. O. Rubiños-López, "Design of optical wide-band log-periodic nanoantennas using surface integral equation techniques," Opt. Commun., Vol. 301-302, 6166, 2013.

34. Obelleiro, F., J. M. Taboada, D. M. Solís, and L. Bote, "Directive antenna nanocoupler to plasmonic gap waveguides," Opt. Lett., Vol. 38, 1630-1632, 2013.

35. Solís, D. M., J. M. Taboada, F. Obelleiro, and L. Landesa, "Optimization of an optical wireless nanolink using directive nanoantennas," Opt. Express, Vol. 21, 2369-2377, 2013.

36. Farrokhtakin, E., D. Rodríguez-Fernndez, V. Mattoli, D. M. Solís, J. M. Taboada, F. Obelleiro, M. Grzelczak, and L. M. Liz-Marzán, "Radial growth of plasmon coupled gold nanowires on colloidal templates," Journal of Colloid and Interface Science, Vol. 449, 87-91, 2015.

37. Fernández-López, C., L. Polavarapu, D. M. Solís, J. M. Taboada, F. Obelleiro, R. Contreras-Caceres, I. Pastoriza-Santos, and J. Perez-Juste, "Gold nanorods-pNIPAM hybrids with reversible plasmon coupling: Synthesis, modeling and sers properties," ACS Applied Materials & Interfaces, Vol. 7, No. 23, 12530-12538, 2015.

38. Shiohara, A., S. M. Novikov, D. M. Solís, J. M. Taboada, F. Obelleiro, and L. M. Liz-Marzán, "Plasmon modes and hot spots in gold nanostarsatellite clusters," Journal of Physical Chemistry C, Vol. 119, No. 20, 10836-10843, 2015.

39. Drude, P., "Zur elektronentheorie der metalle," Ann. Phys., Vol. 306, No. 3, 566-613, 1900.

40. Vial, A., A.-S. Grimault, D. Macías, D. Barchiesi, and M. Lamy 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, 085416, 2005.

41. Ritchie, R. H., "Plasma losses by fast electrons in thin films," Phys. Rev., Vol. 106, No. 5, 874-881, 1957.

42. Ylä-Oijala, P., M. Taskinen, and S. Järvenpää, "Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods," Radio Sci., Vol. 40, No. 6, 1-19, 2005.

43. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propag., Vol. 30, No. 3, 409-418, 1982.

44. Wilton, D. R., S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, "Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains," IEEE Trans. Antennas Propag., Vol. 32, 276-281, 1984.

45. Hodges, R. E. and Y. Rahmat-Samii, "The evaluation of MFIE integrals with the use of vector triangle basis functions," Microwave Opt. Technol. Lett., Vol. 14, 9-14, 1997.

46. Graglia, R. D., "On the numerical integration of the linear shape functions times the 3-D Greens function or its gradient on a plane triangle," IEEE Trans. Antennas Propag., Vol. 41, 1448-1455, 1993.

47. Ylä-Oijala, P. and M. Taskinen, "Calculation of CFIE impedance matrix elements with RWG and nxRWG functions," IEEE Trans. Antennas Propag., Vol. 51, 1837-1846, 2003.

48. Kahan, W., "Branch cuts for complex elementary functions, or much ado about nothing’s sign bit," The State of the Art in Numerical Analysis, A. Iserles and M. J. D. Powell, eds., Clarendon Press, Oxford, 1987.

49. Ziolkowski, R. W. and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E Stat. Nonlin. Soft Matter Phys., Vol. 64, No. 5, 056625, 2001.

50. Standard C++ Library Reference, IBM Corp., 2005.

51. Obelleiro, F., J. M. Taboada, and M. G. Araújo, "Calculation of wave propagation parameters in generalized media," Microwave Opt. Technol. Lett., Vol. 54, No. 12, 2731-2736, 2012.

52. Putnam, J. M. and L. N. Medgyesi-Mitschang, "Combined field integral equation formulation for inhomogneous two- and three-dimensional bodies: The junction problem," IEEE Trans. Antennas Propagat., Vol. 39, No. 5, 667-672, 1991.

53. Ylä-Oijala, P., M. Taskinen, and J. Sarvas, "Surface integral equation method for general composite metallic and dielectric structures with junctions," Progress In Electromagnetics Research, Vol. 52, 81-108, 2005.

54. Coifman, R., V. Rokhlin, and S. Wanzura, "The fast multipole method for the wave equation: A pedestrian prescription," IEEE Antennas Propag. Mag., Vol. 35, 7-12, 1993.

55. Waltz, C., K. Sertel, M. A. Carr, B. C. Usner, and J. L. Volakis, "Massively parallel fast multipole method solutions of large electromagnetic scattering problems," IEEE Trans. Antennas Propag., Vol. 55, No. 6, 1810-1816, 2007.

56. Sols, D. M., M. G. Arajo, L. Landesa, S. Garca, J. M. Taboada, and F. Obelleiro, "MLFMA-MoM for solving the scattering of densely packed plasmonic nanoparticle assemblies," IEEE Photonics Journal, Vol. 7, No. 3, 4800709, 2015.

57. Saad, Y., Iterative Methods for Sparse Linear Systems, PWS, 1996.

58. Philipse, A. P. and A. Vrij, "Preparation and properties of nonaqueous model dispersions of chemically modified, charged silica spheres," J. Colloid Interface Sci., Vol. 128, 121-136, 1989.

59. Mie, G., "Beitrge zur optik truber medien, speziell kolloidaler metallsungen," Ann. Phys. Leipzig, Ger., Vol. 25, 377-445, 1908.

60. Metiu, H., "Surface enhanced spectroscopy," Prog. Surf. Sci., Vol. 17, 153-320, 1984.

61. Moskovits, M., "Surface-enhanced spectroscopy," Rev. Mod. Phys., Vol. 57, 783, 1985.

62. Novotny, L. and B. Hecht, Principles of Nano-Optics, Cambridge Univ. Press, 2006.

63. Schlücker, S., "Surface-enhanced raman spectroscopy: Concepts and chemical applications," Angew. Chem., Int. Ed., Vol. 53, 4756-4795, 2014.

64. Alvarez-Puebla, R. A., A. Agarwal, P. Manna, B. P. Khanal, P. Aldeanueva-Potel, E. Carb-Argibay, N. Pazos-Prez, L. Vigderman, E. R. Zubarev, N. A. Kotov, and L. M. Liz-Marzn, "Gold nanorods 3D-supercrystals as SERS substrates for the rapid detection of scrambled prions," Proc. Natl. Acad. Sci. U.S.A., Vol. 108, 8157-8161, 2011.

65. Alvarez-Puebla, R. A. and L. M. Liz-Marzn, "SERS detection of small inorganic molecules and ions," Angew. Chem. Int. Ed., Vol. 51, 11214-11223, 2012.