Abstract

Although many commercially available electromagnetic tools are conveniently used in RF and microwave applications, only a few of them provide the capability to analyze the optical response of nanometric radiators and scatterers. The assessment of their performance in the visible to near ultraviolet part of the electromagnetic (EM) spectrum becomes more and more important, considering the exponential rise of nanoscale systems. Since the accuracy of these numerical tools has not been fully investigated in literature, in this paper we essentially demonstrate a comparative study of the most widely used EM field solvers in the area of nano-plasmonics: COMSOL, CST and Lumerical. This is done through the investigation of the near and far field characteristics of basic canonical nanoparticles such as spheres, shells, cubes and cuboids, varying their sizes and constituting materials. The benchmarking results clearly show that at this moment not all EM field solvers offer the same accuracy.

© 2017 Optical Society of America

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References

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2015 (2)

2014 (6)

D. Vercruysse, X. Zheng, Y. Sonnefraud, N. Verellen, G. Di Martino, L. Lagae, G. A. E. Vandenbosch, V. V. Moshchalkov, S. A. Maier, and P. Van Dorpe, “Directional fluorescence emission by individual V-antennas explained by mode expansion,” ACS Nano 8(8), 8232–8241 (2014).
[Crossref] [PubMed]

K. Costa and V. Dmitriev, “Simple and efficient computational method to analyze cylindrical plasmonic nanoantennas,” Int. J. Antennas Propag. 2014, 675036 (2014).
[Crossref]

M. O. Sallam, G. A. E. Vandenbosch, G. Gielen, and E. A. Soliman, “Integral equations formulation of plasmonic transmission lines,” Opt. Express 22(19), 22388–22402 (2014).
[Crossref] [PubMed]

V. L. Y. Loke, G. M. Huda, E. U. Donev, V. Schmidt, J. T. Hastings, M. Pinar Mengüç, and T. Wriedt, “Comparison between discrete dipole approximation and other modelling methods for the plasmonic response of gold nanospheres,” Appl. Phys. B 115(2), 237–246 (2014).
[Crossref]

M. W. Knight, N. S. King, L. Liu, H. O. Everitt, P. Nordlander, and N. J. Halas, “Aluminum for plasmonics,” ACS Nano 8(1), 834–840 (2014).
[Crossref] [PubMed]

X. Zheng, V. K. Valev, N. Verellen, V. Volskiy, L. O. Herrmann, P. Van Dorpe, J. J. Baumberg, G. A. E. Vandenbosch, and V. V. Moshchalkov, “Implementation of the natural mode analysis for nanotopologies using a V-MoM algorithm,” IEEE Photonics J. 6(4), 1–13 (2014).
[Crossref]

2013 (2)

E. A. Soliman, “Wideband nanocrescent plasmonic antenna with engineered spectral response,” Microw. Opt. Technol. Lett. 55(3), 624–629 (2013).
[Crossref]

M. Farmahini-Farahani, J. Cheng, and H. Mosallei, “Metasurfaces nanoantennas for light processing,” J. Opt. Soc. Am. B 30(9), 2365–2370 (2013).
[Crossref]

2012 (2)

H. Harutyunyan, G. Volpe, R. Quidant, and L. Novotny, “Enhancing the nonlinear optical response using multifrequency gold-nanowire antennas,” Phys. Rev. Lett. 108(21), 217403 (2012).
[Crossref] [PubMed]

G. A. E. Vandenbosch and Z. Ma, “Upper bounds for the solar energy harvesting efficiency of nano-antennas,” Nano Energy 1(3), 494–502 (2012).
[Crossref]

2011 (5)

2010 (2)

J. Parsons, C. P. Burrows, J. R. Sambles, and W. L. Barnes, “A comparison of techniques used to simulate the scattering of electromagnetic radiation by metallic nanostructures,” J. Mod. Opt. 57(5), 356–365 (2010).
[Crossref]

J. Labille and J. Brant, “Stability of nanoparticles in water,” Nanomedicine (Lond.) 5(6), 985–998 (2010).
[Crossref] [PubMed]

2009 (6)

J. M. McMahon, Y. Wang, L. J. Sherry, R. P. Van Duyne, L. D. Marks, S. K. Gray, and G. C. Schatz, “Correlating the structure, optical spectra, and electrodynamics of single silver nanocubes,” J. Phys. Chem. C 113(7), 2731–2735 (2009).
[Crossref]

J. Smajic, C. Hafner, L. Raguin, K. Tavzarashvili, and M. Mishrikey, “Comparison of numerical methods for the analysis of plasmonic structures,” J. Comput. Theor. Nanosci. 6(3), 763–774 (2009).
[Crossref]

J. Hoffmann, C. Hafner, P. Leidenberger, J. Hesselbarth, and S. Burger, “Comparison of electromagnetic field solvers for the 3D analysis of plasmonic nano antennas,” Proc. SPIE 7390, 73900J (2009).
[Crossref]

W. L. Barnes, “Comparing experiment and theory in plasmonics,” J. Opt. A, Pure Appl. Opt. 11(11), 114002 (2009).
[Crossref]

C. G. Khoury, S. J. Norton, and T. Vo-Dinh, “Plasmonics of 3-D nanoshell dimers using multipole expansion and finite element method,” ACS Nano 3(9), 2776–2788 (2009).
[Crossref] [PubMed]

W. A. Challener, C. Peng, A. V. Itagi, D. Karns, W. Peng, Y. Peng, X. Yang, X. Zhu, N. J. Gokemeijer, Y.-T. Hsia, G. Ju, R. E. Rottmayer, M. A. Seigler, and E. C. Gage, “Heat-assisted magnetic recording by a near-field transducer with efficient optical energy transfer,” Nat. Photonics 3(4), 220–224 (2009).
[Crossref]

2008 (2)

V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. García de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37(9), 1792–1805 (2008).
[Crossref] [PubMed]

Y. Zhang, Y. Chen, P. Westerhoff, K. Hristovski, and J. C. Crittenden, “Stability of commercial metal oxide nanoparticles in water,” Water Res. 42(8–9), 2204–2212 (2008).

2007 (1)

2006 (2)

X. Huang, I. H. El-Sayed, W. Qian, and M. A. El-Sayed, “Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods,” J. Am. Chem. Soc. 128(6), 2115–2120 (2006).
[Crossref] [PubMed]

C. W. Trowbridge and J. K. Sykulski, “Some key developments in computational electromagnetics and their attribution,” IEEE Trans. Magn. 42(4), 503–508 (2006).
[Crossref]

2005 (2)

T. Ishi, J. Fujikata, K. Makita, T. Baba, and K. Ohashi, “Si nano-photodiode with a surface plasmon antenna,” Jpn. J. Appl. Phys. 44(12), 364–366 (2005).

S. Chakraborty, B. Sahoo, I. Teraoka, and R. A. Gross, “Solution properties of starch nanoparticles in water and DMSO as studied by dynamic light scattering,” Carbohydr. Polym. 60(4), 475–481 (2005).
[Crossref]

2001 (1)

J. L. Young and R. O. Nelson, “A summary and systematic analysis of FDTD algorithms for linearly dispersive media,” IEEE Antennas Propag. Mag. 43(1), 61–126 (2001).
[Crossref]

1993 (1)

R. Coifman, V. Rokhlin, and S. Wandzura, “The fast multipole method for the wave equation: a pedestrian prescription,” IEEE Antennas Propag. Mag. 35(3), 7–12 (1993).
[Crossref]

1974 (1)

I. Holland, “Fundamentals of the finite element method,” Comput. Struc. 4(1), 3–15 (1974).
[Crossref]

1973 (1)

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. 6(12), 4370–4379 (1972).
[Crossref]

1966 (2)

A. M. Winslow, “Numerical calculation of static magnetic fields in an irregular triangle mesh,” J. Comput. Phys. 1, 149 (1966).
[Crossref]

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[Crossref]

1965 (1)

Alpay, D.

D. Alpay, L. Peng, and L. D. Marks, “Are nanoparticle corners round?” J. Phys. Chem. C 119(36), 21018–21023 (2015).
[Crossref]

Aslan, K.

Baba, T.

T. Ishi, J. Fujikata, K. Makita, T. Baba, and K. Ohashi, “Si nano-photodiode with a surface plasmon antenna,” Jpn. J. Appl. Phys. 44(12), 364–366 (2005).

Barnes, W. L.

J. Parsons, C. P. Burrows, J. R. Sambles, and W. L. Barnes, “A comparison of techniques used to simulate the scattering of electromagnetic radiation by metallic nanostructures,” J. Mod. Opt. 57(5), 356–365 (2010).
[Crossref]

W. L. Barnes, “Comparing experiment and theory in plasmonics,” J. Opt. A, Pure Appl. Opt. 11(11), 114002 (2009).
[Crossref]

Baumberg, J. J.

X. Zheng, V. K. Valev, N. Verellen, V. Volskiy, L. O. Herrmann, P. Van Dorpe, J. J. Baumberg, G. A. E. Vandenbosch, and V. V. Moshchalkov, “Implementation of the natural mode analysis for nanotopologies using a V-MoM algorithm,” IEEE Photonics J. 6(4), 1–13 (2014).
[Crossref]

Berini, P.

Brant, J.

J. Labille and J. Brant, “Stability of nanoparticles in water,” Nanomedicine (Lond.) 5(6), 985–998 (2010).
[Crossref] [PubMed]

Burger, S.

J. Hoffmann, C. Hafner, P. Leidenberger, J. Hesselbarth, and S. Burger, “Comparison of electromagnetic field solvers for the 3D analysis of plasmonic nano antennas,” Proc. SPIE 7390, 73900J (2009).
[Crossref]

Burrows, C. P.

J. Parsons, C. P. Burrows, J. R. Sambles, and W. L. Barnes, “A comparison of techniques used to simulate the scattering of electromagnetic radiation by metallic nanostructures,” J. Mod. Opt. 57(5), 356–365 (2010).
[Crossref]

Chakraborty, S.

S. Chakraborty, B. Sahoo, I. Teraoka, and R. A. Gross, “Solution properties of starch nanoparticles in water and DMSO as studied by dynamic light scattering,” Carbohydr. Polym. 60(4), 475–481 (2005).
[Crossref]

Challener, W. A.

W. A. Challener, C. Peng, A. V. Itagi, D. Karns, W. Peng, Y. Peng, X. Yang, X. Zhu, N. J. Gokemeijer, Y.-T. Hsia, G. Ju, R. E. Rottmayer, M. A. Seigler, and E. C. Gage, “Heat-assisted magnetic recording by a near-field transducer with efficient optical energy transfer,” Nat. Photonics 3(4), 220–224 (2009).
[Crossref]

Chen, Y.

Y. Zhang, Y. Chen, P. Westerhoff, K. Hristovski, and J. C. Crittenden, “Stability of commercial metal oxide nanoparticles in water,” Water Res. 42(8–9), 2204–2212 (2008).

Cheng, J.

Chowdhury, M. H.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. 6(12), 4370–4379 (1972).
[Crossref]

Coifman, R.

R. Coifman, V. Rokhlin, and S. Wandzura, “The fast multipole method for the wave equation: a pedestrian prescription,” IEEE Antennas Propag. Mag. 35(3), 7–12 (1993).
[Crossref]

Costa, K.

K. Costa and V. Dmitriev, “Simple and efficient computational method to analyze cylindrical plasmonic nanoantennas,” Int. J. Antennas Propag. 2014, 675036 (2014).
[Crossref]

Crittenden, J. C.

Y. Zhang, Y. Chen, P. Westerhoff, K. Hristovski, and J. C. Crittenden, “Stability of commercial metal oxide nanoparticles in water,” Water Res. 42(8–9), 2204–2212 (2008).

De Angelis, F.

Di Fabrizio, E.

Di Martino, G.

D. Vercruysse, X. Zheng, Y. Sonnefraud, N. Verellen, G. Di Martino, L. Lagae, G. A. E. Vandenbosch, V. V. Moshchalkov, S. A. Maier, and P. Van Dorpe, “Directional fluorescence emission by individual V-antennas explained by mode expansion,” ACS Nano 8(8), 8232–8241 (2014).
[Crossref] [PubMed]

Dmitriev, V.

K. Costa and V. Dmitriev, “Simple and efficient computational method to analyze cylindrical plasmonic nanoantennas,” Int. J. Antennas Propag. 2014, 675036 (2014).
[Crossref]

Donev, E. U.

V. L. Y. Loke, G. M. Huda, E. U. Donev, V. Schmidt, J. T. Hastings, M. Pinar Mengüç, and T. Wriedt, “Comparison between discrete dipole approximation and other modelling methods for the plasmonic response of gold nanospheres,” Appl. Phys. B 115(2), 237–246 (2014).
[Crossref]

Du, J.-K.

J.-S. Lee, T.-L. Song, J.-K. Du, and J.-G. Yook, “Near-field to far-field transformation based on Stratton-Chu formula for EMC measurements,” in Proceedings of IEEE Conference on Antennas and Propagation (IEEE, 2013), pp. 606–607.

El-Sayed, I. H.

X. Huang, I. H. El-Sayed, W. Qian, and M. A. El-Sayed, “Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods,” J. Am. Chem. Soc. 128(6), 2115–2120 (2006).
[Crossref] [PubMed]

El-Sayed, M. A.

X. Huang, I. H. El-Sayed, W. Qian, and M. A. El-Sayed, “Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods,” J. Am. Chem. Soc. 128(6), 2115–2120 (2006).
[Crossref] [PubMed]

Everitt, H. O.

M. W. Knight, N. S. King, L. Liu, H. O. Everitt, P. Nordlander, and N. J. Halas, “Aluminum for plasmonics,” ACS Nano 8(1), 834–840 (2014).
[Crossref] [PubMed]

Farmahini-Farahani, M.

Francardi, M.

Fujikata, J.

T. Ishi, J. Fujikata, K. Makita, T. Baba, and K. Ohashi, “Si nano-photodiode with a surface plasmon antenna,” Jpn. J. Appl. Phys. 44(12), 364–366 (2005).

Funston, A. M.

V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. García de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37(9), 1792–1805 (2008).
[Crossref] [PubMed]

Gage, E. C.

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[Crossref]

Vaccari, A.

Valev, V. K.

X. Zheng, V. K. Valev, N. Verellen, V. Volskiy, L. O. Herrmann, P. Van Dorpe, J. J. Baumberg, G. A. E. Vandenbosch, and V. V. Moshchalkov, “Implementation of the natural mode analysis for nanotopologies using a V-MoM algorithm,” IEEE Photonics J. 6(4), 1–13 (2014).
[Crossref]

Van Dorpe, P.

X. Zheng, V. K. Valev, N. Verellen, V. Volskiy, L. O. Herrmann, P. Van Dorpe, J. J. Baumberg, G. A. E. Vandenbosch, and V. V. Moshchalkov, “Implementation of the natural mode analysis for nanotopologies using a V-MoM algorithm,” IEEE Photonics J. 6(4), 1–13 (2014).
[Crossref]

D. Vercruysse, X. Zheng, Y. Sonnefraud, N. Verellen, G. Di Martino, L. Lagae, G. A. E. Vandenbosch, V. V. Moshchalkov, S. A. Maier, and P. Van Dorpe, “Directional fluorescence emission by individual V-antennas explained by mode expansion,” ACS Nano 8(8), 8232–8241 (2014).
[Crossref] [PubMed]

Van Duyne, R. P.

J. M. McMahon, Y. Wang, L. J. Sherry, R. P. Van Duyne, L. D. Marks, S. K. Gray, and G. C. Schatz, “Correlating the structure, optical spectra, and electrodynamics of single silver nanocubes,” J. Phys. Chem. C 113(7), 2731–2735 (2009).
[Crossref]

Vandenbosch, G. A. E.

X. Zheng, V. K. Valev, N. Verellen, V. Volskiy, L. O. Herrmann, P. Van Dorpe, J. J. Baumberg, G. A. E. Vandenbosch, and V. V. Moshchalkov, “Implementation of the natural mode analysis for nanotopologies using a V-MoM algorithm,” IEEE Photonics J. 6(4), 1–13 (2014).
[Crossref]

D. Vercruysse, X. Zheng, Y. Sonnefraud, N. Verellen, G. Di Martino, L. Lagae, G. A. E. Vandenbosch, V. V. Moshchalkov, S. A. Maier, and P. Van Dorpe, “Directional fluorescence emission by individual V-antennas explained by mode expansion,” ACS Nano 8(8), 8232–8241 (2014).
[Crossref] [PubMed]

M. O. Sallam, G. A. E. Vandenbosch, G. Gielen, and E. A. Soliman, “Integral equations formulation of plasmonic transmission lines,” Opt. Express 22(19), 22388–22402 (2014).
[Crossref] [PubMed]

G. A. E. Vandenbosch and Z. Ma, “Upper bounds for the solar energy harvesting efficiency of nano-antennas,” Nano Energy 1(3), 494–502 (2012).
[Crossref]

G. A. E. Vandenbosch, V. Volskiy, N. Verellen, and V. V. Moshchalkov, “On the use of the method of moments in plasmonic applications,” Radio Sci. 46(5), RS0E02 (2011).
[Crossref]

Vercruysse, D.

D. Vercruysse, X. Zheng, Y. Sonnefraud, N. Verellen, G. Di Martino, L. Lagae, G. A. E. Vandenbosch, V. V. Moshchalkov, S. A. Maier, and P. Van Dorpe, “Directional fluorescence emission by individual V-antennas explained by mode expansion,” ACS Nano 8(8), 8232–8241 (2014).
[Crossref] [PubMed]

Verellen, N.

D. Vercruysse, X. Zheng, Y. Sonnefraud, N. Verellen, G. Di Martino, L. Lagae, G. A. E. Vandenbosch, V. V. Moshchalkov, S. A. Maier, and P. Van Dorpe, “Directional fluorescence emission by individual V-antennas explained by mode expansion,” ACS Nano 8(8), 8232–8241 (2014).
[Crossref] [PubMed]

X. Zheng, V. K. Valev, N. Verellen, V. Volskiy, L. O. Herrmann, P. Van Dorpe, J. J. Baumberg, G. A. E. Vandenbosch, and V. V. Moshchalkov, “Implementation of the natural mode analysis for nanotopologies using a V-MoM algorithm,” IEEE Photonics J. 6(4), 1–13 (2014).
[Crossref]

G. A. E. Vandenbosch, V. Volskiy, N. Verellen, and V. V. Moshchalkov, “On the use of the method of moments in plasmonic applications,” Radio Sci. 46(5), RS0E02 (2011).
[Crossref]

Vo-Dinh, T.

C. G. Khoury, S. J. Norton, and T. Vo-Dinh, “Plasmonics of 3-D nanoshell dimers using multipole expansion and finite element method,” ACS Nano 3(9), 2776–2788 (2009).
[Crossref] [PubMed]

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H. Harutyunyan, G. Volpe, R. Quidant, and L. Novotny, “Enhancing the nonlinear optical response using multifrequency gold-nanowire antennas,” Phys. Rev. Lett. 108(21), 217403 (2012).
[Crossref] [PubMed]

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X. Zheng, V. K. Valev, N. Verellen, V. Volskiy, L. O. Herrmann, P. Van Dorpe, J. J. Baumberg, G. A. E. Vandenbosch, and V. V. Moshchalkov, “Implementation of the natural mode analysis for nanotopologies using a V-MoM algorithm,” IEEE Photonics J. 6(4), 1–13 (2014).
[Crossref]

G. A. E. Vandenbosch, V. Volskiy, N. Verellen, and V. V. Moshchalkov, “On the use of the method of moments in plasmonic applications,” Radio Sci. 46(5), RS0E02 (2011).
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R. Coifman, V. Rokhlin, and S. Wandzura, “The fast multipole method for the wave equation: a pedestrian prescription,” IEEE Antennas Propag. Mag. 35(3), 7–12 (1993).
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J. M. McMahon, Y. Wang, L. J. Sherry, R. P. Van Duyne, L. D. Marks, S. K. Gray, and G. C. Schatz, “Correlating the structure, optical spectra, and electrodynamics of single silver nanocubes,” J. Phys. Chem. C 113(7), 2731–2735 (2009).
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A. M. Winslow, “Numerical calculation of static magnetic fields in an irregular triangle mesh,” J. Comput. Phys. 1, 149 (1966).
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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(9), 8939–8953 (2011).
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W. A. Challener, C. Peng, A. V. Itagi, D. Karns, W. Peng, Y. Peng, X. Yang, X. Zhu, N. J. Gokemeijer, Y.-T. Hsia, G. Ju, R. E. Rottmayer, M. A. Seigler, and E. C. Gage, “Heat-assisted magnetic recording by a near-field transducer with efficient optical energy transfer,” Nat. Photonics 3(4), 220–224 (2009).
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K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
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J.-S. Lee, T.-L. Song, J.-K. Du, and J.-G. Yook, “Near-field to far-field transformation based on Stratton-Chu formula for EMC measurements,” in Proceedings of IEEE Conference on Antennas and Propagation (IEEE, 2013), pp. 606–607.

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J. L. Young and R. O. Nelson, “A summary and systematic analysis of FDTD algorithms for linearly dispersive media,” IEEE Antennas Propag. Mag. 43(1), 61–126 (2001).
[Crossref]

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Zhang, Y.

Y. Zhang, Y. Chen, P. Westerhoff, K. Hristovski, and J. C. Crittenden, “Stability of commercial metal oxide nanoparticles in water,” Water Res. 42(8–9), 2204–2212 (2008).

Zheng, X.

X. Zheng, V. K. Valev, N. Verellen, V. Volskiy, L. O. Herrmann, P. Van Dorpe, J. J. Baumberg, G. A. E. Vandenbosch, and V. V. Moshchalkov, “Implementation of the natural mode analysis for nanotopologies using a V-MoM algorithm,” IEEE Photonics J. 6(4), 1–13 (2014).
[Crossref]

D. Vercruysse, X. Zheng, Y. Sonnefraud, N. Verellen, G. Di Martino, L. Lagae, G. A. E. Vandenbosch, V. V. Moshchalkov, S. A. Maier, and P. Van Dorpe, “Directional fluorescence emission by individual V-antennas explained by mode expansion,” ACS Nano 8(8), 8232–8241 (2014).
[Crossref] [PubMed]

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W. A. Challener, C. Peng, A. V. Itagi, D. Karns, W. Peng, Y. Peng, X. Yang, X. Zhu, N. J. Gokemeijer, Y.-T. Hsia, G. Ju, R. E. Rottmayer, M. A. Seigler, and E. C. Gage, “Heat-assisted magnetic recording by a near-field transducer with efficient optical energy transfer,” Nat. Photonics 3(4), 220–224 (2009).
[Crossref]

ACS Nano (3)

D. Vercruysse, X. Zheng, Y. Sonnefraud, N. Verellen, G. Di Martino, L. Lagae, G. A. E. Vandenbosch, V. V. Moshchalkov, S. A. Maier, and P. Van Dorpe, “Directional fluorescence emission by individual V-antennas explained by mode expansion,” ACS Nano 8(8), 8232–8241 (2014).
[Crossref] [PubMed]

C. G. Khoury, S. J. Norton, and T. Vo-Dinh, “Plasmonics of 3-D nanoshell dimers using multipole expansion and finite element method,” ACS Nano 3(9), 2776–2788 (2009).
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Appl. Phys. B (1)

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IEEE Antennas Propag. Mag. (2)

R. Coifman, V. Rokhlin, and S. Wandzura, “The fast multipole method for the wave equation: a pedestrian prescription,” IEEE Antennas Propag. Mag. 35(3), 7–12 (1993).
[Crossref]

J. L. Young and R. O. Nelson, “A summary and systematic analysis of FDTD algorithms for linearly dispersive media,” IEEE Antennas Propag. Mag. 43(1), 61–126 (2001).
[Crossref]

IEEE Photonics J. (1)

X. Zheng, V. K. Valev, N. Verellen, V. Volskiy, L. O. Herrmann, P. Van Dorpe, J. J. Baumberg, G. A. E. Vandenbosch, and V. V. Moshchalkov, “Implementation of the natural mode analysis for nanotopologies using a V-MoM algorithm,” IEEE Photonics J. 6(4), 1–13 (2014).
[Crossref]

IEEE Trans. Antenn. Propag. (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[Crossref]

IEEE Trans. Magn. (1)

C. W. Trowbridge and J. K. Sykulski, “Some key developments in computational electromagnetics and their attribution,” IEEE Trans. Magn. 42(4), 503–508 (2006).
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D. Alpay, L. Peng, and L. D. Marks, “Are nanoparticle corners round?” J. Phys. Chem. C 119(36), 21018–21023 (2015).
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J. M. McMahon, Y. Wang, L. J. Sherry, R. P. Van Duyne, L. D. Marks, S. K. Gray, and G. C. Schatz, “Correlating the structure, optical spectra, and electrodynamics of single silver nanocubes,” J. Phys. Chem. C 113(7), 2731–2735 (2009).
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T. Ishi, J. Fujikata, K. Makita, T. Baba, and K. Ohashi, “Si nano-photodiode with a surface plasmon antenna,” Jpn. J. Appl. Phys. 44(12), 364–366 (2005).

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E. A. Soliman, “Wideband nanocrescent plasmonic antenna with engineered spectral response,” Microw. Opt. Technol. Lett. 55(3), 624–629 (2013).
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Nano Energy (1)

G. A. E. Vandenbosch and Z. Ma, “Upper bounds for the solar energy harvesting efficiency of nano-antennas,” Nano Energy 1(3), 494–502 (2012).
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J. Labille and J. Brant, “Stability of nanoparticles in water,” Nanomedicine (Lond.) 5(6), 985–998 (2010).
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Nat. Photonics (1)

W. A. Challener, C. Peng, A. V. Itagi, D. Karns, W. Peng, Y. Peng, X. Yang, X. Zhu, N. J. Gokemeijer, Y.-T. Hsia, G. Ju, R. E. Rottmayer, M. A. Seigler, and E. C. Gage, “Heat-assisted magnetic recording by a near-field transducer with efficient optical energy transfer,” Nat. Photonics 3(4), 220–224 (2009).
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H. Harutyunyan, G. Volpe, R. Quidant, and L. Novotny, “Enhancing the nonlinear optical response using multifrequency gold-nanowire antennas,” Phys. Rev. Lett. 108(21), 217403 (2012).
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Proc. SPIE (1)

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Radio Sci. (1)

G. A. E. Vandenbosch, V. Volskiy, N. Verellen, and V. V. Moshchalkov, “On the use of the method of moments in plasmonic applications,” Radio Sci. 46(5), RS0E02 (2011).
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M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science 332(6030), 702–704 (2011).
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Water Res. (1)

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J.-S. Lee, T.-L. Song, J.-K. Du, and J.-G. Yook, “Near-field to far-field transformation based on Stratton-Chu formula for EMC measurements,” in Proceedings of IEEE Conference on Antennas and Propagation (IEEE, 2013), pp. 606–607.

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CST, https://www.cst.com/products/cstmws .

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U. S. Inan and R. A. Marshall, Numerical Electromagnetics: The FDTD Method (Cambridge University, 2011).

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Figures (9)

Fig. 1
Fig. 1 Studied nanoparticles: from left to right a single sphere, a multilayered sphere (with a shell), a cube and a cuboid. Due to the practical incapability of nanotechnology to produce ideally sharp corners [48], the cube and cuboid edges are rounded with 5-nm-radius spheres.
Fig. 2
Fig. 2 Relative permittivity of optical materials, namely gold, silver, aluminum, copper, and silica. (a) Real and (b) imaginary part. Material data used can be found in literature [44–47].
Fig. 3
Fig. 3 Simulation setup of a spherical nanoparticle (orange). (a) CST the bounding box (blue) surrounds the structure-under-study; (b) COMSOL a multilayered spherical configuration (the surrounding medium and the PML, blue) contains the nanoparticle; (c) Lumerical – the nanoparticle is enclosed by the following boxes: the TFSF source (grey) with a pink arrow pointing in the direction of the wave propagation, the scattering cross section (yellow), the calculation domain (red).
Fig. 4
Fig. 4 Benchmarking study case: 30-nm-radius sphere in water solution. The rows are representing the optical response of the spherical particle, with constituting materials: gold, (a)–(c); silver, (d)–(f); aluminum, (g)–(i); and copper, (j)–(l). In the far right corner, polar plots with normalized circle radii show the E-plane radiation patterns at the indicated far field resonating wavelengths corresponding to the maxima of the analytical Mie scattering cross section.
Fig. 5
Fig. 5 Same as Fig. 4, but for 70-nm-radius sphere in water solution.
Fig. 6
Fig. 6 Benchmarking study case: shell in vacuum. The external 10 nm thick metallic layers, namely gold, (a)–(c); silver, (d)–(f); aluminum, (g)–(i); and copper, (j)–(l), are surrounding the 40-nm-radius silica core. Polar plots represent the H-plane radiation patterns at the indicated near field resonating wavelengths associated with the maxima of the analytical Mie E-field intensity.
Fig. 7
Fig. 7 Benchmarking study case: 50-nm-sized cube with rounded corners in water solution. Optical metals: gold, (a)–(c); silver, (d)–(f); aluminum, (g)–(i); and copper, (j)–(l), are constituting the structure-under-study. The E-plane radiation patterns are investigated at the indicated near field resonating wavelengths associated with the maxima of the reference E-field intensity calculated with COMSOL.
Fig. 8
Fig. 8 Same as Fig. 7, but for 70-nm-sized cube with rounded corners in water solution, and with E-plane radiation patterns observed at the indicated far field resonating wavelengths, corresponding to the maxima of the reference scattering cross section calculated with COMSOL.
Fig. 9
Fig. 9 Same as Fig. 8, but for cuboid with rounded corners and dimensions 80 nm, 80 nm, and 30 nm in water solution.

Tables (7)

Tables Icon

Table 1 Overview of Advantages and Disadvantages of Numerical Techniques

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Table 2 NRMSE Study of Optical Response of Single and Multilayered Nanospheres b

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Table 3 Spectrum Shifts for Single and Multilayered Nanospheres c

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Table 4 NRMSE Study of Optical Response of Nanocubes and Nanocuboids d

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Table 5 Spectrum Shifts for Nanocubes and Nanocuboids e

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Table 6 Number of Unknowns and Meshing Elements f

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Table 7 Time and Memory Requirements

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

R M S E = [ 1 N i = 1 N ( r i o i ) 2 ] 1 / 2
N R M S E = R M S E o i , max o i , min

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