Abstract

Four widely used electromagnetic field solvers are applied to the problem of scattering by a spherical or spheroidal silver nanoparticle in glass. The solvers are tested in a frequency range where the imaginary part of the scatterer refractive index is relatively large. The scattering efficiencies and near-field results obtained by the different methods are compared to each other, as well as to recent experiments on laser-induced shape transformation of silver nanoparticles in glass.

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References

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  1. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys.-Leipzig 330, 377–445 (1908).
    [CrossRef]
  2. A. Taflove and S. C. Hagness, Computational Electrodynamics, Third Edition. (Artech House 2005).
  3. J. Niegemann, M. Konig, K. Stannigel, and K. Busch, “Higher order time-domain methods for the analysis of nano-photonic systems,” Photon. Nanostructures 7(1), 2–11 (2009).
    [CrossRef]
  4. P. Monk, Finite Element Method for Maxwell’s Equations, (Oxford, 2006).
  5. A. C. Cangellaris and D. B. Wright, “Analysis of the numerical error caused by stair-stepped approximation of a conduction boundary in FDTD simulations of electromagnetic phenomena,” IEEE Trans. Antenn. Propag. 39(10), 1518–1525 (1991).
    [CrossRef]
  6. D. W. Lynch and W. R. Hunter, “Comments on the Optical Constants of Metals and an Introduction to the Data for Several Metals,” in Handbook of Optical Constants of Solids, vol. 1, E. D. Palik, ed (Academic, San Diego, 1985).
  7. A. Vial and T. Laroche, “Description of dispersion properties of metals by means of the critical points model and application to the study of resonant structures using the FDTD method,” J. Phys. D Appl. Phys. 40(22), 7152–7158 (2007).
    [CrossRef]
  8. A. Doicu, T. Wriedt and Yu. Eremin, Light Scattering by Systems of Particles, Null-Field Method with Discrete Sources: Theory and Programs (Springer 2006).
  9. A. Doicu and T. Wriedt, “Near-field computation using the null-field method,” J. Quant. Spectrosc. Radiat. Transf. 111(3), 466–473 (2010).
    [CrossRef]
  10. B. T. Draine and P. J. Flatau, “Discrete dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11(4), 1491–1499 (1994).
    [CrossRef]
  11. B. T. Draine and P. J. Flatau, “User Guide to the Discrete Dipole Approximation Code DDSCAT 7.1”, http://arXiv.org/abs/1002.1505v1 (2010).
  12. COMSOL Multiphysics demonstration CD-ROM can be requested at http://www.comsol.com
  13. C. Hafner and L. Bomholt, The 3D electromagnetic wave simulator (Wiley 1993).
  14. A. Stalmashonak, A. Podlipensky, G. Seifert, and H. Graener, “Intensity-driven, laser induced transformation of Ag nanospheres to anisotropic shapes,” Appl. Phys. B 94(3), 459–465 (2009).
    [CrossRef]
  15. A. Stalmashonak, G. Seifert, and H. Graener, “Spectral range extension of laser-induced dichroism in composite glass with silver nanoparticles,” J. Opt. A, Pure Appl. Opt. 11(6), 065001 (2009).
    [CrossRef]
  16. A. Stalmashonak, C. Matyssek, O. Kiriyenko, W. Hergert, H. Graener, and G. Seifert, “Preparing large-aspect-ratio prolate metal nanoparticles in glass by simultaneous femtosecond multicolor irradiation,” Opt. Lett. 35(10), 1671–1673 (2010).
    [CrossRef] [PubMed]
  17. W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19(9), 1505–1509 (1980).
    [CrossRef] [PubMed]
  18. D. Gutkowicz-Krusin and B. T. Draine, “Propagation of electromagnetic waves on a rectangular lattice of polarizable points”, http://xxx.arxiv.org/abs/astro-ph/0403082 (2004).
  19. M. A. Yurkin, “Discrete dipole simulations of light scattering by blood cells”, Dissertation (2007), ISBN 90–5776–169–6

2010 (2)

2009 (3)

A. Stalmashonak, A. Podlipensky, G. Seifert, and H. Graener, “Intensity-driven, laser induced transformation of Ag nanospheres to anisotropic shapes,” Appl. Phys. B 94(3), 459–465 (2009).
[CrossRef]

A. Stalmashonak, G. Seifert, and H. Graener, “Spectral range extension of laser-induced dichroism in composite glass with silver nanoparticles,” J. Opt. A, Pure Appl. Opt. 11(6), 065001 (2009).
[CrossRef]

J. Niegemann, M. Konig, K. Stannigel, and K. Busch, “Higher order time-domain methods for the analysis of nano-photonic systems,” Photon. Nanostructures 7(1), 2–11 (2009).
[CrossRef]

2007 (1)

A. Vial and T. Laroche, “Description of dispersion properties of metals by means of the critical points model and application to the study of resonant structures using the FDTD method,” J. Phys. D Appl. Phys. 40(22), 7152–7158 (2007).
[CrossRef]

1994 (1)

1991 (1)

A. C. Cangellaris and D. B. Wright, “Analysis of the numerical error caused by stair-stepped approximation of a conduction boundary in FDTD simulations of electromagnetic phenomena,” IEEE Trans. Antenn. Propag. 39(10), 1518–1525 (1991).
[CrossRef]

1980 (1)

1908 (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys.-Leipzig 330, 377–445 (1908).
[CrossRef]

Busch, K.

J. Niegemann, M. Konig, K. Stannigel, and K. Busch, “Higher order time-domain methods for the analysis of nano-photonic systems,” Photon. Nanostructures 7(1), 2–11 (2009).
[CrossRef]

Cangellaris, A. C.

A. C. Cangellaris and D. B. Wright, “Analysis of the numerical error caused by stair-stepped approximation of a conduction boundary in FDTD simulations of electromagnetic phenomena,” IEEE Trans. Antenn. Propag. 39(10), 1518–1525 (1991).
[CrossRef]

Doicu, A.

A. Doicu and T. Wriedt, “Near-field computation using the null-field method,” J. Quant. Spectrosc. Radiat. Transf. 111(3), 466–473 (2010).
[CrossRef]

Draine, B. T.

Flatau, P. J.

Graener, H.

A. Stalmashonak, C. Matyssek, O. Kiriyenko, W. Hergert, H. Graener, and G. Seifert, “Preparing large-aspect-ratio prolate metal nanoparticles in glass by simultaneous femtosecond multicolor irradiation,” Opt. Lett. 35(10), 1671–1673 (2010).
[CrossRef] [PubMed]

A. Stalmashonak, G. Seifert, and H. Graener, “Spectral range extension of laser-induced dichroism in composite glass with silver nanoparticles,” J. Opt. A, Pure Appl. Opt. 11(6), 065001 (2009).
[CrossRef]

A. Stalmashonak, A. Podlipensky, G. Seifert, and H. Graener, “Intensity-driven, laser induced transformation of Ag nanospheres to anisotropic shapes,” Appl. Phys. B 94(3), 459–465 (2009).
[CrossRef]

Hergert, W.

Kiriyenko, O.

Konig, M.

J. Niegemann, M. Konig, K. Stannigel, and K. Busch, “Higher order time-domain methods for the analysis of nano-photonic systems,” Photon. Nanostructures 7(1), 2–11 (2009).
[CrossRef]

Laroche, T.

A. Vial and T. Laroche, “Description of dispersion properties of metals by means of the critical points model and application to the study of resonant structures using the FDTD method,” J. Phys. D Appl. Phys. 40(22), 7152–7158 (2007).
[CrossRef]

Matyssek, C.

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys.-Leipzig 330, 377–445 (1908).
[CrossRef]

Niegemann, J.

J. Niegemann, M. Konig, K. Stannigel, and K. Busch, “Higher order time-domain methods for the analysis of nano-photonic systems,” Photon. Nanostructures 7(1), 2–11 (2009).
[CrossRef]

Podlipensky, A.

A. Stalmashonak, A. Podlipensky, G. Seifert, and H. Graener, “Intensity-driven, laser induced transformation of Ag nanospheres to anisotropic shapes,” Appl. Phys. B 94(3), 459–465 (2009).
[CrossRef]

Seifert, G.

A. Stalmashonak, C. Matyssek, O. Kiriyenko, W. Hergert, H. Graener, and G. Seifert, “Preparing large-aspect-ratio prolate metal nanoparticles in glass by simultaneous femtosecond multicolor irradiation,” Opt. Lett. 35(10), 1671–1673 (2010).
[CrossRef] [PubMed]

A. Stalmashonak, G. Seifert, and H. Graener, “Spectral range extension of laser-induced dichroism in composite glass with silver nanoparticles,” J. Opt. A, Pure Appl. Opt. 11(6), 065001 (2009).
[CrossRef]

A. Stalmashonak, A. Podlipensky, G. Seifert, and H. Graener, “Intensity-driven, laser induced transformation of Ag nanospheres to anisotropic shapes,” Appl. Phys. B 94(3), 459–465 (2009).
[CrossRef]

Stalmashonak, A.

A. Stalmashonak, C. Matyssek, O. Kiriyenko, W. Hergert, H. Graener, and G. Seifert, “Preparing large-aspect-ratio prolate metal nanoparticles in glass by simultaneous femtosecond multicolor irradiation,” Opt. Lett. 35(10), 1671–1673 (2010).
[CrossRef] [PubMed]

A. Stalmashonak, G. Seifert, and H. Graener, “Spectral range extension of laser-induced dichroism in composite glass with silver nanoparticles,” J. Opt. A, Pure Appl. Opt. 11(6), 065001 (2009).
[CrossRef]

A. Stalmashonak, A. Podlipensky, G. Seifert, and H. Graener, “Intensity-driven, laser induced transformation of Ag nanospheres to anisotropic shapes,” Appl. Phys. B 94(3), 459–465 (2009).
[CrossRef]

Stannigel, K.

J. Niegemann, M. Konig, K. Stannigel, and K. Busch, “Higher order time-domain methods for the analysis of nano-photonic systems,” Photon. Nanostructures 7(1), 2–11 (2009).
[CrossRef]

Vial, A.

A. Vial and T. Laroche, “Description of dispersion properties of metals by means of the critical points model and application to the study of resonant structures using the FDTD method,” J. Phys. D Appl. Phys. 40(22), 7152–7158 (2007).
[CrossRef]

Wiscombe, W. J.

Wriedt, T.

A. Doicu and T. Wriedt, “Near-field computation using the null-field method,” J. Quant. Spectrosc. Radiat. Transf. 111(3), 466–473 (2010).
[CrossRef]

Wright, D. B.

A. C. Cangellaris and D. B. Wright, “Analysis of the numerical error caused by stair-stepped approximation of a conduction boundary in FDTD simulations of electromagnetic phenomena,” IEEE Trans. Antenn. Propag. 39(10), 1518–1525 (1991).
[CrossRef]

Ann. Phys.-Leipzig (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys.-Leipzig 330, 377–445 (1908).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

A. Stalmashonak, A. Podlipensky, G. Seifert, and H. Graener, “Intensity-driven, laser induced transformation of Ag nanospheres to anisotropic shapes,” Appl. Phys. B 94(3), 459–465 (2009).
[CrossRef]

IEEE Trans. Antenn. Propag. (1)

A. C. Cangellaris and D. B. Wright, “Analysis of the numerical error caused by stair-stepped approximation of a conduction boundary in FDTD simulations of electromagnetic phenomena,” IEEE Trans. Antenn. Propag. 39(10), 1518–1525 (1991).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

A. Stalmashonak, G. Seifert, and H. Graener, “Spectral range extension of laser-induced dichroism in composite glass with silver nanoparticles,” J. Opt. A, Pure Appl. Opt. 11(6), 065001 (2009).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. D Appl. Phys. (1)

A. Vial and T. Laroche, “Description of dispersion properties of metals by means of the critical points model and application to the study of resonant structures using the FDTD method,” J. Phys. D Appl. Phys. 40(22), 7152–7158 (2007).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transf. (1)

A. Doicu and T. Wriedt, “Near-field computation using the null-field method,” J. Quant. Spectrosc. Radiat. Transf. 111(3), 466–473 (2010).
[CrossRef]

Opt. Lett. (1)

Photon. Nanostructures (1)

J. Niegemann, M. Konig, K. Stannigel, and K. Busch, “Higher order time-domain methods for the analysis of nano-photonic systems,” Photon. Nanostructures 7(1), 2–11 (2009).
[CrossRef]

Other (9)

P. Monk, Finite Element Method for Maxwell’s Equations, (Oxford, 2006).

A. Taflove and S. C. Hagness, Computational Electrodynamics, Third Edition. (Artech House 2005).

A. Doicu, T. Wriedt and Yu. Eremin, Light Scattering by Systems of Particles, Null-Field Method with Discrete Sources: Theory and Programs (Springer 2006).

D. W. Lynch and W. R. Hunter, “Comments on the Optical Constants of Metals and an Introduction to the Data for Several Metals,” in Handbook of Optical Constants of Solids, vol. 1, E. D. Palik, ed (Academic, San Diego, 1985).

B. T. Draine and P. J. Flatau, “User Guide to the Discrete Dipole Approximation Code DDSCAT 7.1”, http://arXiv.org/abs/1002.1505v1 (2010).

COMSOL Multiphysics demonstration CD-ROM can be requested at http://www.comsol.com

C. Hafner and L. Bomholt, The 3D electromagnetic wave simulator (Wiley 1993).

D. Gutkowicz-Krusin and B. T. Draine, “Propagation of electromagnetic waves on a rectangular lattice of polarizable points”, http://xxx.arxiv.org/abs/astro-ph/0403082 (2004).

M. A. Yurkin, “Discrete dipole simulations of light scattering by blood cells”, Dissertation (2007), ISBN 90–5776–169–6

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Figures (12)

Fig. 1
Fig. 1

(a) The refractive index of silver. (b) The test scattering problem.

Fig. 2
Fig. 2

The ε 2 near-field error, relative to the MMP 3D result, as function of displacement from the spherical nanoparticle; λ0 = 410nm.

Fig. 3
Fig. 3

Scattering efficiency vs. incident wavelength for the prolate spheroidal nanoparticle.

Fig. 4
Fig. 4

The ε 2 near-field error, relative to the MMP 3D result, as function of displacement from the prolate spheroidal nanoparticle; λ0 = 318nm.

Fig. 5
Fig. 5

The ε 2 near-field error, relative to the MMP 3D result, as function of displacement from the prolate spheroidal nanoparticle; λ0 = 688nm.

Fig. 6
Fig. 6

The ε 2 near-field error, relative to the MMP 3D result, as function of displacement from the prolate spheroidal nanoparticle; λ0 = 318nm.

Fig. 7
Fig. 7

The ε 2 near-field error, relative to the MMP 3D result,as function of displacement from the prolate spheroidal nanoparticle; λ0 = 688nm.

Fig. 8
Fig. 8

λ0 = 318nm, xz-plane. (a) NFM-DS, (b) DDSCAT, (c) COMSOL, (d) MMP 3D.

Fig. 9
Fig. 9

λ0 = 318nm, yz-plane. (a) NFM-DS, (b) DDSCAT, (c) COMSOL, (d) MMP 3D.

Fig. 10
Fig. 10

λ0 = 688nm, xz-plane. (a) NFM-DS, (b) DDSCAT, (c) COMSOL, (d) MMP 3D.

Fig. 11
Fig. 11

λ0 = 688nm, yz-plane. (a) NFM-DS, (b) DDSCAT, (c) COMSOL, (d) MMP 3D.

Fig. 12
Fig. 12

Surface average of the normal field component enhancement as a function of the aspect ratio for wavelengths around those used in the experiment. Enhancements are normalized to the values for a sphere at the respective wavelengths.

Equations (10)

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E i ν = 1 N μ = ν ν ( a μ ν M μ ν 1 + b μ ν N μ ν 1 ) ,     E i n t ν = 1 N μ = ν ν ( c μ ν M μ ν 1 + d μ ν N μ ν 1 ) ,    
E s ν = 1 N μ = ν ν ( e μ ν M μ ν 3 + f μ ν N μ ν 3 )
( c μ ν d μ ν ) = T i i n t ( a μ ν b μ ν ) , ( e μ ν f μ ν ) = T i n t s ( c μ ν d μ ν ) .
A μ ν = e i k r μ ν r μ ν ( k 2 ( r ^ μ ν r ^ μ ν I 3 × 3 ) + i k r μ ν 1 r μ ν 2 ( 3 r ^ μ ν r ^ μ ν I 3 × 3 ) ) ,       μ ν ,
ν = 1 N A μ ν P ν = E μ i ,       μ = 1 , , N
E s j = 1 n ν = 1 N μ = ν ν ( e μ ν ( j ) M μ ν 3 , ( j ) + f μ ν ( j ) N μ ν 3 , ( j ) ) ,       E i n t j = 1 n ν = 1 N μ = ν ν ( c μ ν ( j ) M μ ν 1 , ( j ) + d μ ν ( j ) N μ ν 1 , ( j ) )    
E ε 2 2 = ( x j , z j ) G x j 2 + z j 2 > ( ε a ) 2 | E ( x j , z j ) | 2 ,       1 < ε < 3 ,
E ε 2 2 = ( x j , z j ) G x j 2 / a 2 + z j 2 / b 2 > ε 2 | E ( x j , z j ) | 2
| E | | E M M P | ε 2 E M M P ε 2
F n = | n E | d A

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