Abstract

The time-average energy density of the optical near-field generated around a metallic sphere is computed using the finite-difference time-domain method. To check the accuracy, the numerical results are compared with the rigorous solutions by Mie theory. The Lorentz-Drude model, which is coupled with Maxwell’s equation via motion equations of an electron, is applied to simulate the dispersion relation of metallic materials. The distributions of the optical near-filed generated around a metallic hemisphere and a metallic spheroid are also computed, and strong optical near-fields are obtained at the rim of them.

© 2007 Optical Society of America

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Errata

Takashi Yamaguchi and Takashi Hinata, "Optical near-field analysis of spherical metals: Application of the FDTD method combined with the ADE method: errata," Opt. Express 16, 4375-4375 (2008)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-16-6-4375

References

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  1. M Ohtsu and K. Kobayashi, Optical Near Field (Springer-Verlag, Berlin, 2004).
  2. M. Ohtsu, ed., Progress in Nano-Electro-Optics III-Industrial Applications and Dynamics of the Nano-Optical System (Springer, 2004).
    [PubMed]
  3. T. Matsumoto, T. Shimano, H. Saga, H. Sukeda, and M. Kiguchi, "Highly efficient probe with a wedge-shaped metallic plate for high density near-field optical recording," J. Appl. Phys. 95, 3901-3906 (2004).
    [CrossRef]
  4. T. Matsumoto, "Near-Field Optical-Head Technology for High-Density, Near-Field Optical Recording," in Progress in Nano-Electro-Optics III, M. Ohtsu, ed., (Springer, 2004).
  5. T. Uno, Finite Difference Time Domain Method for Electromagnetic Field and Antennas, in Japanese (Corona Publishing Co., Ltd, 1998).
  6. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Third Edition (Artech House, 2005).
  7. W. A. Challener, I. K. Sendur, and C. Peng, "Scattered field formulation of finite difference time domain for a focused light beam in dense media with lossy materials," Opt. Express 11, 3160-3170 (2003).
    [CrossRef] [PubMed]
  8. R. J. Zhu, J. Wang, and G. F. Jin, "Mie scattering calculation by FDTD employing a modified Debye model for Gold material," Optik 116, 419-422 (2005).
    [CrossRef]
  9. H. Tamaru and K. Miyano, "Localized Surface Plasmon Resonances of Metal Nanoparticles: Numerical Simulations and Their Experimental Verification," Kogaku Japanese Journal of Optics 33, 165-170 (2004).
  10. A. D. Rakiæ, A. B. Djurišiæ, J. M. Elazar, and M. L. Majewski, "Optical Properties of Metallic Films for Vertical-Cavity Optoelectronic devices," Appl. Opt. 37, 5271-5283 (1998).
    [CrossRef]
  11. T. Kashiwa and I. Fukai, "A treatment by FDTD method of dispersive characteristics associated with electronic polarization," Microwave Optics Tech. Lett. 3, 203-205 (1990).
    [CrossRef]
  12. T. Yamaguchi, T. Yamasaki, and T. Hinata, "FDTD Analysis of Optical Near-field Around a Metallic Sphere," in The Papers of Technical Meeting on Electromagnetic Theory (IEE, Japan, 2006), pp. 143-148.
  13. J. A. Roden and S. D. Gedney, "Convolutional PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media," Microwave Optical Tech. Lett. 27, 334-339 (2000).
    [CrossRef]
  14. J. De Moerloose and M. A. Stuchly, "Behavior of Berenger’s ABC for evanescent waves," IEEE Microwave Guided Wave Lett. 5, 344-346 (1995).
    [CrossRef]
  15. J. P. Bérenger, "Improved PML for the FDTD Solution of Wave-Structure Interaction Problems," IEEE Trans. Antennas Propag. 45, 466-473 (1997).
    [CrossRef]
  16. J. P. Bérenger, "Evanescent Waves in PML’s: Origin of the Numerical Reflection in Wave-Structure Interaction Problems," IEEE Trans. Antennas Propag. 47, 1497-1503 (1999).
    [CrossRef]
  17. T. Yamaguchi, "Numerical Analysis of Pulse Reflection from Anisotropic Dielectric Layer," Special Issue of Nihon Univ. CST 2006 Annual Conf. Short Note 1, 113-116 (2007).
  18. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).
  19. T. Hosono, The Foundation of Electromagnetic Wave Theory, in Japanese (Shoko-do, 1973).
  20. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander. Jr., and C. A. Ward, "Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared," Appl. Opt. 22, 1099-1119 (1983).
    [CrossRef] [PubMed]
  21. J. B. Judkins and R. W. Ziolkowski, "Finite-difference time-domain modeling of nonperfectly conducting metallic thin-film gratings," J. Opt. Soc. Am. A 12, 1974-1983 (1995).
    [CrossRef]
  22. P. B. Johnson and R.W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  23. M. Bordovsky, P. Catrysse, S. Dods, M. Freitas, J. Klein, L. Kotacka, V. Tzolov, I. Uzunov, and J. Zhang, "Waveguide design, modeling, and optimization - from photonic nano-devices to integrated photonic circuits," Proc. SPIE 5355, 65-80 (2004).
    [CrossRef]

2007

T. Yamaguchi, "Numerical Analysis of Pulse Reflection from Anisotropic Dielectric Layer," Special Issue of Nihon Univ. CST 2006 Annual Conf. Short Note 1, 113-116 (2007).

2005

R. J. Zhu, J. Wang, and G. F. Jin, "Mie scattering calculation by FDTD employing a modified Debye model for Gold material," Optik 116, 419-422 (2005).
[CrossRef]

2004

H. Tamaru and K. Miyano, "Localized Surface Plasmon Resonances of Metal Nanoparticles: Numerical Simulations and Their Experimental Verification," Kogaku Japanese Journal of Optics 33, 165-170 (2004).

T. Matsumoto, T. Shimano, H. Saga, H. Sukeda, and M. Kiguchi, "Highly efficient probe with a wedge-shaped metallic plate for high density near-field optical recording," J. Appl. Phys. 95, 3901-3906 (2004).
[CrossRef]

M. Bordovsky, P. Catrysse, S. Dods, M. Freitas, J. Klein, L. Kotacka, V. Tzolov, I. Uzunov, and J. Zhang, "Waveguide design, modeling, and optimization - from photonic nano-devices to integrated photonic circuits," Proc. SPIE 5355, 65-80 (2004).
[CrossRef]

2003

2000

J. A. Roden and S. D. Gedney, "Convolutional PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media," Microwave Optical Tech. Lett. 27, 334-339 (2000).
[CrossRef]

1999

J. P. Bérenger, "Evanescent Waves in PML’s: Origin of the Numerical Reflection in Wave-Structure Interaction Problems," IEEE Trans. Antennas Propag. 47, 1497-1503 (1999).
[CrossRef]

1998

1997

J. P. Bérenger, "Improved PML for the FDTD Solution of Wave-Structure Interaction Problems," IEEE Trans. Antennas Propag. 45, 466-473 (1997).
[CrossRef]

1995

J. B. Judkins and R. W. Ziolkowski, "Finite-difference time-domain modeling of nonperfectly conducting metallic thin-film gratings," J. Opt. Soc. Am. A 12, 1974-1983 (1995).
[CrossRef]

J. De Moerloose and M. A. Stuchly, "Behavior of Berenger’s ABC for evanescent waves," IEEE Microwave Guided Wave Lett. 5, 344-346 (1995).
[CrossRef]

1990

T. Kashiwa and I. Fukai, "A treatment by FDTD method of dispersive characteristics associated with electronic polarization," Microwave Optics Tech. Lett. 3, 203-205 (1990).
[CrossRef]

1983

1972

P. B. Johnson and R.W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Appl. Opt.

IEEE Microwave Guided Wave Lett.

J. De Moerloose and M. A. Stuchly, "Behavior of Berenger’s ABC for evanescent waves," IEEE Microwave Guided Wave Lett. 5, 344-346 (1995).
[CrossRef]

IEEE Trans. Antennas Propag.

J. P. Bérenger, "Improved PML for the FDTD Solution of Wave-Structure Interaction Problems," IEEE Trans. Antennas Propag. 45, 466-473 (1997).
[CrossRef]

J. P. Bérenger, "Evanescent Waves in PML’s: Origin of the Numerical Reflection in Wave-Structure Interaction Problems," IEEE Trans. Antennas Propag. 47, 1497-1503 (1999).
[CrossRef]

J. Appl. Phys.

T. Matsumoto, T. Shimano, H. Saga, H. Sukeda, and M. Kiguchi, "Highly efficient probe with a wedge-shaped metallic plate for high density near-field optical recording," J. Appl. Phys. 95, 3901-3906 (2004).
[CrossRef]

J. Opt. Soc. Am. A

Kogaku Japanese Journal of Optics

H. Tamaru and K. Miyano, "Localized Surface Plasmon Resonances of Metal Nanoparticles: Numerical Simulations and Their Experimental Verification," Kogaku Japanese Journal of Optics 33, 165-170 (2004).

Microwave Optical Tech. Lett.

J. A. Roden and S. D. Gedney, "Convolutional PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media," Microwave Optical Tech. Lett. 27, 334-339 (2000).
[CrossRef]

Microwave Optics Tech. Lett.

T. Kashiwa and I. Fukai, "A treatment by FDTD method of dispersive characteristics associated with electronic polarization," Microwave Optics Tech. Lett. 3, 203-205 (1990).
[CrossRef]

Opt. Express

Optik

R. J. Zhu, J. Wang, and G. F. Jin, "Mie scattering calculation by FDTD employing a modified Debye model for Gold material," Optik 116, 419-422 (2005).
[CrossRef]

Phys. Rev. B

P. B. Johnson and R.W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Proc. SPIE

M. Bordovsky, P. Catrysse, S. Dods, M. Freitas, J. Klein, L. Kotacka, V. Tzolov, I. Uzunov, and J. Zhang, "Waveguide design, modeling, and optimization - from photonic nano-devices to integrated photonic circuits," Proc. SPIE 5355, 65-80 (2004).
[CrossRef]

Short Note

T. Yamaguchi, "Numerical Analysis of Pulse Reflection from Anisotropic Dielectric Layer," Special Issue of Nihon Univ. CST 2006 Annual Conf. Short Note 1, 113-116 (2007).

Other

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

T. Hosono, The Foundation of Electromagnetic Wave Theory, in Japanese (Shoko-do, 1973).

T. Yamaguchi, T. Yamasaki, and T. Hinata, "FDTD Analysis of Optical Near-field Around a Metallic Sphere," in The Papers of Technical Meeting on Electromagnetic Theory (IEE, Japan, 2006), pp. 143-148.

M Ohtsu and K. Kobayashi, Optical Near Field (Springer-Verlag, Berlin, 2004).

M. Ohtsu, ed., Progress in Nano-Electro-Optics III-Industrial Applications and Dynamics of the Nano-Optical System (Springer, 2004).
[PubMed]

T. Matsumoto, "Near-Field Optical-Head Technology for High-Density, Near-Field Optical Recording," in Progress in Nano-Electro-Optics III, M. Ohtsu, ed., (Springer, 2004).

T. Uno, Finite Difference Time Domain Method for Electromagnetic Field and Antennas, in Japanese (Corona Publishing Co., Ltd, 1998).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Third Edition (Artech House, 2005).

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Figures (10)

Fig. 1.
Fig. 1.

Dielectric constants for Au (Re[εr ]+jIm[εr ]).

Fig. 2.
Fig. 2.

Shapes of the spherical objects.

Fig. 3.
Fig. 3.

Energy density versus distance for the sphere.

Fig. 4.
Fig. 4.

Energy density versus wavelength for the sphere.

Fig. 5.
Fig. 5.

Energy density versus angle for the sphere.

Fig. 6.
Fig. 6.

Distribution of the energy density around a silver hemisphere.

Fig. 7.
Fig. 7.

Energy density versus wavelength for the metallic hemisphere.

Fig. 8.
Fig. 8.

Distribution of the energy density around a silver spheroid.

Fig. 9.
Fig. 9.

Energy density versus wavelength for the metallic spheroid.

Fig. 10.
Fig. 10.

Energy density versus wavelength for the gold spheroid.

Tables (1)

Tables Icon

Table 1. Dependence of FDTD results on cell size.

Equations (14)

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

E ( i ) = u x E 0 e jk 0 z j ω t ,
p 0 = 4 π ε 0 [ { ε r ( ω ) 1 } { ε r ( ω ) + 2 } ] a 3 E 0 .
Re [ ε r ( ω ) ] = 2.0 ,
ε r ( ω ) = 1 A 0 ω p 2 { ω ( ω + j ν 0 ) } + j = 1 K χ j ( ω ) ,
χ j ( ω ) = A j ω p 2 [ ( ω j 2 ω 2 ) j ω ν j ] ,
J j n + 1 = α j J j n + β j ( E n + 1 + E n ) γ j P j n ,
P j n + 1 = P j n + Δ t ( J j n + 1 + J j n ) 2 ,
{ α j = ( 1 ξ j ) { 1 Δ t ( 2 ν j + ω j 2 Δ t ) } , β j = ε 0 A j ω p 2 Δ t ( 2 ξ j ) , γ j = ω j 2 Δ t ξ j , ξ j = 1 + Δ t ( 2 ν j + ω j 2 Δ t ) ,
E n + 1 = C 1 E n + C 2 [ × H n + 1 2 1 2 j = 0 K { ( 1 + α j ) J j n γ j P j n } ] ,
H n + 1 2 = H n 1 2 Δ t μ 0 ( × E n ) ,
{ C 1 = ( 2 ε 0 Δ t j = 0 K β j ) ( 2 ε 0 + Δ t j = 0 K β j ) C 2 = Δ t ( 2 ε 0 + Δ t j = 0 K β j ) .
w N = W ¯ W ¯ 0 = [ ε 0 E 2 + μ 0 H 2 ] [ ε 0 E ( i ) 2 + μ 0 H ( i ) 2 ] ,
E x n + 1 2 = { E x i + 1 2 , j , k n + E x i 1 2 , j , k n + E x i + 1 2 , j , k n + 1 + E x i 1 2 , j , k n + 1 } 4 , H x n + 1 2 = { H x i , j + 1 2 , k + 1 2 n + 1 2 + H x i , j 1 2 , k + 1 2 n + 1 2 + H x i , j + 1 2 , k 1 2 n + 1 2 + H x i , j 1 2 , k 1 2 n + 1 2 } 4 . ]
w N 1 2 ε r ( ω ) 1 ε r ( ω ) + 2 2 ( a r ) 6 ( 3 sin 2 θ cos ϕ + 1 )

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