Abstract

Staircasing of media properties is one of the intrinsic problems of the finite-difference time-domain method, which reduces its accuracy. There are different approaches for solving this problem, and the most successful of them are based on correct approximation of inverse permittivity tensor ε̂1 at the material interface. We report an application of this tensor method for conductive and dispersive media. For validation, comparisons with analytical solutions and various other subpixel smoothing methods are performed for the Mie scattering from a small sphere.

© 2007 Optical Society of America

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References

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2007

I. Valuev, A. Deinega, A. Knizhnik, and B. Potapkin, Lect. Notes Comput. Sci. 4707, 213 (2007).
[CrossRef]

2006

2005

2003

J. Nadobny, D. Sullivan, W. Wlodarczyk, P. Deuflhard, and P. Wust, Lect. Notes Math. 51, 1760 (2003).

1999

J.-Y. Lee and N.-H. Myung, Microwave Opt. Technol. Lett. 23, 245 (1999).
[CrossRef]

S. Dey and R. Mittra, IEEE Trans. Microwave Theory Tech. 47, 1737 (1999).
[CrossRef]

1997

N. Kaneda, B. Houshmand, and T. Itoh, IEEE Trans. Microwave Theory Tech. 45, 1645 (1997).
[CrossRef]

M. Okoniewski, M. Mrozowski, and M. A. Stuchly, IEEE Microw. Guid. Wave Lett. 7, 123 (1997).
[CrossRef]

1992

T. G. Jurgens, A. Taflove, K. Umashankar, and T. G. Moore, IEEE Trans. Antennas Propag. 40, 357 (1992).
[CrossRef]

1991

S. S. Zivanovic, K. S. Yee, and K. K. Mei, IEEE Trans. Microwave Theory Tech. 38, 471 (1991).
[CrossRef]

1990

V. Shankar, A. Mohammadian, and W. F. Hall, Electromagnetics 10, 127 (1990).
[CrossRef]

1983

Appl. Opt.

Electromagnetics

V. Shankar, A. Mohammadian, and W. F. Hall, Electromagnetics 10, 127 (1990).
[CrossRef]

IEEE Microw. Guid. Wave Lett.

M. Okoniewski, M. Mrozowski, and M. A. Stuchly, IEEE Microw. Guid. Wave Lett. 7, 123 (1997).
[CrossRef]

IEEE Trans. Antennas Propag.

T. G. Jurgens, A. Taflove, K. Umashankar, and T. G. Moore, IEEE Trans. Antennas Propag. 40, 357 (1992).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

S. S. Zivanovic, K. S. Yee, and K. K. Mei, IEEE Trans. Microwave Theory Tech. 38, 471 (1991).
[CrossRef]

S. Dey and R. Mittra, IEEE Trans. Microwave Theory Tech. 47, 1737 (1999).
[CrossRef]

N. Kaneda, B. Houshmand, and T. Itoh, IEEE Trans. Microwave Theory Tech. 45, 1645 (1997).
[CrossRef]

Lect. Notes Comput. Sci.

I. Valuev, A. Deinega, A. Knizhnik, and B. Potapkin, Lect. Notes Comput. Sci. 4707, 213 (2007).
[CrossRef]

Lect. Notes Math.

J. Nadobny, D. Sullivan, W. Wlodarczyk, P. Deuflhard, and P. Wust, Lect. Notes Math. 51, 1760 (2003).

Microwave Opt. Technol. Lett.

J.-Y. Lee and N.-H. Myung, Microwave Opt. Technol. Lett. 23, 245 (1999).
[CrossRef]

Opt. Express

Opt. Lett.

Other

A. Taflove and S. H. Hagness, Computational Electrodynamics: the Finite Difference Time-Domain Method (Artech House, 2000).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983).

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Figures (5)

Fig. 1
Fig. 1

Schematic view of the simulation geometry.

Fig. 2
Fig. 2

Efficiency factor for scattering Q s c a versus radius for a conductive sphere with ϵ = 4 ϵ 0 and σ = 2 at λ = 25 . The length is measured in the mesh space steps.

Fig. 3
Fig. 3

Error relative to the Mie theory for Q s c a and the setup of the Fig. 2 as a function of the sphere radius R.

Fig. 4
Fig. 4

Efficiency factor for scattering Q s c a versus radius for lead sphere, λ = 1.5 μ m .

Fig. 5
Fig. 5

S 11 scattering matrix element of lead r = 250 nm sphere as a function of the scattering angle, λ = 1.5 μ m .

Equations (6)

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ϵ ̂ 1 = P ϵ 1 + ( 1 P ) ϵ 1 ,
i ω E = P [ f 1 ϵ 1 ( ω ) + 1 f 1 ϵ 2 ( ω ) ] ( × H ) + 1 P f 1 ϵ 1 ( ω ) + ( 1 f 1 ) ϵ 2 ( ω ) ( × H ) ,
E = E 1 + E 2 + E 3 ,
i ω ϵ 1 ( ω ) E k 1 = f 1 j = 1 3 P k j ( × H ) j ,
i ω ϵ 2 ( ω ) E k 2 = ( 1 f 1 ) j = 1 3 P k j ( × H ) j ,
i ω [ f 1 ϵ 1 ( w ) + ( 1 f 1 ) ϵ 2 ( w ) ] E k 3 = ( × H ) k j = 1 3 P k j ( × H ) j .

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