Abstract

A near-to-far-field transformation algorithm for three-dimensional finite-difference time-domain is presented in this Letter. This approach is based directly on the polarization current of the scatterer, not the scattered near fields. It therefore eliminates the numerical errors originating from the spatial offset of the E and H fields, inherent in the standard near-to-far-field transformation. The proposed method is validated via direct comparisons with the analytical Lorentz–Mie solutions of plane waves scattered by large dielectric and metallic spheres with strong forward-scattering lobes.

© 2009 Optical Society of America

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References

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M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, Nat. Photonics 2, 614 (2008).
[CrossRef]

J. Lermé, C. Bonnet, M. Broyer, E. Cottancin, S. Marhaba, and M. Pellarin, Phys. Rev. B 77, 245406 (2008).
[CrossRef]

2007 (4)

T.-D. Onuta, M. Waegele, C. C. DuFort, W. L. Schaich, and B. Dragnea, Nano Lett. 7, 557 (2007).
[CrossRef] [PubMed]

D. J. Robinson and J. B. Schneider, IEEE Antennas Wireless Propag. Lett. 55, 3204 (2007).

A. Deinega and I. Valuev, Opt. Lett. 32, 3429 (2007).
[CrossRef] [PubMed]

M. A. Yurkin, A. G. Hoekstra, R. S. Brock, and J. Q. Lu, Opt. Express 15, 17902 (2007).
[CrossRef] [PubMed]

2006 (2)

2005 (3)

R. Scott Brock, X.-H. Hu, P. Yang, and J. Lu, Opt. Express 13, 5279 (2005).
[CrossRef] [PubMed]

C.-C. Oetting and L. Klinkenbusch, IEEE Trans. Antennas Propag. 53, 2054 (2005).
[CrossRef]

X. Li, A. Taflove, and V. Backman, IEEE Antennas Wireless Propag. Lett. 4, 35 (2005).
[CrossRef]

2004 (1)

2003 (1)

2000 (1)

1999 (1)

1996 (1)

1983 (1)

A. Taflove and K. R. Umashankar, IEEE Trans. Electromagn. Compat. 25, 433 (1983).
[CrossRef]

1982 (1)

K. R. Umashankar and A. Taflove, IEEE Trans. Electromagn. Compat. 24, 397 (1982).
[CrossRef]

Albin, S.

Backman, V.

X. Li, A. Taflove, and V. Backman, IEEE Antennas Wireless Propag. Lett. 4, 35 (2005).
[CrossRef]

Bermel, P.

Bonnet, C.

J. Lermé, C. Bonnet, M. Broyer, E. Cottancin, S. Marhaba, and M. Pellarin, Phys. Rev. B 77, 245406 (2008).
[CrossRef]

Brock, R. S.

Broyer, M.

J. Lermé, C. Bonnet, M. Broyer, E. Cottancin, S. Marhaba, and M. Pellarin, Phys. Rev. B 77, 245406 (2008).
[CrossRef]

Burr, G. W.

Busch, K.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, Nat. Photonics 2, 614 (2008).
[CrossRef]

Cottancin, E.

J. Lermé, C. Bonnet, M. Broyer, E. Cottancin, S. Marhaba, and M. Pellarin, Phys. Rev. B 77, 245406 (2008).
[CrossRef]

Deinega, A.

Dragnea, B.

T.-D. Onuta, M. Waegele, C. C. DuFort, W. L. Schaich, and B. Dragnea, Nano Lett. 7, 557 (2007).
[CrossRef] [PubMed]

Drezek, R.

DuFort, C. C.

T.-D. Onuta, M. Waegele, C. C. DuFort, W. L. Schaich, and B. Dragnea, Nano Lett. 7, 557 (2007).
[CrossRef] [PubMed]

Dunn, A.

Farjadpour, A.

Feth, N.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, Nat. Photonics 2, 614 (2008).
[CrossRef]

Fu, Q.

Guo, S.

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the finite-difference time-domain method, 3rd ed., (Artech House, 2005).

Hoekstra, A. G.

Hu, X.-H.

Husnik, M.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, Nat. Photonics 2, 614 (2008).
[CrossRef]

Ibanescu, M.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed., (John Wiley & Sons, 1975).

Joannopoulos, J. D.

Johnson, S. G.

Kattawar, G. W.

Kim, S.-H.

S.-H. Kim, S.-K. Kim, and Y.-H. Lee, Phys. Rev. B 73, 235117 (2006).
[CrossRef]

Kim, S.-K.

S.-H. Kim, S.-K. Kim, and Y.-H. Lee, Phys. Rev. B 73, 235117 (2006).
[CrossRef]

Klein, M. W.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, Nat. Photonics 2, 614 (2008).
[CrossRef]

Klinkenbusch, L.

C.-C. Oetting and L. Klinkenbusch, IEEE Trans. Antennas Propag. 53, 2054 (2005).
[CrossRef]

König, M.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, Nat. Photonics 2, 614 (2008).
[CrossRef]

Lee, Y. K.

Lee, Y.-H.

S.-H. Kim, S.-K. Kim, and Y.-H. Lee, Phys. Rev. B 73, 235117 (2006).
[CrossRef]

Lermé, J.

J. Lermé, C. Bonnet, M. Broyer, E. Cottancin, S. Marhaba, and M. Pellarin, Phys. Rev. B 77, 245406 (2008).
[CrossRef]

Li, X.

X. Li, A. Taflove, and V. Backman, IEEE Antennas Wireless Propag. Lett. 4, 35 (2005).
[CrossRef]

Linden, S.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, Nat. Photonics 2, 614 (2008).
[CrossRef]

Liou, K. N.

Lu, J.

Lu, J. Q.

Marhaba, S.

J. Lermé, C. Bonnet, M. Broyer, E. Cottancin, S. Marhaba, and M. Pellarin, Phys. Rev. B 77, 245406 (2008).
[CrossRef]

Niegemann, J.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, Nat. Photonics 2, 614 (2008).
[CrossRef]

Oetting, C.-C.

C.-C. Oetting and L. Klinkenbusch, IEEE Trans. Antennas Propag. 53, 2054 (2005).
[CrossRef]

Onuta, T.-D.

T.-D. Onuta, M. Waegele, C. C. DuFort, W. L. Schaich, and B. Dragnea, Nano Lett. 7, 557 (2007).
[CrossRef] [PubMed]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids, (Academic, 1985).

Pellarin, M.

J. Lermé, C. Bonnet, M. Broyer, E. Cottancin, S. Marhaba, and M. Pellarin, Phys. Rev. B 77, 245406 (2008).
[CrossRef]

Richards-Kortum, R.

Robinson, D. J.

D. J. Robinson and J. B. Schneider, IEEE Antennas Wireless Propag. Lett. 55, 3204 (2007).

Rodriguez, A.

Roundy, D.

Schaich, W. L.

T.-D. Onuta, M. Waegele, C. C. DuFort, W. L. Schaich, and B. Dragnea, Nano Lett. 7, 557 (2007).
[CrossRef] [PubMed]

Schneider, J. B.

D. J. Robinson and J. B. Schneider, IEEE Antennas Wireless Propag. Lett. 55, 3204 (2007).

Scott Brock, R.

Sun, W.

Taflove, A.

X. Li, A. Taflove, and V. Backman, IEEE Antennas Wireless Propag. Lett. 4, 35 (2005).
[CrossRef]

A. Taflove and K. R. Umashankar, IEEE Trans. Electromagn. Compat. 25, 433 (1983).
[CrossRef]

K. R. Umashankar and A. Taflove, IEEE Trans. Electromagn. Compat. 24, 397 (1982).
[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: the finite-difference time-domain method, 3rd ed., (Artech House, 2005).

Umashankar, K. R.

A. Taflove and K. R. Umashankar, IEEE Trans. Electromagn. Compat. 25, 433 (1983).
[CrossRef]

K. R. Umashankar and A. Taflove, IEEE Trans. Electromagn. Compat. 24, 397 (1982).
[CrossRef]

Valuev, I.

Waegele, M.

T.-D. Onuta, M. Waegele, C. C. DuFort, W. L. Schaich, and B. Dragnea, Nano Lett. 7, 557 (2007).
[CrossRef] [PubMed]

Wegener, M.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, Nat. Photonics 2, 614 (2008).
[CrossRef]

Yang, P.

Yurkin, M. A.

Zhai, P. W.

Appl. Opt. (3)

IEEE Antennas Wireless Propag. Lett. (2)

X. Li, A. Taflove, and V. Backman, IEEE Antennas Wireless Propag. Lett. 4, 35 (2005).
[CrossRef]

D. J. Robinson and J. B. Schneider, IEEE Antennas Wireless Propag. Lett. 55, 3204 (2007).

IEEE Trans. Antennas Propag. (1)

C.-C. Oetting and L. Klinkenbusch, IEEE Trans. Antennas Propag. 53, 2054 (2005).
[CrossRef]

IEEE Trans. Electromagn. Compat. (2)

K. R. Umashankar and A. Taflove, IEEE Trans. Electromagn. Compat. 24, 397 (1982).
[CrossRef]

A. Taflove and K. R. Umashankar, IEEE Trans. Electromagn. Compat. 25, 433 (1983).
[CrossRef]

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

Nano Lett. (1)

T.-D. Onuta, M. Waegele, C. C. DuFort, W. L. Schaich, and B. Dragnea, Nano Lett. 7, 557 (2007).
[CrossRef] [PubMed]

Nat. Photonics (1)

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, Nat. Photonics 2, 614 (2008).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. B (2)

J. Lermé, C. Bonnet, M. Broyer, E. Cottancin, S. Marhaba, and M. Pellarin, Phys. Rev. B 77, 245406 (2008).
[CrossRef]

S.-H. Kim, S.-K. Kim, and Y.-H. Lee, Phys. Rev. B 73, 235117 (2006).
[CrossRef]

Other (3)

J. D. Jackson, Classical Electrodynamics, 2nd ed., (John Wiley & Sons, 1975).

A. Taflove and S. C. Hagness, Computational Electrodynamics: the finite-difference time-domain method, 3rd ed., (Artech House, 2005).

E. D. Palik, Handbook of Optical Constants of Solids, (Academic, 1985).

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Figures (2)

Fig. 1
Fig. 1

Forward- and backward-scattering magnitudes of 1 μ m and 3 μ m diameter dielectric spheres with ε r = 1.21 . Both numerical FDTD solution and rigorous Lorentz–Mie solution are presented. The cell size employed in FDTD simulation is 25 nm . The corresponding S-NTFF results can be found from Fig. 1 of [15].

Fig. 2
Fig. 2

Far-field-scattering spectra of 1 μ m diameter gold sphere. Both the numerical FDTD solution and the rigorous Lorentz–Mie solution are presented. The cell size employed in FDTD simulation is 10 nm .

Equations (10)

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B = 0 , × E = B t ,
D = 0 , × H = D t .
2 A 1 c 2 2 A t 2 = μ 0 J ( t ) ,
2 A + k 2 A = μ 0 J ( ω ) ,
A ( r ) A ( 0 ) ( r ) = μ 0 4 π v J ( r ) e i k r r r r d r .
r r r n r ,
lim r A ( r ) μ 0 e i k r 4 π r v J ( r ) e i k n r d r μ 0 e i k r 4 π r p .
B = i k μ 0 4 π r e i k r n × p , E = c B × n .
d P d Ω = 1 2 Re [ r 2 n E × H * ] = k 2 η 0 32 π 2 ( n × p ) × n 2 ,
ψ ( r ) = 1 4 π S e i k R R [ ψ + i k ( 1 + i k R ) R R ψ ] d s ,

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