Abstract

In this Letter, we have shown that the subpixel smoothing technique that eliminates the staircasing error in the finite-difference time-domain method can be extended to material interface between dielectric and dispersive media by local coordinate rotation. First, we show our method is equivalent to the subpixel smoothing method for dielectric interface, then we extend it to a more general case where dispersive/dielectric interface is present. Finally, we provide a numerical example on a scattering problem to demonstrate that we were able to significantly improve the accuracy.

© 2012 Optical Society of America

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References

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  1. K. S. Yee, IEEE Trans. Antennas Propag. 14, 302 (1966).
    [CrossRef]
  2. A. Taflove and M. E. Brodwin, IEEE Trans. Microwave Theory Tech. 23, 623 (1975).
    [CrossRef]
  3. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd Ed. (Artech House, 2005).
  4. N. Kaneda, B. Houshmand, and T. Itoh, IEEE Trans. Microwave Theory Tech. 45, 1645 (1997).
    [CrossRef]
  5. S. Dey and R. Mittra, IEEE Trans. Microwave Theory Tech. 47, 1737 (1999).
    [CrossRef]
  6. A. Mohammadi, H. Nadgaran, and M. Agio, Opt. Express 13, 10367 (2005).
    [CrossRef]
  7. A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, Opt. Lett. 31, 2972 (2006).
    [CrossRef]
  8. A. F. Oskooi, C. Kottke, and S. G. Johnson, Opt. Lett. 34, 2778 (2009).
    [CrossRef]
  9. G. R. Werner and J. R. Cary, J. Comput. Phys. 226, 1085 (2007).
    [CrossRef]
  10. T. Hirono, Y. Yoshikuni, and T. Yamanaka, Appl. Opt. 49, 1080 (2010).
    [CrossRef]
  11. A. Deinega and I. Valuev, Opt. Lett. 32, 3429 (2007).
    [CrossRef]
  12. A. Deinega and S. John, Opt. Lett. 37, 112 (2012).
    [CrossRef]

2012 (1)

2010 (1)

2009 (1)

2007 (2)

G. R. Werner and J. R. Cary, J. Comput. Phys. 226, 1085 (2007).
[CrossRef]

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

2006 (1)

2005 (1)

1999 (1)

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

1997 (1)

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

1975 (1)

A. Taflove and M. E. Brodwin, IEEE Trans. Microwave Theory Tech. 23, 623 (1975).
[CrossRef]

1966 (1)

K. S. Yee, IEEE Trans. Antennas Propag. 14, 302 (1966).
[CrossRef]

Agio, M.

Bermel, P.

Brodwin, M. E.

A. Taflove and M. E. Brodwin, IEEE Trans. Microwave Theory Tech. 23, 623 (1975).
[CrossRef]

Burr, G. W.

Cary, J. R.

G. R. Werner and J. R. Cary, J. Comput. Phys. 226, 1085 (2007).
[CrossRef]

Deinega, A.

Dey, S.

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

Farjadpour, A.

Hagness, S.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd Ed. (Artech House, 2005).

Hirono, T.

Houshmand, B.

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

Ibanescu, M.

Itoh, T.

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

Joannopoulos, J. D.

John, S.

Johnson, S. G.

Kaneda, N.

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

Kottke, C.

Mittra, R.

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

Mohammadi, A.

Nadgaran, H.

Oskooi, A. F.

Rodriguez, A.

Roundy, D.

Taflove, A.

A. Taflove and M. E. Brodwin, IEEE Trans. Microwave Theory Tech. 23, 623 (1975).
[CrossRef]

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd Ed. (Artech House, 2005).

Valuev, I.

Werner, G. R.

G. R. Werner and J. R. Cary, J. Comput. Phys. 226, 1085 (2007).
[CrossRef]

Yamanaka, T.

Yee, K. S.

K. S. Yee, IEEE Trans. Antennas Propag. 14, 302 (1966).
[CrossRef]

Yoshikuni, Y.

Appl. Opt. (1)

IEEE Trans. Antennas Propag. (1)

K. S. Yee, IEEE Trans. Antennas Propag. 14, 302 (1966).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (3)

A. Taflove and M. E. Brodwin, IEEE Trans. Microwave Theory Tech. 23, 623 (1975).
[CrossRef]

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

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

J. Comput. Phys. (1)

G. R. Werner and J. R. Cary, J. Comput. Phys. 226, 1085 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Other (1)

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd Ed. (Artech House, 2005).

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Figures (3)

Fig. 1.
Fig. 1.

Electric fields near the material interface. Ex and Ey are the electric fields in Cartesian coordinates. EN and ET correspond to the electric fields perpendicular and tangential to the material interface, respectively.

Fig. 2.
Fig. 2.

Electric fields intensity along the x axis passing through the center of a cylinder (radius is 1 μm). The incident TE plane wave (wavelength 2.5 μm) propagates in x direction.

Fig. 3.
Fig. 3.

Relative error versus resolution for a cylinder illuminated by the TE plane wave.

Tables (1)

Tables Icon

Table 1. Comparison of CPU Time and Memory Usage

Equations (20)

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E=ϵ01ϵ˜1D,
(ENET)=(cosϕsinϕsinϕcosϕ)(ExEy)=R(ExEy),
(ENET)=1ϵ0(ϵ100ϵ1)(DNDT),
(ExEy)=1ϵ0R1(ϵ100ϵ1)R(DxDy).
ϵ˜1=Pϵ1+(1P)ϵ1,
(DNDT)=R(DxDy);
(ExEy)=R1(ENET).
EN=1ϵ0ϵ1DN,
ET=1ϵ0ϵ1DT.
ϵ2(ω)=ϵαωp2ω2iγωωp2.
ϵ=βϵ2(ω)+(1β)ϵ1,
ϵ=ϵ^α^ω^p2ω2iγ^ωω^p2,
DT=ϵ0ϵET=ϵ0(ϵ^ET+PT),
PT=α^ω^p2ω2iγ^ωω^p2ET.
2PTt2+γ^PTt+ω^p2PT=α^ω^p2ET.
ϵ1=β1ϵ2(ω)+(1β)1ϵ1,
1ϵ1=ϵ˘α˘ω˘p2ω2iωγ˘ω˘p2,
DN=ϵ01ϵ1EN=ϵ0(ϵ˘EN+PN),
PN=α˘ω˘p2ω2iγ˘ωω˘p2EN.
En2Ee2=i,j(|En(i,j)|2|Ee(i,j)|2|Ee(i,j)|2)2,

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