Abstract

The study of periodic structures illuminated by a normally incident plane wave is a simple task that can be numerically simulated by the finite-difference time-domain (FDTD) method. On the contrary, for off-normal incidence, a widely modified algorithm must be developed in order to bypass the frequency dependence appearing in the periodic boundary conditions. After recently implementing this FDTD algorithm for pure dielectric materials, we here extend it to the study of metallic structures where dispersion can be described by analytical models. The accuracy of our code is demonstrated through comparisons with already-published results in the case of 1D and 3D structures.

© 2009 Optical Society of America

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References

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  1. A. Taflove and S. C. Hagness, Computational Electrodynamics, the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2005).
  2. J. A. Roden, S. D. Gedney, M. P. Kesler, J. G. Maloney, and P. H. Harms, IEEE Trans. Microwave Theory Tech. 46, 420 (1998).
    [CrossRef]
  3. A. Belkhir and F. I. Baida, Phys. Rev. E 77, 056701 (2008).
    [CrossRef]
  4. I. Valuev, A. Deinega, and S. Belousov, Opt. Lett. 33, 1491 (2008).
    [CrossRef] [PubMed]
  5. R. M. Joseph, S. C. Hagness, and A. Taflove, Opt. Lett. 16, 1412 (1991).
    [CrossRef] [PubMed]
  6. A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M.-L. de la Chapelle, Phys. Rev. B 71, 085416 (2005).
    [CrossRef]
  7. T. O. Körner and W. Fichtner, Opt. Lett. 22, 1586 (1997).
    [CrossRef]
  8. 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] [PubMed]

2008

2006

2005

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M.-L. de la Chapelle, Phys. Rev. B 71, 085416 (2005).
[CrossRef]

1998

J. A. Roden, S. D. Gedney, M. P. Kesler, J. G. Maloney, and P. H. Harms, IEEE Trans. Microwave Theory Tech. 46, 420 (1998).
[CrossRef]

1997

1991

Baida, F. I.

A. Belkhir and F. I. Baida, Phys. Rev. E 77, 056701 (2008).
[CrossRef]

Barchiesi, D.

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M.-L. de la Chapelle, Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Belkhir, A.

A. Belkhir and F. I. Baida, Phys. Rev. E 77, 056701 (2008).
[CrossRef]

Belousov, S.

Bermel, P.

Burr, G. W.

de la Chapelle, M.-L.

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M.-L. de la Chapelle, Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Deinega, A.

Farjadpour, A.

Fichtner, W.

Gedney, S. D.

J. A. Roden, S. D. Gedney, M. P. Kesler, J. G. Maloney, and P. H. Harms, IEEE Trans. Microwave Theory Tech. 46, 420 (1998).
[CrossRef]

Grimault, A.-S.

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M.-L. de la Chapelle, Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Hagness, S. C.

R. M. Joseph, S. C. Hagness, and A. Taflove, Opt. Lett. 16, 1412 (1991).
[CrossRef] [PubMed]

A. Taflove and S. C. Hagness, Computational Electrodynamics, the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2005).

Harms, P. H.

J. A. Roden, S. D. Gedney, M. P. Kesler, J. G. Maloney, and P. H. Harms, IEEE Trans. Microwave Theory Tech. 46, 420 (1998).
[CrossRef]

Ibanescu, M.

Joannopoulos, J. D.

Johnson, S. G.

Joseph, R. M.

Kesler, M. P.

J. A. Roden, S. D. Gedney, M. P. Kesler, J. G. Maloney, and P. H. Harms, IEEE Trans. Microwave Theory Tech. 46, 420 (1998).
[CrossRef]

Körner, T. O.

Macías, D.

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M.-L. de la Chapelle, Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Maloney, J. G.

J. A. Roden, S. D. Gedney, M. P. Kesler, J. G. Maloney, and P. H. Harms, IEEE Trans. Microwave Theory Tech. 46, 420 (1998).
[CrossRef]

Roden, J. A.

J. A. Roden, S. D. Gedney, M. P. Kesler, J. G. Maloney, and P. H. Harms, IEEE Trans. Microwave Theory Tech. 46, 420 (1998).
[CrossRef]

Rodriguez, A.

Roundy, D.

Taflove, A.

R. M. Joseph, S. C. Hagness, and A. Taflove, Opt. Lett. 16, 1412 (1991).
[CrossRef] [PubMed]

A. Taflove and S. C. Hagness, Computational Electrodynamics, the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2005).

Valuev, I.

Vial, A.

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M.-L. de la Chapelle, Phys. Rev. B 71, 085416 (2005).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

J. A. Roden, S. D. Gedney, M. P. Kesler, J. G. Maloney, and P. H. Harms, IEEE Trans. Microwave Theory Tech. 46, 420 (1998).
[CrossRef]

Opt. Lett.

Phys. Rev. B

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M.-L. de la Chapelle, Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Phys. Rev. E

A. Belkhir and F. I. Baida, Phys. Rev. E 77, 056701 (2008).
[CrossRef]

Other

A. Taflove and S. C. Hagness, Computational Electrodynamics, the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2005).

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Figures (3)

Fig. 1
Fig. 1

Comparison of the transmission of the monolayer structure depicted in the inset when illuminated at 45° calculated by the three methods mentioned in the legend. The transmission is defined as the total flux of the transmitted Poynting vector divided by the incident one. In the SFM-FDTD simulation, the spatial step is fixed to the period over 80.

Fig. 2
Fig. 2

Transmission coefficients through 20 - nm -thick silver [(a)–(d)] and gold [(e)–(h)] films suspended in air. In all eight subfigures, the circles correspond to the FDTD calculation ( T FDTD ) , the solid curves are analytical data ( T Ana ) , and the dotted curves correspond to the error signal. (a), (b) and (e), (f) correspond to TE polarization, while (c), (d) and (g), (h) correspond to TM one. In (a), (c) and (e), (g) the wavelength is fixed to λ = 700 nm . The error signal is calculated as | T FDTD T Ana | T Ana . In (b), (d) and (f), (h) the incidence angle is set to θ = 45 ° . The parameters of the Drude model are ω p = 1.374 × 10 16 rad s and γ = 3.21 × 10 13 rad s . For the Drude–Lorentz model we consider the parameters given in Table I of [6]. In all simulations, the spatial step is set to 0.5 nm .

Fig. 3
Fig. 3

Relative error deduced from analytical data (dashed curves) for a thickness uncertainty of 0.25 nm in comparison with the SFM-FDTD one (solid curves) in the case of h = 20 - nm -thick gold film. (a) Transmission angular spectrum at λ = 700 nm and (b) transmission versus wavelength at θ = 45 ° .

Equations (3)

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ϵ ( ω ) = ϵ r + Δ ϵ α i ω τ ,
L a t = Q .
ϵ 0 ϵ r τ P a t + ϵ 0 ( ϵ r α + Δ ϵ ) P a = τ L a t + α L a .

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