Abstract

Normal incidence of a plane electromagnetic wave on a periodical structure can be simulated by the finite-difference time-domain method using a single unit cell with periodical boundary conditions imposed on its borders. For the oblique wave incidence, the boundary conditions would contain time delays and thus are difficult to implement in the time-domain method. We propose a method of oblique incidence simulation, based on an iterative algorithm. The accuracy of this method is demonstrated by comparing it with the layer Korringa–Kohn–Rostoker frequency-domain method for calculation of transmission spectra of a monolayered photonic crystal.

© 2008 Optical Society of America

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References

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  1. A. Taflove and S. H. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2000).
  2. M. Veysoglu, R. Shin, and J. Kong, J. Electromagn. Waves Appl. 7, 1595 (1993).
    [CrossRef]
  3. Y. C. A. Kao and R. G. Atkins, in Proceedings of IEEE Antennas and Propagation Society International Symposium (IEEE, 1996), pp. 1432-1436.
  4. 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]
  5. P. Harms, R. Mittra, and W. Ko, IEEE Trans. Antennas Propag. 42, 1317 (1994).
    [CrossRef]
  6. A. Aminian and Y. Rahmat-Samii, IEEE Trans. Antennas Propag. 54, 1818 (2006).
    [CrossRef]
  7. J. Ren, O. P. Gandhi, L. R. Walker, J. Fraschilla, and C. R. Boerman, IEEE Microw. Guid. Wave Lett. 4, 109 (1994).
    [CrossRef]
  8. I. Valuev, A. Deinega, A. Knizhnik, and B. Potapkin, Lect. Notes Comput. Sci. 4707, 213 (2007).
    [CrossRef]
  9. A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, Opt. Lett. 31, 2972 (2006).
    [CrossRef] [PubMed]
  10. A. Deinega and I. Valuev, Opt. Lett. 32, 3429 (2007).
    [CrossRef] [PubMed]
  11. N. Stefanou, N. Yannopapas, and D. Modinos, Comput. Phys. Commun. 113, 49 (1998).
    [CrossRef]

2007 (2)

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

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

2006 (2)

1998 (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]

N. Stefanou, N. Yannopapas, and D. Modinos, Comput. Phys. Commun. 113, 49 (1998).
[CrossRef]

1994 (2)

P. Harms, R. Mittra, and W. Ko, IEEE Trans. Antennas Propag. 42, 1317 (1994).
[CrossRef]

J. Ren, O. P. Gandhi, L. R. Walker, J. Fraschilla, and C. R. Boerman, IEEE Microw. Guid. Wave Lett. 4, 109 (1994).
[CrossRef]

1993 (1)

M. Veysoglu, R. Shin, and J. Kong, J. Electromagn. Waves Appl. 7, 1595 (1993).
[CrossRef]

Aminian, A.

A. Aminian and Y. Rahmat-Samii, IEEE Trans. Antennas Propag. 54, 1818 (2006).
[CrossRef]

Atkins, R. G.

Y. C. A. Kao and R. G. Atkins, in Proceedings of IEEE Antennas and Propagation Society International Symposium (IEEE, 1996), pp. 1432-1436.

Bermel, P.

Boerman, C. R.

J. Ren, O. P. Gandhi, L. R. Walker, J. Fraschilla, and C. R. Boerman, IEEE Microw. Guid. Wave Lett. 4, 109 (1994).
[CrossRef]

Burr, G.

Deinega, A.

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

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

Farjadpour, A.

Fraschilla, J.

J. Ren, O. P. Gandhi, L. R. Walker, J. Fraschilla, and C. R. Boerman, IEEE Microw. Guid. Wave Lett. 4, 109 (1994).
[CrossRef]

Gandhi, O. P.

J. Ren, O. P. Gandhi, L. R. Walker, J. Fraschilla, and C. R. Boerman, IEEE Microw. Guid. Wave Lett. 4, 109 (1994).
[CrossRef]

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]

Hagness, S. H.

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

Harms, P.

P. Harms, R. Mittra, and W. Ko, IEEE Trans. Antennas Propag. 42, 1317 (1994).
[CrossRef]

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.

Kao, Y. C. A.

Y. C. A. Kao and R. G. Atkins, in Proceedings of IEEE Antennas and Propagation Society International Symposium (IEEE, 1996), pp. 1432-1436.

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]

Knizhnik, A.

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

Ko, W.

P. Harms, R. Mittra, and W. Ko, IEEE Trans. Antennas Propag. 42, 1317 (1994).
[CrossRef]

Kong, J.

M. Veysoglu, R. Shin, and J. Kong, J. Electromagn. Waves Appl. 7, 1595 (1993).
[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]

Mittra, R.

P. Harms, R. Mittra, and W. Ko, IEEE Trans. Antennas Propag. 42, 1317 (1994).
[CrossRef]

Modinos, D.

N. Stefanou, N. Yannopapas, and D. Modinos, Comput. Phys. Commun. 113, 49 (1998).
[CrossRef]

Potapkin, B.

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

Rahmat-Samii, Y.

A. Aminian and Y. Rahmat-Samii, IEEE Trans. Antennas Propag. 54, 1818 (2006).
[CrossRef]

Ren, J.

J. Ren, O. P. Gandhi, L. R. Walker, J. Fraschilla, and C. R. Boerman, IEEE Microw. Guid. Wave Lett. 4, 109 (1994).
[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.

Shin, R.

M. Veysoglu, R. Shin, and J. Kong, J. Electromagn. Waves Appl. 7, 1595 (1993).
[CrossRef]

Stefanou, N.

N. Stefanou, N. Yannopapas, and D. Modinos, Comput. Phys. Commun. 113, 49 (1998).
[CrossRef]

Taflove, A.

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

Valuev, I.

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

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

Veysoglu, M.

M. Veysoglu, R. Shin, and J. Kong, J. Electromagn. Waves Appl. 7, 1595 (1993).
[CrossRef]

Walker, L. R.

J. Ren, O. P. Gandhi, L. R. Walker, J. Fraschilla, and C. R. Boerman, IEEE Microw. Guid. Wave Lett. 4, 109 (1994).
[CrossRef]

Yannopapas, N.

N. Stefanou, N. Yannopapas, and D. Modinos, Comput. Phys. Commun. 113, 49 (1998).
[CrossRef]

Comput. Phys. Commun. (1)

N. Stefanou, N. Yannopapas, and D. Modinos, Comput. Phys. Commun. 113, 49 (1998).
[CrossRef]

IEEE Microw. Guid. Wave Lett. (1)

J. Ren, O. P. Gandhi, L. R. Walker, J. Fraschilla, and C. R. Boerman, IEEE Microw. Guid. Wave Lett. 4, 109 (1994).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

P. Harms, R. Mittra, and W. Ko, IEEE Trans. Antennas Propag. 42, 1317 (1994).
[CrossRef]

A. Aminian and Y. Rahmat-Samii, IEEE Trans. Antennas Propag. 54, 1818 (2006).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

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]

J. Electromagn. Waves Appl. (1)

M. Veysoglu, R. Shin, and J. Kong, J. Electromagn. Waves Appl. 7, 1595 (1993).
[CrossRef]

Lect. Notes Comput. Sci. (1)

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

Opt. Lett. (2)

Other (2)

Y. C. A. Kao and R. G. Atkins, in Proceedings of IEEE Antennas and Propagation Society International Symposium (IEEE, 1996), pp. 1432-1436.

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

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Figures (5)

Fig. 1
Fig. 1

Iterative method geometry; PMLs are used to absorb scattering waves. 1, 2, generating (TF/SF) borders where transferred fields are taken as a source; 1 , 2 , corresponding image locations; 3, TF/SF border with analytic oblique source; 4, detectors for signal analysis.

Fig. 2
Fig. 2

First and fifth iterations of the experiment with oblique incidence on a metallic plate; θ = 45 ° wave energy is plotted. The incident and reflected waves are clearly seen on the fifth iteration.

Fig. 3
Fig. 3

Scattered field energy flux through borders 1 and 2 of the computational volume (numerical error) for the setup of Fig. 2.

Fig. 4
Fig. 4

Transmittance of a photonic crystal monolayer (frequency dependence); θ = 45 ° .

Fig. 5
Fig. 5

Transmittance of a photonic crystal monolayer (incidence angle dependence); f = 0.6 a .

Equations (5)

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

F ( x , t ) = F ( x + a , t + ( k a ) ( k c ) ) ,
Δ t b = ( k a b ) ( k c ) = ± a 1 , 2 sin θ 1 , 2 c ,
F ( x b , t ) = F ( x b + a b , t + Δ t b ) = F ( x b + a b , t ) exp ( j α b ) ,
F i ( x 2 , t ) = F i ( x 2 , t Δ t ) ,
F i ( x 1 , t ) = F i 1 ( x 1 , t + Δ t ) .

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