Abstract

A hybrid transfer-matrix finite-difference time-domain (FDTD) method is proposed for modeling the optical properties of finite-width planar periodic structures. This method can also be applied for calculation of the photonic bands in infinite photonic crystals. We describe the procedure of evaluating the transfer-matrix elements by a special numerical FDTD simulation. The accuracy of the new method is tested by comparing computed transmission spectra of a 32-layered photonic crystal composed of spherical or ellipsoidal scatterers with the results of direct FDTD and layer-multiple-scattering calculations.

© 2009 Optical Society of America

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2008

2007

2006

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]

G. Gantzounis and N. Stefanou, Phys. Rev. B 73, 035115 (2006).
[CrossRef]

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

2003

Z. Y. Li and L. L. Lin, Phys. Rev. E 67, 046607 (2003).
[CrossRef]

2000

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 132, 189 (2000).
[CrossRef]

1996

S. Fan, P. Villeneuve, and J. Joannopoulos, Phys. Rev. B 54, 11245 (1996).
[CrossRef]

1995

A. Moroz, Phys. Rev. B 51, 2068 (1995).
[CrossRef]

1994

J. B. Pendry, J. Mod. Opt. 41, 209 (1994).
[CrossRef]

1990

K.-M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef] [PubMed]

Aminian, A.

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

Belousov, S.

Bermel, P.

Burr, G.

Chan, C. T.

K.-M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef] [PubMed]

Deinega, A.

Fan, S.

S. Fan, P. Villeneuve, and J. Joannopoulos, Phys. Rev. B 54, 11245 (1996).
[CrossRef]

Farjadpour, A.

Gantzounis, G.

G. Gantzounis and N. Stefanou, Phys. Rev. B 73, 035115 (2006).
[CrossRef]

Hagness, S. H.

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

Ho, K.-M.

K.-M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef] [PubMed]

Ibanescu, M.

Joannopoulos, J.

S. Fan, P. Villeneuve, and J. Joannopoulos, Phys. Rev. B 54, 11245 (1996).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

Li, Z. Y.

Z. Y. Li and L. L. Lin, Phys. Rev. E 67, 046607 (2003).
[CrossRef]

Lin, L. L.

Z. Y. Li and L. L. Lin, Phys. Rev. E 67, 046607 (2003).
[CrossRef]

Modinos, A.

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 132, 189 (2000).
[CrossRef]

Moroz, A.

A. Moroz, Phys. Rev. B 51, 2068 (1995).
[CrossRef]

Pendry, J. B.

J. B. Pendry, J. Mod. Opt. 41, 209 (1994).
[CrossRef]

Rahmat-Samii, Y.

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

Rodriguez, A.

Roundy, D.

Soukoulis, C. M.

K.-M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef] [PubMed]

Stefanou, N.

G. Gantzounis and N. Stefanou, Phys. Rev. B 73, 035115 (2006).
[CrossRef]

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 132, 189 (2000).
[CrossRef]

Taflove, A.

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

Valuev, I.

Villeneuve, P.

S. Fan, P. Villeneuve, and J. Joannopoulos, Phys. Rev. B 54, 11245 (1996).
[CrossRef]

Yannopapas, V.

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 132, 189 (2000).
[CrossRef]

Comput. Phys. Commun.

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 132, 189 (2000).
[CrossRef]

IEEE Trans. Antennas Propag.

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

J. Mod. Opt.

J. B. Pendry, J. Mod. Opt. 41, 209 (1994).
[CrossRef]

Opt. Lett.

Phys. Rev. B

S. Fan, P. Villeneuve, and J. Joannopoulos, Phys. Rev. B 54, 11245 (1996).
[CrossRef]

G. Gantzounis and N. Stefanou, Phys. Rev. B 73, 035115 (2006).
[CrossRef]

A. Moroz, Phys. Rev. B 51, 2068 (1995).
[CrossRef]

Phys. Rev. E

Z. Y. Li and L. L. Lin, Phys. Rev. E 67, 046607 (2003).
[CrossRef]

Phys. Rev. Lett.

K.-M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef] [PubMed]

Other

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

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Figures (2)

Fig. 1
Fig. 1

Transmittance of a 32-layered cubic lattice slab of conducting spheres or ellipsoids as scattering elements. Inset, scheme of the FDTD simulation geometry; 1, generating a (TF/SF) border; 2 and 2 , detector arrays for reflected and transmitted signals.

Fig. 2
Fig. 2

Relative error in transmittance of a 32-layered cubic lattice slab of conducting spheres measured with respect to the direct FDTD calculation. The case ( k z ) 2 > 0 corresponds to the neglect of evanescent modes in the hybrid transfer-matrix FDTD method.

Equations (4)

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q g ± = k + g ± [ q 2 ( k + g ) 2 ] 1 2 u z ,
E q k ( r ) = s = ± i = 1 2 g [ E ] g i s exp ( i q g s r ) u i .
[ E ] g i ± = i = 1 2 g M g i , g i ± + [ E in ] g i + .
E ( r , t ) = Re ( F ̂ ω [ A ( ω ) u i e i z μ ϵ ( ω c ) 2 g 2 ] e i g r ) ,

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