Abstract

In general, Maxwell equations are coupled when governing light propagation through one-dimensional inhomogeneous anisotropic dielectric structures. However, for on-axis propagation in one-dimensional in homogeneous uniaxially anisotropic dielectric structures with any orientation of the optic axis, and biaxially anisotropic structures with certain orientations of principal axes, we show that the equations can be decoupled into two wave equations satisfied by the two independent polarizations of light. Furthermore, the dielectric tensor in the original Maxwell equations is replaced with effective dielectric constants for each polarization of the light. We also give specialized results for anisotropic multilayer dielectric structures and one-dimensional anisotropic photonic crystals.

© 2009 Optical Society of America

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2008 (1)

L. Jiang, G. Zheng, L. Shi, J. Yuan, and X. Li, Opt. Commun. 281, 4882 (2008).
[CrossRef]

2007 (2)

Y.-T. Fang and J. Zhou, J. Russ. Laser Res. 28, 372 (2007).
[CrossRef]

S. W. Kim, B. Park, and Y. P. Lee, Appl. Phys. Lett. 90, 161108 (2007).
[CrossRef]

2006 (5)

2004 (2)

M. Shokooh-Saremi, M. Nourian, M. M. Mirsalehi, and S. H. Keshmiri, Opt. Commun. 233, 57 (2004).
[CrossRef]

G. Liang, P. Han, and H. Wang, Opt. Lett. 29, 192 (2004).
[CrossRef] [PubMed]

2002 (1)

B. A. Usievich and V. A. Sychugov, Quantum Electron. 32, 531 (2002).
[CrossRef]

2001 (1)

Z. M. Jiang, B. Shi, D. T. Zhao, J. Liu, and X. Wang, Appl. Phys. Lett. 79, 3395 (2001).
[CrossRef]

1998 (1)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

1996 (2)

D. R. Beltrami, J. D. Love, A. Durandet, A. Samoc, M. Samoc, B. Luther-Davies, and R. W. Boswell, Electron. Lett. 32, 549 (1996).
[CrossRef]

T. Boudet, P. Chaton, L. Herault, G. Gonon, L. Jouanet, and P. Keller, Appl. Opt. 35, 6219 (1996).
[CrossRef] [PubMed]

1992 (1)

E. Michielssen, S. Ranjithan, and R. Mittra, IEE Proc. J Optoelectron. 139, 413 (1992).
[CrossRef]

1990 (1)

Alagappan, G.

Beltrami, D. R.

D. R. Beltrami, J. D. Love, A. Durandet, A. Samoc, M. Samoc, B. Luther-Davies, and R. W. Boswell, Electron. Lett. 32, 549 (1996).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1999).
[PubMed]

Boswell, R. W.

D. R. Beltrami, J. D. Love, A. Durandet, A. Samoc, M. Samoc, B. Luther-Davies, and R. W. Boswell, Electron. Lett. 32, 549 (1996).
[CrossRef]

Boudet, T.

Chang, C. P.

Chaton, P.

Chen, C.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

Chen, L.

X. Cheng, Z. S. Wang, Z. Zhang, F. Wang, and L. Chen, Opt. Commun. 265, 197 (2006).
[CrossRef]

Cheng, X.

X. Cheng, Z. S. Wang, Z. Zhang, F. Wang, and L. Chen, Opt. Commun. 265, 197 (2006).
[CrossRef]

Doan, M. T.

Drescher, M.

Durandet, A.

D. R. Beltrami, J. D. Love, A. Durandet, A. Samoc, M. Samoc, B. Luther-Davies, and R. W. Boswell, Electron. Lett. 32, 549 (1996).
[CrossRef]

Fan, S.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

Fang, Y. -T.

Y.-T. Fang and J. Zhou, J. Russ. Laser Res. 28, 372 (2007).
[CrossRef]

Fink, Y.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

Gonon, G.

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

Han, P.

Heinzmann, U.

Herault, L.

Jiang, L.

L. Jiang, G. Zheng, L. Shi, J. Yuan, and X. Li, Opt. Commun. 281, 4882 (2008).
[CrossRef]

Jiang, Z. M.

Z. M. Jiang, B. Shi, D. T. Zhao, J. Liu, and X. Wang, Appl. Phys. Lett. 79, 3395 (2001).
[CrossRef]

Joannopoulos, J. D.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

Jouanet, L.

Kabachnik, N. M.

Keller, P.

Keshmiri, S. H.

M. Shokooh-Saremi, M. Nourian, M. M. Mirsalehi, and S. H. Keshmiri, Opt. Commun. 233, 57 (2004).
[CrossRef]

Kim, S. W.

S. W. Kim, B. Park, and Y. P. Lee, Appl. Phys. Lett. 90, 161108 (2007).
[CrossRef]

Kleineberg, U.

Krausz, F.

Lee, Y. H.

Lee, Y. P.

S. W. Kim, B. Park, and Y. P. Lee, Appl. Phys. Lett. 90, 161108 (2007).
[CrossRef]

Li, X.

L. Jiang, G. Zheng, L. Shi, J. Yuan, and X. Li, Opt. Commun. 281, 4882 (2008).
[CrossRef]

Liang, G.

Liu, J.

Z. M. Jiang, B. Shi, D. T. Zhao, J. Liu, and X. Wang, Appl. Phys. Lett. 79, 3395 (2001).
[CrossRef]

Love, J. D.

D. R. Beltrami, J. D. Love, A. Durandet, A. Samoc, M. Samoc, B. Luther-Davies, and R. W. Boswell, Electron. Lett. 32, 549 (1996).
[CrossRef]

Luther-Davies, B.

D. R. Beltrami, J. D. Love, A. Durandet, A. Samoc, M. Samoc, B. Luther-Davies, and R. W. Boswell, Electron. Lett. 32, 549 (1996).
[CrossRef]

Michel, J.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

Michielssen, E.

E. Michielssen, S. Ranjithan, and R. Mittra, IEE Proc. J Optoelectron. 139, 413 (1992).
[CrossRef]

Mirsalehi, M. M.

M. Shokooh-Saremi, M. Nourian, M. M. Mirsalehi, and S. H. Keshmiri, Opt. Commun. 233, 57 (2004).
[CrossRef]

Mittra, R.

E. Michielssen, S. Ranjithan, and R. Mittra, IEE Proc. J Optoelectron. 139, 413 (1992).
[CrossRef]

Neuhäusler, U.

Nourian, M.

M. Shokooh-Saremi, M. Nourian, M. M. Mirsalehi, and S. H. Keshmiri, Opt. Commun. 233, 57 (2004).
[CrossRef]

Park, B.

S. W. Kim, B. Park, and Y. P. Lee, Appl. Phys. Lett. 90, 161108 (2007).
[CrossRef]

Ranjithan, S.

E. Michielssen, S. Ranjithan, and R. Mittra, IEE Proc. J Optoelectron. 139, 413 (1992).
[CrossRef]

Samoc, A.

D. R. Beltrami, J. D. Love, A. Durandet, A. Samoc, M. Samoc, B. Luther-Davies, and R. W. Boswell, Electron. Lett. 32, 549 (1996).
[CrossRef]

Samoc, M.

D. R. Beltrami, J. D. Love, A. Durandet, A. Samoc, M. Samoc, B. Luther-Davies, and R. W. Boswell, Electron. Lett. 32, 549 (1996).
[CrossRef]

Shi, B.

Z. M. Jiang, B. Shi, D. T. Zhao, J. Liu, and X. Wang, Appl. Phys. Lett. 79, 3395 (2001).
[CrossRef]

Shi, L.

L. Jiang, G. Zheng, L. Shi, J. Yuan, and X. Li, Opt. Commun. 281, 4882 (2008).
[CrossRef]

Shokooh-Saremi, M.

M. Shokooh-Saremi, M. Nourian, M. M. Mirsalehi, and S. H. Keshmiri, Opt. Commun. 233, 57 (2004).
[CrossRef]

Shum, P.

Sun, X. W.

Sychugov, V. A.

B. A. Usievich and V. A. Sychugov, Quantum Electron. 32, 531 (2002).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

Thomas, E. L.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

Uiberacker, M.

Uphues, T.

Usievich, B. A.

B. A. Usievich and V. A. Sychugov, Quantum Electron. 32, 531 (2002).
[CrossRef]

Vandenbem, C.

Vigneron, J. P.

Vigoureux, J. M.

Wang, F.

X. Cheng, Z. S. Wang, Z. Zhang, F. Wang, and L. Chen, Opt. Commun. 265, 197 (2006).
[CrossRef]

Wang, H.

Wang, X.

Z. M. Jiang, B. Shi, D. T. Zhao, J. Liu, and X. Wang, Appl. Phys. Lett. 79, 3395 (2001).
[CrossRef]

Wang, Z. S.

X. Cheng, Z. S. Wang, Z. Zhang, F. Wang, and L. Chen, Opt. Commun. 265, 197 (2006).
[CrossRef]

Winn, J. N.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1999).
[PubMed]

Wonisch, A.

Wu, S. Y.

Yakovlev, V.

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 2003), Chap. 6.

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 2003), Chap. 6.

Yu, M. B.

Yuan, J.

L. Jiang, G. Zheng, L. Shi, J. Yuan, and X. Li, Opt. Commun. 281, 4882 (2008).
[CrossRef]

Zhang, Z.

X. Cheng, Z. S. Wang, Z. Zhang, F. Wang, and L. Chen, Opt. Commun. 265, 197 (2006).
[CrossRef]

Zhao, D. T.

Z. M. Jiang, B. Shi, D. T. Zhao, J. Liu, and X. Wang, Appl. Phys. Lett. 79, 3395 (2001).
[CrossRef]

Zheng, G.

L. Jiang, G. Zheng, L. Shi, J. Yuan, and X. Li, Opt. Commun. 281, 4882 (2008).
[CrossRef]

Zhou, J.

Y.-T. Fang and J. Zhou, J. Russ. Laser Res. 28, 372 (2007).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (2)

S. W. Kim, B. Park, and Y. P. Lee, Appl. Phys. Lett. 90, 161108 (2007).
[CrossRef]

Z. M. Jiang, B. Shi, D. T. Zhao, J. Liu, and X. Wang, Appl. Phys. Lett. 79, 3395 (2001).
[CrossRef]

Electron. Lett. (1)

D. R. Beltrami, J. D. Love, A. Durandet, A. Samoc, M. Samoc, B. Luther-Davies, and R. W. Boswell, Electron. Lett. 32, 549 (1996).
[CrossRef]

IEE Proc. J Optoelectron. (1)

E. Michielssen, S. Ranjithan, and R. Mittra, IEE Proc. J Optoelectron. 139, 413 (1992).
[CrossRef]

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

J. Opt. Soc. Am. B (2)

J. Russ. Laser Res. (1)

Y.-T. Fang and J. Zhou, J. Russ. Laser Res. 28, 372 (2007).
[CrossRef]

Opt. Commun. (3)

L. Jiang, G. Zheng, L. Shi, J. Yuan, and X. Li, Opt. Commun. 281, 4882 (2008).
[CrossRef]

M. Shokooh-Saremi, M. Nourian, M. M. Mirsalehi, and S. H. Keshmiri, Opt. Commun. 233, 57 (2004).
[CrossRef]

X. Cheng, Z. S. Wang, Z. Zhang, F. Wang, and L. Chen, Opt. Commun. 265, 197 (2006).
[CrossRef]

Opt. Lett. (2)

Quantum Electron. (1)

B. A. Usievich and V. A. Sychugov, Quantum Electron. 32, 531 (2002).
[CrossRef]

Science (1)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

Other (3)

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1999).
[PubMed]

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 2003), Chap. 6.

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Figures (2)

Fig. 1
Fig. 1

Schematic of a multilayer with different anisotropic dielectric tensors.

Fig. 2
Fig. 2

Orientation of the optic axis ( z p m ) with respect to the fixed x axis of the multilayer. The other two principal axes, x p m and y p m , of the uniaxial material can be arbitrarily chosen in the plane perpendicular to the z p m axis. The y and the z axes of the multilayer can be arbitrarily chosen in the plane perpendicular to the x axis.

Equations (17)

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μ o H x t = 0 ,
E z x = μ o H y t ,
E y x = μ o H z t ,
ε o ε 11 ( x ) E x t + ε o ε 12 ( x ) E y t + ε o ε 13 ( x ) E z t = 0 ,
H z x = ε o ε 21 ( x ) E x t ε o ε 22 ( x ) E y t ε o ε 23 ( x ) E z t ,
H y x = ε o ε 31 ( x ) E x t + ε o ε 32 ( x ) E y t + ε o ε 33 ( x ) E z t ,
μ o H x t = 0 ,
E z x = μ o H y t ,
H y x = ε o ε 33 ( x ) E z t .
{ x 1 ε H ( x ) x } H y 1 c 2 2 H y t 2 = 0 ,
E y x = μ o H z t ,
ε o ε 11 ( x ) E x t + ε o ε 12 ( x ) E y t = 0 ,
H z x = ε o ε 21 ( x ) E x t ε o ε 22 ( x ) E y t .
{ x ( ε 22 ( x ) ε 12 ( x ) ε 21 ( x ) ε 11 ( x ) ) 1 x } H z 1 c 2 2 H z t 2 = 0.
ε ̃ ( x ) = ε ̃ 1 + m = 2 M ( ε ̃ m ε ̃ 1 ) [ p ( x d m 1 ) p ( x d m ) ] ,
ε E ( x ) = ε 1 , E + m = 2 M ( ε m , E ε 1 , E ) [ p ( x d m 1 ) p ( x d m ) ] ,
ε H ( x ) = ε 1 , H + m = 2 M ( ε m , H ε 1 , H ) [ p ( x d m 1 ) p ( x d m ) ] ,

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