Abstract

We present a theoretical analysis of wave propagation in rectangular- and square-lattice photonic crystals by approximating the arbitrary refractive-index function with a staircase profile. This profile has a number of tunable parameters that allow one to fit the band structures of the staircase and the desired structure over a large frequency range. The staircase profile is such that its corresponding two-dimensional wave equation decomposes into two one-dimensional equations by means of a constant decoupling parameter. We show that basic features of the band structure and Bloch waves in photonic crystals can be analyzed theoretically through this simple approximation.

© 2003 Optical Society of America

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  1. J. D. Joannopolous, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).
  2. P. Tran, Phys. Rev. B 52, 10673 (1995).
  3. B. Garlak, S. Enoch, and G. Tayeb, J. Opt. Soc. Am. A 17, 1012 (2000).
  4. D. Felbaque, G. Tayeb, and D. Maystre, J. Opt. Soc. Am. A 11, 2526 (1994).
  5. B. Garlak, S. Enoch, and G. Tayeb, J. Opt. Soc. Am. A 19, 1547 (2002).
  6. D. C. Dobson, J. Comput. Phys. 149, 363 (1999).
  7. S. Chaowei, C. H. Chan, and K. F. Chan, in Proceedings of IEEE Antennas and Propagation Society International Symposium, 2002 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2002), Vol. 4, pp. 356–359.
  8. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  9. S. Khorasani and A. Adibi, Opt. Commun. 216, 439 (2003).
  10. A. Krokhin, P. Halevi, and J. Arriaga, Phys. Rev. B 65, 115220 (2002).

2003

S. Khorasani and A. Adibi, Opt. Commun. 216, 439 (2003).

2002

A. Krokhin, P. Halevi, and J. Arriaga, Phys. Rev. B 65, 115220 (2002).

B. Garlak, S. Enoch, and G. Tayeb, J. Opt. Soc. Am. A 19, 1547 (2002).

S. Chaowei, C. H. Chan, and K. F. Chan, in Proceedings of IEEE Antennas and Propagation Society International Symposium, 2002 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2002), Vol. 4, pp. 356–359.

2000

1999

D. C. Dobson, J. Comput. Phys. 149, 363 (1999).

1995

J. D. Joannopolous, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

P. Tran, Phys. Rev. B 52, 10673 (1995).

1994

D. Felbaque, G. Tayeb, and D. Maystre, J. Opt. Soc. Am. A 11, 2526 (1994).

1984

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Adibi, A.

S. Khorasani and A. Adibi, Opt. Commun. 216, 439 (2003).

Arriaga, J.

A. Krokhin, P. Halevi, and J. Arriaga, Phys. Rev. B 65, 115220 (2002).

Chan, C. H.

S. Chaowei, C. H. Chan, and K. F. Chan, in Proceedings of IEEE Antennas and Propagation Society International Symposium, 2002 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2002), Vol. 4, pp. 356–359.

Chan, K. F.

S. Chaowei, C. H. Chan, and K. F. Chan, in Proceedings of IEEE Antennas and Propagation Society International Symposium, 2002 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2002), Vol. 4, pp. 356–359.

Chaowei, S.

S. Chaowei, C. H. Chan, and K. F. Chan, in Proceedings of IEEE Antennas and Propagation Society International Symposium, 2002 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2002), Vol. 4, pp. 356–359.

Dobson, D. C.

D. C. Dobson, J. Comput. Phys. 149, 363 (1999).

Enoch, S.

Felbaque, D.

D. Felbaque, G. Tayeb, and D. Maystre, J. Opt. Soc. Am. A 11, 2526 (1994).

Garlak, B.

Halevi, P.

A. Krokhin, P. Halevi, and J. Arriaga, Phys. Rev. B 65, 115220 (2002).

Joannopolous, J. D.

J. D. Joannopolous, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Khorasani, S.

S. Khorasani and A. Adibi, Opt. Commun. 216, 439 (2003).

Krokhin, A.

A. Krokhin, P. Halevi, and J. Arriaga, Phys. Rev. B 65, 115220 (2002).

Maystre, D.

D. Felbaque, G. Tayeb, and D. Maystre, J. Opt. Soc. Am. A 11, 2526 (1994).

Meade, R. D.

J. D. Joannopolous, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Tayeb, G.

Tran, P.

P. Tran, Phys. Rev. B 52, 10673 (1995).

Winn, J. N.

J. D. Joannopolous, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

J. Comput. Phys.

D. C. Dobson, J. Comput. Phys. 149, 363 (1999).

J. Opt. Soc. Am. A

D. Felbaque, G. Tayeb, and D. Maystre, J. Opt. Soc. Am. A 11, 2526 (1994).

J. Opt. Soc. Am. A

Opt. Commun.

S. Khorasani and A. Adibi, Opt. Commun. 216, 439 (2003).

Phys. Rev. B

A. Krokhin, P. Halevi, and J. Arriaga, Phys. Rev. B 65, 115220 (2002).

P. Tran, Phys. Rev. B 52, 10673 (1995).

Other

J. D. Joannopolous, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

S. Chaowei, C. H. Chan, and K. F. Chan, in Proceedings of IEEE Antennas and Propagation Society International Symposium, 2002 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2002), Vol. 4, pp. 356–359.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

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