Abstract

A novel way of approaching wave propagation in two-dimensional (2-D) photonic crystal guides with finite length is presented. It is shown that the main propagation features can be captured by borrowing simple concepts of propagation in transmission lines and combining them with other concepts taken from the theory of periodic structures.

© 2002 IEEE

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  1. E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Broemmer and J. D. Joannopoulos, "Donor and acceptor modes in photonic band structures", Phys. Rev. Lett., vol. 67, pp. 3380-3383, 1991.
  2. M. Plihal and A. A. Maradudin, "Photonic band structures of two-dimensional systems: The triangular lattice", Phys. Rev. B, vol. 44, pp. 8565-8571, 1991.
  3. E. Yablonovitch, "Photonic band-gap structures", J. Opt. Soc. Amer. B, vol. 10, p. 283, 1993.
  4. J. D. Joannopoulos, R. D. Meade and J. N. Winn, Photonic Crystals, Princeton, NJ: Princeton Univ. Press, 1995.
  5. J. D. Joannopoulos, P. R. Villeneuve and S. Fan, "Photonic crystals: Putting a new twist on light", Nature, vol. 387, pp. 143-149, 1997.
  6. D. Labilloy, H. Benitsy, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. bardinal, R. Houdre, U. Oesterle, D. Cassagne and C. Jouanin, "Quantitative measurement of transmission, reflection and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths", Phys. Rev. Lett., vol. 79, pp. 4147-4150, 1997.
  7. K. Busch and S. John, "Photonic band gap formation in certain self-organizing systems", Phys. Rev. E, vol. 58, pp. 3896-3908, 1998.
  8. T. F. Krauss and R. M. De La Rue, "Photonic crystals in the optical regime-Past, present and future", Prog. Quantum Electron., vol. 23, pp. 51-96, 1999.
  9. E. A. J. Marcatili, "Bends in optical dielectric guides", Bell Syst. Tech. J., vol. 48, pp. 2103-2132, 1969.
  10. R. D. Meade, A. Devenyl, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith and K. Kash, "Novel applications of photonic band gap materials: Low-loss bends and high Q cavities", J. Appl. Phys., vol. 75, pp. 4753-4755, 1994.
  11. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal", Phys. Rev. Lett., vol. 77, pp. 3787-3790, 1996.
  12. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos and L. A. Kolodziejski, "Guided modes in photonic crystal slabs", Phys. Rev. B, vol. 60, pp. 5751-5758, 1999.
  13. S. G. Johnson, P. R. Villeneuve, S. Fan and J. D. Joannopouols, "Linear waveguides in photonic-crystal slabs", Phys. Rev. B, vol. 62, pp. 8212-8222, 2000.
  14. T. Sondergaard and K. H. Dridi, "Energy flow in photonic crystal waveguides", Phys. Rev. B, vol. 61, pp. 15 688-15 696, 1999.
  15. R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos and O. L. Alerhand, "Accurate theoretical analysis of photonic band-gap materials", Phys. Rev. B, vol. 48, pp. 8434-8437, 1993.
  16. C. G. Someda, Electromagnetic Waves, London: Chapman & Hall, 1998, ch. 7.
  17. G. Tayeb and D. Maystre, "Rigorous theoretical study of finite-size two-dimensional photonic crystals doped by microcavities", J. Opt. Soc. Amer. A, vol. 14, p. 3323, 1997.
  18. R. E. Collin, Foundations for Microwave Engineering, New York: McGraw-Hill, 1992.
  19. R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos and O. L. Alerhand, "Accurate theoretical analysis of photonic band-gap materials", Phys. Rev. B, vol. 55, p. 15 942, 1997.

Other (19)

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Broemmer and J. D. Joannopoulos, "Donor and acceptor modes in photonic band structures", Phys. Rev. Lett., vol. 67, pp. 3380-3383, 1991.

M. Plihal and A. A. Maradudin, "Photonic band structures of two-dimensional systems: The triangular lattice", Phys. Rev. B, vol. 44, pp. 8565-8571, 1991.

E. Yablonovitch, "Photonic band-gap structures", J. Opt. Soc. Amer. B, vol. 10, p. 283, 1993.

J. D. Joannopoulos, R. D. Meade and J. N. Winn, Photonic Crystals, Princeton, NJ: Princeton Univ. Press, 1995.

J. D. Joannopoulos, P. R. Villeneuve and S. Fan, "Photonic crystals: Putting a new twist on light", Nature, vol. 387, pp. 143-149, 1997.

D. Labilloy, H. Benitsy, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. bardinal, R. Houdre, U. Oesterle, D. Cassagne and C. Jouanin, "Quantitative measurement of transmission, reflection and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths", Phys. Rev. Lett., vol. 79, pp. 4147-4150, 1997.

K. Busch and S. John, "Photonic band gap formation in certain self-organizing systems", Phys. Rev. E, vol. 58, pp. 3896-3908, 1998.

T. F. Krauss and R. M. De La Rue, "Photonic crystals in the optical regime-Past, present and future", Prog. Quantum Electron., vol. 23, pp. 51-96, 1999.

E. A. J. Marcatili, "Bends in optical dielectric guides", Bell Syst. Tech. J., vol. 48, pp. 2103-2132, 1969.

R. D. Meade, A. Devenyl, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith and K. Kash, "Novel applications of photonic band gap materials: Low-loss bends and high Q cavities", J. Appl. Phys., vol. 75, pp. 4753-4755, 1994.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal", Phys. Rev. Lett., vol. 77, pp. 3787-3790, 1996.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos and L. A. Kolodziejski, "Guided modes in photonic crystal slabs", Phys. Rev. B, vol. 60, pp. 5751-5758, 1999.

S. G. Johnson, P. R. Villeneuve, S. Fan and J. D. Joannopouols, "Linear waveguides in photonic-crystal slabs", Phys. Rev. B, vol. 62, pp. 8212-8222, 2000.

T. Sondergaard and K. H. Dridi, "Energy flow in photonic crystal waveguides", Phys. Rev. B, vol. 61, pp. 15 688-15 696, 1999.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos and O. L. Alerhand, "Accurate theoretical analysis of photonic band-gap materials", Phys. Rev. B, vol. 48, pp. 8434-8437, 1993.

C. G. Someda, Electromagnetic Waves, London: Chapman & Hall, 1998, ch. 7.

G. Tayeb and D. Maystre, "Rigorous theoretical study of finite-size two-dimensional photonic crystals doped by microcavities", J. Opt. Soc. Amer. A, vol. 14, p. 3323, 1997.

R. E. Collin, Foundations for Microwave Engineering, New York: McGraw-Hill, 1992.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos and O. L. Alerhand, "Accurate theoretical analysis of photonic band-gap materials", Phys. Rev. B, vol. 55, p. 15 942, 1997.

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