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Two Dimensional Photonic Crystal Modes and Resonances in Three-dimensional Structures

  • Shanhui Fan (a1) and J. D. Joannopoulos (a2)


We present three-dimensional analysis of two-dimensional guided resonances in photonic crystalslab structures. This analysis leads to a new understanding of the complex spectral properties of such systems. Specifically, we calculate the dispersion diagrams, the modal patterns, and transmission and reflection spectra of these resonances. From these calculations, a key observation emerges involving the presence of two temporal pathways for transmission and eflection processes. Using this insight, we introduce a general physical model that explains the essential features of complex spectral properties. Finally, we show that the quality factors of these resonances are strongly influenced by the symmetry of the modes, and the strength ofthe index modulation.



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1. Fan, S., Villeneuve, P. R., Joannopoulos, J. D., and Schubert, E. F., Phys. Rev. Lett. 78, 3294–7 (1997).
2. Johnson, S. G., Fan, S., Villeneuve, P. R., and Joannopoulos, J. D. and Kolodzjeski, L. A., Phys. Rev. B 60, 5751–8 (1999).
3. Painter, O., Vuckovic, T., and Scherer, A., J. Opt. Soc. Am. B 16, 275–85 (1999).
4. Baba, T., Fukaya, N., and Yonekura, J., Electron. Lett. 35, 654–5 (1999).
5. Kuchinsky, S., Allan, D. C., Borrelli, N. F., and Cotteverte, J. -C., Opt. Commun. 175, 147 (2000).
6. Lin, S. Y., Chow, E., Johnson, S. G., Joannopoulos, J. D., Opt. Lett. 25, 1297–9 (2000).
7. Benistry, al, Appl. Phys. Lett. 76, 531–3 (2000).
8. Chutinan, A. and Noda, S., Phys. Rev. B 62, 4488–92 (2000).
9. Kanskar, M., Paddon, P., Pacradouni, V., Morin, R., Busch, A., Young, J. F., Johnson, S. R., MacKenzie, J. and Tiedje, T., Appl. Phys. Lett. 70, 1438–40 (1997).
10. Villeneuve, P. R., Fan, S., Johnson, S. G., and Joannopoulos, J. D., IEE Proceedings: Optoelectronics 145, 384 (1998).
11. Boroditsky, M., Vrijen, R., Krauss, T. F., Coccioli, R., Bhat, R., and Yablonovitch, E., J. Lighwave Technol. 17, 2096–112 (1999).
12. Astratov, V. N., Chushaw, I. S., Stevenson, R. M., Whittaker, D. M., Skolnick, M. S., Krauss, T. F., and Rue, R. M.De la, J. LightwaveTechnol. 17, 2050–8 (1999).
13. Paddon, P. and Young, J. F., Phys. Rev. B 61, 20902101(2000).
14. Pacardoni, V., Mandeville, W. J., Crown, A. R., Paddon, P., Young, J. F. and Johnson, S. R., Phys. Rev. B. 62,4204–7 (2000).
15. Cowan, A. R., Paddon, P., Pacradouni, V., and Young, J. F., J. Opt. Soc. Am. 16, 1160–70 (2001).
16. Erchak, A. A., Ripin, D. J., Fan, S., Joannopoulos, J. D., Ippen, E. P., Petrich, G. S., and Kolodzjeski, L. A., Appl. Phys. Lett. 78, 563–5 (2001).
17. Meier, M., Mekis, A., Dodabalapur, A., Timko, A., Slusher, R. E., Joannopoulos, J. D., Appl. Phys. Lett. 74, 79 (1999).
18. Imada, M., Noda, S., Chutinan, A., Tokuda, T., Murata, M. and Sasaki, G., Appl. Phys. Lett. 75, .3168 (1999)
19. Mekis, A., Dodabalapur, A., Slusher, R. E., and Joannopoulos, J. D., Opt. Lett. 25, 942–4 (2000).
20. Peng, S. and Morris, G. M., J. Opt. Soc. Am. A 13, 9931005 (1996).
21. Joannopoulos, J. D., Meade, R. D. and Winn, J. N., “Photonic crystals: molding the flow of light” (Princeton University Press, Princeton, 1995).
22.For a review on finite difference time domain methods, see Kunz, K. S. and Luebbers, R. J., “The finite difference time domain methods for electromagnetics”, (CRC press, Boca Raton, 1993); A. Taflove and S. C. Hagness, “Computational Electrodynamics: the finite-difference time-domain method”, (Artech House, Boston, 2000).
23. Berenger, J. P., J. Computational Physics 114, 185200 (1994).
24. Wang, S. S. and Magnusson, R., Appl. Phys. Lett. 61, 1022–24 (1992).
25. Ochiai, T. and Sakoda, K., Phys. Rev. B 63, 125107–1 (2001).
26. Wang, S. S. and Magnusson, R., Opt. Lett. 19, 919921 (1994).
27. Sharon, A., Rosenblatt, D., Friesem, A. A., Opt. Lett. 21, pp.15646 (1996).
28. Tamir, T. and Zhang, S., J. Opt. Soc. Am A 14, 16071616(1997)
29. Norton, S. M., Erdogan, T. and Morris, G. M., J. Opt. Soc. Am. A 14, 629639 (1997).
30. Norton, S. M., Morris, G. M. and Erdogan, T., J. Opt. Soc. Am A 15, 464472 (1998).
31. Levy-Yurista, G. and Friesem, A. A., Appl. Phys. Lett. 77, 15961598 (2000).
32. Fano, U., Phys. Rev. 124, 1866–77 (1961).
33. Andaloro, R. V., Simon, H. J., and Deck, R. T., Appl. Opt. 33, 6340–7 (1994).
34. Yeh, P., “Optical waves in layered media”, (John Wiley & Sons, New York, 1988).
35. Fan, S., Villeneuve, P. R., and Joannopoulos, J. D., IEEE J. Quantum Electron. 36, 1123–30 (2000).


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