Hostname: page-component-7dc689bd49-rf6jd Total loading time: 0 Render date: 2023-03-20T16:21:02.785Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

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

Published online by Cambridge University Press:  17 March 2011

Shanhui Fan
Department of Electrical Engineering, Stanford University, Stanford, CA 94305, U. S. A
J. D. Joannopoulos
Department of Physics and Center for Material Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, U. S. A
Get access


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.

Research Article
Copyright © Materials Research Society 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


1. Fan, S., Villeneuve, P. R., Joannopoulos, J. D., and Schubert, E. F., Phys. Rev. Lett. 78, 3294–7 (1997).CrossRefGoogle Scholar
2. Johnson, S. G., Fan, S., Villeneuve, P. R., and Joannopoulos, J. D. and Kolodzjeski, L. A., Phys. Rev. B 60, 5751–8 (1999).CrossRefGoogle Scholar
3. Painter, O., Vuckovic, T., and Scherer, A., J. Opt. Soc. Am. B 16, 275–85 (1999).CrossRefGoogle Scholar
4. Baba, T., Fukaya, N., and Yonekura, J., Electron. Lett. 35, 654–5 (1999).CrossRefGoogle Scholar
5. Kuchinsky, S., Allan, D. C., Borrelli, N. F., and Cotteverte, J. -C., Opt. Commun. 175, 147 (2000).CrossRefGoogle Scholar
6. Lin, S. Y., Chow, E., Johnson, S. G., Joannopoulos, J. D., Opt. Lett. 25, 1297–9 (2000).CrossRefGoogle Scholar
7. Benistry, al, Appl. Phys. Lett. 76, 531–3 (2000).Google Scholar
8. Chutinan, A. and Noda, S., Phys. Rev. B 62, 4488–92 (2000).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
10. Villeneuve, P. R., Fan, S., Johnson, S. G., and Joannopoulos, J. D., IEE Proceedings: Optoelectronics 145, 384 (1998).Google Scholar
11. Boroditsky, M., Vrijen, R., Krauss, T. F., Coccioli, R., Bhat, R., and Yablonovitch, E., J. Lighwave Technol. 17, 2096–112 (1999).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
13. Paddon, P. and Young, J. F., Phys. Rev. B 61, 20902101(2000).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
15. Cowan, A. R., Paddon, P., Pacradouni, V., and Young, J. F., J. Opt. Soc. Am. 16, 1160–70 (2001).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
17. Meier, M., Mekis, A., Dodabalapur, A., Timko, A., Slusher, R. E., Joannopoulos, J. D., Appl. Phys. Lett. 74, 79 (1999).CrossRefGoogle Scholar
18. Imada, M., Noda, S., Chutinan, A., Tokuda, T., Murata, M. and Sasaki, G., Appl. Phys. Lett. 75, .3168 (1999)CrossRefGoogle Scholar
19. Mekis, A., Dodabalapur, A., Slusher, R. E., and Joannopoulos, J. D., Opt. Lett. 25, 942–4 (2000).CrossRefGoogle Scholar
20. Peng, S. and Morris, G. M., J. Opt. Soc. Am. A 13, 9931005 (1996).CrossRefGoogle Scholar
21. Joannopoulos, J. D., Meade, R. D. and Winn, J. N., “Photonic crystals: molding the flow of light” (Princeton University Press, Princeton, 1995).Google Scholar
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).Google Scholar
23. Berenger, J. P., J. Computational Physics 114, 185200 (1994).CrossRefGoogle Scholar
24. Wang, S. S. and Magnusson, R., Appl. Phys. Lett. 61, 1022–24 (1992).Google Scholar
25. Ochiai, T. and Sakoda, K., Phys. Rev. B 63, 125107–1 (2001).CrossRefGoogle Scholar
26. Wang, S. S. and Magnusson, R., Opt. Lett. 19, 919921 (1994).CrossRefGoogle Scholar
27. Sharon, A., Rosenblatt, D., Friesem, A. A., Opt. Lett. 21, pp.15646 (1996).CrossRefGoogle Scholar
28. Tamir, T. and Zhang, S., J. Opt. Soc. Am A 14, 16071616(1997)CrossRefGoogle Scholar
29. Norton, S. M., Erdogan, T. and Morris, G. M., J. Opt. Soc. Am. A 14, 629639 (1997).CrossRefGoogle Scholar
30. Norton, S. M., Morris, G. M. and Erdogan, T., J. Opt. Soc. Am A 15, 464472 (1998).CrossRefGoogle Scholar
31. Levy-Yurista, G. and Friesem, A. A., Appl. Phys. Lett. 77, 15961598 (2000).CrossRefGoogle Scholar
32. Fano, U., Phys. Rev. 124, 1866–77 (1961).CrossRefGoogle Scholar
33. Andaloro, R. V., Simon, H. J., and Deck, R. T., Appl. Opt. 33, 6340–7 (1994).CrossRefGoogle Scholar
34. Yeh, P., “Optical waves in layered media”, (John Wiley & Sons, New York, 1988).Google Scholar
35. Fan, S., Villeneuve, P. R., and Joannopoulos, J. D., IEEE J. Quantum Electron. 36, 1123–30 (2000).CrossRefGoogle Scholar