Localized defect states in two-dimensional photonic crystal slab waveguides: A simple model based upon symmetry analysis

Physical Review B - Condensed Matter and Materials Physics

Volumn 68, Issue 3, 2003, Pages 351101-3511023

  Painter, Oskar ^a   Srinivasan, Kartik ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CALCULATION; CRYSTAL STRUCTURE; MODEL; PHOTOLUMINESCENCE; PHOTON; SIMULATION; SPECTRAL SENSITIVITY;

EID: 0344307554     PISSN: 10980121     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (40)

1. D. M. Atkin, P. S. J. Russell, T. A. Birks, and P. J. Roberts, J. Mod. Opt. 43, 1035 (1996).
2. P. S. J. Russell, D. M. Atkin, and T. A. Birks, Bound Modes Of Two-Dimensional Photonic Crystal Waveguides (Kluwer Academic, The Netherlands, 1996), pp. 203-218.
3. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejaki, Phys. Rev. B 60, 5751 (1999).
4. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
5. E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, and J. D. Joannopoulos, Opt. Lett. 26, 286 (2001).
6. T. Baba, N. Fukaya, and J. Yonekura, IEE Electron Lett. 35, 654 (1999).
7. M. Lončar, T. Doll, J. Vučkovič, and A. Scherer, J. Lightwave Technol. 18, 1402 (2000).
8. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Opt. Lett. 24, 711 (1999).
9. S. Olivier, C. Smith, M. Rattier, H. Benisty, C. Weisbuch, T. Krauss, R. Houdré, and U. Oesterlé, Opt. Lett. 26, 1019 (2001).
10. C. Smith, R. De la Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. Krauss, U. Oesterlé, and R. Houdré, Appl. Phys. Lett. 78, 1487 (2001).
11. S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Opt. Express 3, 4 (1998); http://www.opticsexpress.org/abstract.cfm URI=OPEX-3-1-4.
12. S. Noda, A. Chutinan, and M. Imada, Nature (London) 407, 608 (2000).
13. J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature (London) 390, 143 (1997).
14. O. Painter, J. Vučkovič, and A. Scherer, J. Opt. Soc. Am. B 16, 275 (1999).
15. R. Coccioli, M. Boroditsky, K. M. Kim, Y. Rahmat-Samii, and E. Yablonovitch, IEE Proc.: Optoelectron. 145, 391 (1998).
16. O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O'Brien, P. D. Dapkus, and I. Kim, Science 284, 1819 (1999).
17. O. Painter, A. Husain, A. Scherer, P. T. Lee, I. Kim, J. D. O'Brien, and P. D. Dapkus, IEEE Photonics Technol. Lett. 12, 1126 (2000).
18. O. Painter, K. Srinivasan, J. D. O'Brien, A. Scherer, and P. D. Dapkus, J. Opt. A, Pure Appl. Opt. 3, S161 (2001).
19. K. Srinivasan and O. Painter, Opt. Express 10, 670 (2002).
20. P. Barclay, K. Srinivasan, M. Borselli, and O. Painter, IEEE-Electron. Lett. 39(11), May 29 (2003).
21. O. J. Painter, Ph.D. thesis, California Institute of Technology, 2001.
22. K. Sakoda, Phys. Rev. B 52, 7982 (1995).
23. W. Ludwig and C. Falter, Symmetries in Physics: Group Theory Applied to Physical Problems, 2nd ed., Springer Series in Solid-State Sciences, Vol. 64 (Springer-Verlag, New York, 1996).
24. G. H. Wannier, Rev. Mod. Phys. 34, 645 (1962).
25. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University, Princeton, NJ, 1995).
26. O. J. Painter, A. Husain, A. Scherer, J. D. O'Brien, I. Kim, and P. D. Dapkus, J. Lightwave Technol. 17, 2082 (1999).
27. In this calculation a 2D hexagonal PC with a host dielectric constant given by the effective index of the fundamental TE mode of the half-wavelength thick slab is analyzed (Ref. 14).
28. M. Tinkham, Group Theory and Quantum Mechanics, International Series in Pure and Applied Physics (McGraw-Hill, New York, 1964).
29. For the highly localized defect cavities studied here the energy associated with the curvature of a higher-order envelope function within the defect region is on the order of the energy associated with the Bloch part of the field.
30. As a result of nonidealities in the fabrication process (Ref. 26), the air holes near the center of the cavity are larger than those at the perimeter in the fabricated devices. A linear grading of the hole radius of 10% is quite common.
31. 6υ point group.
32. O. Painter and K. Srinivasan, Opt. Lett. 27, 339 (2002).
33. P. R. Villeneuve, S. Fan, S. G. Johnson, and J. D. Joannopoulos, IEE Proc.: Optoelectron. 145, 384 (1998).
34. J. M. Lutinger and W. Kohn, Phys. Rev. 97, 869 (1955).
35. C. Kittel and A. H. Mitchell, Phys. Rev. 96, 1488 (1954).
36. O. Painter and K. Srinivasan (unpublished).
37. P. C. Sercel and K. J. Vahala, Phys. Rev. B 42, 3690 (1990).
38. W. Kohn and J. M. Luttinger, Phys. Rev. 98, 915 (1955).
39. A. Baldereschi, Phys. Rev. B 1, 4673 (1970).
40. This can be checked for the representation of the lth band using the Herring criteria (Ref. 23).