Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals

Physical Review B - Condensed Matter and Materials Physics

Volumn 68, Issue 3, 2003, Pages 352141-3521413

  Painter, Oskar ^a   Srinivasan, Kartik ^a   Barclay, Paul E ^a  

^a California Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CALCULATION; CRYSTAL; DIELECTRIC CONSTANT; ELECTRON; MATHEMATICAL ANALYSIS; OPTICS; PHOTON; THEORY;

EID: 0242400220     PISSN: 10980121     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (41)

1. E. M. Purcell, Phys. Rev. 69, 681 (1946).
2. D. Kleppner, Phys. Rev. Lett. 47, 233 (1981).
3. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
4. D. M. Atkin, P. S. J. Russell, T. A. Birks, and P. J. Roberts, J. Mod. Opt. 43, 1035 (1996).
5. P. S. J. Russell, D. M. Atkin, and T. A. Birks, Bound Modes Of Two-Dimensional Photonic Crystal Waveguides (Kluwer, Dordrecht, 1996), pp. 203-218.
6. S. G. Johnson, S. Fan, P.R. Villeneuve, J. D. Joannopoulos, and L.A. Kolodziejaki, Phys. Rev. B 60, 5751 (1999).
7. 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).
8. O. Painter, J. Vučković, and A. Scherer, J. Opt. Soc. Am. B 16, 275 (1999).
9. R. Coccioli, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, IEE Proc.: Optoelectron. 145, 391 (1998).
10. O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O'Brien, P. D. Dapkus, and I. Kim, Science 284, 1819 (1999).
11. S. Noda, A. Chutinan, and M. Imada, Nature (London) 407, 608 (2000).
12. N. Stefanou and A. Modinos, Phys. Rev. B 57, 12 127 (1998).
13. A. Yariv, Optical Electronics, 4th ed. (Saunders College Publishing, Orlando, FL, 1991).
14. S. Olivier, C. Smith, M. Rattier, H. Benisty, C. Weisbuch, T. Krauss, R. Houdré, and U. Oesterlé, Opt. Lett. 26, 1019 (2001).
15. E. Ozbay, M. Bayindir, I. Bulu, and E. Cubukcu, IEEE J. Quantum Electron. 38, 837 (2002).
16. P. S. J. Russell and T. A. Birks, J. Lightwave Technol. 17, 1982 (1999).
17. P. S. J. Russell and T. A. Birks, Bloch Wave Optics in Photonic Crystals: Physics and Applications (Kluwer, Dordrecht, 1996), pp. 71-91.
18. G. H. Wannier, Phys. Rev. 52, 191 (1937).
19. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College Publishing, New York, 1976).
20. J. Arnaud, IEE Electron. Lett. 21, 538 (1985).
21. J. E. Sipe, L. Poladian, and C. M. de Sterke, J. Opt. Soc. Am. A 11, 1307 (1994).
22. C. M. de Sterke, D. J. Salinas, and J. E. Sipe, Phys. Rev. E 54, 1969 (1996).
23. J. C. Slater, Phys. Rev. 76, 1592 (1949).
24. C. Kittel and A. H. Mitchell, Phys. Rev. 96, 1488 (1954).
25. J. M. Luttinger and W. Kohn, Phys. Rev. 97, 869 (1955).
26. G. H. Wannier, Rev. Mod. Phys. 34, 645 (1962).
27. N. F. Johnson and P. M. Hui, Phys. Rev. B 48, 10 118 (1993).
28. M. Charbonneau-Lefort, E. Istrate, M. Allard, J. Poon, and E. H. Sargent, Phys. Rev. B 65, 125318 (2002).
29. E. Istrate, M. Charbonneau-Lefort, and E. H. Sargent, Phys. Rev. B 66, 075121 (2002).
30. A. Baldereschi, Phys. Rev. B 1, 4673 (1970).
31. M. Lončar, T. Doll, J. Vučković, and A. Scherer, J. Lightwave Technol. 18, 1402 (2000).
32. P. C. Sercel and K. J. Vahala, Phys. Rev. B 42, 3690 (1990).
33. W. Kohn and J. M. Luttinger, Phys. Rev. 98, 915 (1955).
34. O. Painter and K. Srinivasan, Phys. Rev. B (unpublished).
35. M. Tinkham, Group Theory and Quantum Mechanics, International Series in Pure and Applied Physics (McGaw-Hill, Inc., New York, 1964).
36. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University Press, Princeton, NJ, 1995).
37. O. Painter, K. Srinivasan, J. D. O'Brien, A. Scherer, and P. D. Dapkus, J. Opt. Soc. Am. A 3, S161 (2001).
38. J. E. Sipe, Phys. Rev. E 62, 5672 (2000).
39. It should be noted that the envelope is always a scalar field, regardless of the vector nature of the electric or magnetic field.
40. l,ko are not complete in the space of lattice periodic functions due to the divergenceless nature of the magnetic field. In order to form a complete basis one must include zero frequency unphysical solutions. As we neglect the contribution of remote bands in our analysis, which the zero frequency solutions certainly are, no significant additional error is to be expected.
41. We use the term "mass" here in analogy to solid-state physics where the curvature of the band structure is related to the inverse of an effective elecron mass. The m* as defined here is unitless.