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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 16, Iss. 2 — Feb. 1, 1999
  • pp: 275–285

Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab

O. Painter, J. Vučković, and A. Scherer  »View Author Affiliations

JOSA B, Vol. 16, Issue 2, pp. 275-285 (1999)

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We present a three-dimensional finite-difference time-domain analysis of localized defect modes in an optically thin dielectric slab that is patterned with a two-dimensional array of air holes. The symmetry, quality factor, and radiation pattern of the defect modes and their dependence on the slab thickness are investigated.

© 1999 Optical Society of America

OCIS Codes
(140.5960) Lasers and laser optics : Semiconductor lasers
(250.0250) Optoelectronics : Optoelectronics

O. Painter, J. Vučkovič, and A. Scherer, "Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab," J. Opt. Soc. Am. B 16, 275-285 (1999)

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  1. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
  2. D. Kleppner, “Inhibited spontaneous emission,” Phys. Rev. Lett. 47, 233–236 (1981). [CrossRef]
  3. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059 (1987). [CrossRef] [PubMed]
  4. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).
  5. S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991). [CrossRef] [PubMed]
  6. E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band-structure,” Phys. Rev. Lett. 67, 3380–3383 (1991). [CrossRef] [PubMed]
  7. B. P. V. der Gaag and A. Scherer, Appl. Phys. Lett. 56, 481–483 (1989). [CrossRef]
  8. C. C. Cheng, A. Scherer, V. Arbet-Engels, and E. Yablonovitch, “Lithographic band gap tuning in photonic band gap crystals,” J. Vac. Sci. Technol. B 14, 4110–4119 (1996). [CrossRef]
  9. T. Krauss, Y. P. Song, S. Thoms, C. D. W. Wilkinson, and R. M. D. L. Rue, “Fabrication of 2-D photonic bandgap structures in GaAs/AlGaAs,” Electron. Lett. 30, 1444–1446 (1994). [CrossRef]
  10. G. Feiertag, W. Ehrfeld, H. Freimuth, H. Kolle, H. Lehr, M. Schmidt, M. M. Sigalas, C. M. Soukoulis, G. Kiriakidis, T. Pederson, J. Kuhl, and W. Koenig, “Fabrication of photonic crystals by deep x-ray lithography,” Appl. Phys. Lett. 71, 1441–1443 (1997). [CrossRef]
  11. K. Inoue, M. Wada, K. Sakoda, M. Hayashi, T. Fukushima, and A. Yamanaka, “Near-infrared photonic band gap of two-dimensional triangular air-rod lattices as revealed by transmittance measurement,” Phys. Rev. B 53, 1010–1013 (1996). [CrossRef]
  12. J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-cavity surface-emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. QE-27, 1332–1346 (1996).
  13. A. F. J. Levi, S. L. McCall, S. J. Pearton, and R. A. Logan, “Room temperature operation of submicrometre radius disk laser,” Electron. Lett. 29, 1666–1667 (1993). [CrossRef]
  14. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode lasers,” Appl. Phys. Lett. 60, 289–291 (1992). [CrossRef]
  15. D. Y. Chu and S.-T. Ho, “Spontaneous emission from excitons in cylindrical dielectric waveguides and the spontaneous-emission factor of microcavity ring lasers,” J. Opt. Soc. Am. B 10, 381–390 (1993). [CrossRef]
  16. 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, “Photonic-bandgap microcavities in optical waveguides,” Nature (London) 390, 143–145 (1997). [CrossRef]
  17. J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, R. M. Joseph, A. Taflove, C. W. Tu, and S. T. Ho, “Nanofabrication of 1-D photonic bandgap structures along a photonic wire,” IEEE Photonics Technol. Lett. 8, 491–493 (1996). [CrossRef]
  18. T. F. Krauss, B. Vögele, C. R. Stanley, and R. M. D. L. Rue, “Waveguide microcavity based on photonic microstructures,” IEEE Photonics Technol. Lett. 9, 176–178 (1997). [CrossRef]
  19. T. F. Krauss, R. M. D. L. Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature (London) 383, 699–702 (1996). [CrossRef]
  20. J. O’Brien, O. Painter, C. C. Cheng, R. Lee, A. Scherer, and A. Yariv, “Lasers incorporating 2D photonic bandgap mirrors,” Electron. Lett. 32, 2243–2244 (1996). [CrossRef]
  21. T. Baba and T. Matsuzaki, “Fabrication and photoluminescence of GaInAsP/InP 2D photonic crystals,” Jpn. J. Appl. Phys., Part 2 35, 1348–1352 (1996). [CrossRef]
  22. T. Hamano, H. Hirayama, and Y. Aoyyagi, “Optical characterization of GaAs 2D photonic bandgap crystal fabricated by selective MOVPE,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 528–529.
  23. T. Baba, “Photonic crystals and microdisk cavities based on GaInAsP-InP system,” IEEE J. Sel. Topics Quantum Electron. 3, 808–830 (1997). [CrossRef]
  24. P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996). [CrossRef]
  25. H. Yokoyama, “Physics and device application of optical microcavities,” Science 256, 66–70 (1992). [CrossRef] [PubMed]
  26. I. Schnitzer, E. Yablonovitch, A. Scherer, and T. J. Gmitter, in Photonic Band Gaps and Localization (Kluwer Academic, Dordrecht, The Netherlands, 1996), pp. 369–378.
  27. K. S. Yee, “Numerical solution of boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966). [CrossRef]
  28. G. Björk and Y. Yamamoto, “Analysis of semiconductor microcavity lasers using rate equations,” IEEE J. Quantum Electron. QE-27, 2386–2396 (1991). [CrossRef]
  29. D. J. Heinzen, J. J. Childs, J. E. Thomas, and M. S. Feld, “Enhanced and inhibited visible spontaneous emission by atoms in a confocal resonator,” Phys. Rev. Lett. 58, 1320–1323 (1987). [CrossRef] [PubMed]
  30. L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, New York, 1995).
  31. O. Painter, R. Lee, A. Yariv, A. Scherer, and J. O’Brien, “Photonic bandgap membrane microresonator,” in Integrated Photonics Research, Vol. 4 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 221–223.
  32. Y. Zou, J. S. Osinski, P. Grodzinski, P. D. Dapkus, W. Rideout, W. F. Sharfim, and F. D. Crawford, “Experimental verification of strain benefits in 1.5 μm semiconductor lasers by carrier lifetime and gain measurements,” IEEE Photonics Technol. Lett. 4, 1315–1318 (1992). [CrossRef]
  33. S. Adachi, “Material parameters of In1−xGaxAsyP1−y and related binaries,” J. Appl. Phys. 53, 8775–8792 (1982). [CrossRef]
  34. M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: the triangular lattice,” Phys. Rev. B 44, 8565–8571 (1991). [CrossRef]
  35. D. M. Atkin, P. S. J. Russell, T. A. Birks, and P. J. Roberts, “Photonic band structure of guided Bloch modes in high index films fully etched through with periodic microstructure,” J. Mod. Opt. 43, 1035–1053 (1996). [CrossRef]
  36. C. T. Chan, Q. L. Yu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51, 16, 635–16, 642 (1995). [CrossRef]
  37. G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. 23, 377–382 (1981). [CrossRef]
  38. P. S. J. Russell, D. M. Atkin, and T. A. Birks, in Microcavi ties and Photonic Bandgaps (Kluwer Academic, Dordrecht, The Netherlands, 1996), pp. 203–218.
  39. K. Chamberlain and L. Gordon, “Modeling good conductors using the finite-difference, time-domain technique,” IEEE Trans. Electromagn. Compat. 37, 210–216 (1995). [CrossRef]
  40. B. D’Urso, O. Painter, J. O’Brien, T. Tombrello, A. Scherer, and A. Yariv, “Modal reflectivity in finite-depth two-dimensional photonic-crystal microcavities,” J. Opt. Soc. Am. B 15, 1155–1159 (1998). [CrossRef]
  41. D. H. Choi and W. J. R. Hoefer, “The finite-difference-time-domain method and its application to eigenvalue problems,” IEEE Trans. Microwave Theory Tech. 34, 1464–1469 (1986). [CrossRef]
  42. K. Sakoda, “Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic crystals,” Phys. Rev. B 52, 7982–7986 (1995). [CrossRef]
  43. M. Tinkham, Group Theory and Quantum Mechanics (McGraw-Hill, New York, 1964).
  44. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962).
  45. O. Painter, J. Vučković, and A. Scherer, in an unpublished study, analyze similar microcavities, as presented in this paper, although with different bottom substrates of the waveguide and with increasing number of photonic crystal layers. Calculations of QT, Q, and Q versus frequency of the defect mode with seven layers of photonic crystal shows a smooth peak for all the Q’s, with none of the structure present for only three layers.

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