OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry M. Van Driel
  • Vol. 24, Iss. 9 — Sep. 1, 2007
  • pp: 2249–2258

Numerical stable method for the analysis of Bloch waves in a general one-dimensional photonic crystal cavity

W. J. Hsueh and J. C. Lin  »View Author Affiliations


JOSA B, Vol. 24, Issue 9, pp. 2249-2258 (2007)
http://dx.doi.org/10.1364/JOSAB.24.002249


View Full Text Article

Enhanced HTML    Acrobat PDF (603 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We present a numerical stable method to accurately solve band structures and the eigenvalues of a multilayer-basis photonic crystal cavity. We derive a set of band-edge equations to determine the band structures rather than use the cosine of the Bloch phase, which is traditionally used but may induce numerical instability. Moreover, two novel formulas are proposed to solve the eigenvalues for the cavity modes. The eigenvalues solved by the method are accurate without including the spurious solutions. Thus, it is not required to eliminate the spurious solutions from the results. Finally, numerical examples of binary and Fibonacci multilayers in each cell are studied to demonstrate that this method has better numerical stability in computing the band structure and cavity modes than traditional methods.

© 2007 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(130.2790) Integrated optics : Guided waves

ToC Category:
Photonic Crystals

History
Original Manuscript: March 9, 2007
Revised Manuscript: May 27, 2007
Manuscript Accepted: May 28, 2007
Published: August 20, 2007

Citation
W. J. Hsueh and J. C. Lin, "Numerical stable method for the analysis of Bloch waves in a general one-dimensional photonic crystal cavity," J. Opt. Soc. Am. B 24, 2249-2258 (2007)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-24-9-2249


Sort:  Year  |  Journal  |  Reset  

References

  1. E. Istrate and E. H. Sargent, "Photonic crystal heterostructures and interfaces," Rev. Mod. Phys. 78, 455-481 (2006). [CrossRef]
  2. P. R. Berman, Cavity Quantum Electrodynamics (Academic, 1994).
  3. J. Rarity and C. Weisbuch, Microcavities and Photonic Bandgaps: Physics and Applications (Kluwer, 1996).
  4. Y. Yamamoto, S. Machida, K. Igeta, and G. Bjork, "Microcavity semiconductor laser with enhanced spontaneous emission," Phys. Rev. A 44, 657-668 (1991). [CrossRef] [PubMed]
  5. 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 390, 143-145 (1997). [CrossRef]
  6. Y. Zhang and B. Y. Gu, "Aperiodic photonic quantum-well structures for multiple channeled filtering at arbitrary preassigned frequencies," Opt. Express 12, 5910-5915 (2004). [CrossRef] [PubMed]
  7. G. Ma, J. Shen, Z. Zhang, Z. Hua, and A. H. Tang, "Ultrafast all-optical switching in one-dimensional photonic crystal with two defect," Opt. Express 14, 858-865 (2006). [CrossRef] [PubMed]
  8. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett. 24, 711-713 (1999). [CrossRef]
  9. N. H. Liu, "Defect modes of stratified dielectric media," Phys. Rev. B 55, 4097-4101 (1997). [CrossRef]
  10. H. Y. Sang, Z. Y. Li, and B. Y. Gu, "Propagation properties of planar Bragg waveguides studied by an analytical Bloch-mode method," J. Appl. Phys. 98, 043114 (2005). [CrossRef]
  11. K. M. Leung, "Defect modes in photonic band structures: a Green's function approach using vector Wannier functions," J. Opt. Soc. Am. B 10, 303-306 (1993). [CrossRef]
  12. D. R. Smith, R. Dalichaouch, N. Kroll, and S. Schultz, "Photonic band structure and defects in one and two dimensions," J. Opt. Soc. Am. B 10, 314-321 (1993). [CrossRef]
  13. G. Liang, P. Han, and H. Wang, "Narrow frequency and sharp angular defect mode in one-dimensional photonic crystals from a photonic heterostructure," Opt. Lett. 29, 192-194 (2004). [CrossRef] [PubMed]
  14. L. G. Wang and S. Y. Zhu, "Giant lateral shift of a light beam at the defect mode in one-dimensional photonic crystals," Opt. Lett. 31, 101-103 (2006). [CrossRef] [PubMed]
  15. J. A. Gaspar-Armenta and F. Villa, "Band-structure properties of one-dimensional photonic crystals under the formalism of equivalent systems," J. Opt. Soc. Am. B 21, 405-412 (2004). [CrossRef]
  16. H. Nemec, L. Duvillaret, F. Quemeneur, and P. Kuzel, "Defect modes caused by twinning in one-dimensional photonic crystals," J. Opt. Soc. Am. B 21, 548-553 (2004). [CrossRef]
  17. H. S. Sözüer and K. Sevim, "Robustness of one-dimensional photonic band gaps under random variations of geometrical parameters," Phys. Rev. B 72, 195101 (2005). [CrossRef]
  18. H. Miyazaki, Y. Jimba, and T. Watanabe, "Multiphotonic lattices and Stark localization of electromagnetic fields in one dimension," Phys. Rev. A 53, 2877-2880 (1996). [CrossRef] [PubMed]
  19. M. V. Erementchouk, L. I. Deych, and A. A. Lisyansky, "Optical properties of one-dimensional photonic crystals based on multiple-quantum-well structures," Phys. Rev. B 71, 235335 (2005). [CrossRef]
  20. L. M. Zhao and B. Y. Gu, "Enhanced second-hamonic generation for multiple wavelengths by defect modes in one-dimensional photonic crystals," Opt. Lett. 31, 1510-1512 (2006). [CrossRef] [PubMed]
  21. P. Tran, "Optical limiting and switching of short pulses by use of a nonlinear photonic bandgap structure with a defect," J. Opt. Soc. Am. B 14, 2589-2595 (1997). [CrossRef]
  22. J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, "Optical necklace states in Anderson localized 1D systems," Phys. Rev. Lett. 94, 113903 (2005). [CrossRef] [PubMed]
  23. L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, "Light transport through the band-edge states of Fibonacci quasicrystals," Phys. Rev. Lett. 90, 055501 (2003). [CrossRef] [PubMed]
  24. D. Lusk, I. Abdulhalim, and F. Placido, "Omnidirectional reflection from Fibnacci quasi-periodic one-dimensional photonic crystal," Opt. Commun. 198, 273-279 (2001). [CrossRef]
  25. J. M. Cervero and A. Rodriguez, "Infinite chain of N different deltas: a simple model for a quantum wire," Eur. Phys. J. B 30, 239-251 (2002). [CrossRef]
  26. F. Szmulowicz, "Tangent formulation of the Kronig-Penney problem for N-period layered systems with application to photonic crystals," Phys. Rev. B 72, 235103 (2005). [CrossRef]
  27. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1988).
  28. P. Yeh, A. Yariv, and C. S. Hong, "Electromagnetic propagation in periodic stratified media. I. General theory," J. Opt. Soc. Am. 67, 423-438 (1977). [CrossRef]
  29. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998). [CrossRef] [PubMed]
  30. D. Felbacq, B. Guizal, and F. Zolla, "Wave propagation in one-dimensional photonic crystals," Opt. Commun. 152, 119-126 (1998). [CrossRef]
  31. J. Mendialdua, A. Rodriguez, M. More, A. Akjouj, and L. Dobrzynski, "Bulk and surface phonon polaritons in three-layer superlattices," Phys. Rev. B 50, 14605-14608 (1994). [CrossRef]
  32. K. C. Huang, E. Lidorikis, X. Jiang, J. D. Joannopoulos, and K. A. Nelson, "Nature of lossy Bloch states in polaritonic photonic crystals," Phys. Rev. B 69, 195111 (2004). [CrossRef]
  33. Z. Y. Li and L. L. Lin, "Photonic band structures solved by a plane-wave-based transfer-matrix method," Phys. Rev. E 67, 046607 (2003). [CrossRef]
  34. S. Mishra and S. Satpathy, "One-dimensional photonic crystal: the Kronig-Penney model," Phys. Rev. B 68, 045121 (2003). [CrossRef]
  35. F. Ramos-Mendieta and R. Halevi, "Electromagnetic surface modes of a dielectric superlattice: the supercell method," J. Opt. Soc. Am. B 14, 370-381 (1997). [CrossRef]
  36. A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
  37. W. J. Hsueh and J. C. Lin, "Stable and accurate method for modal analysis of multilayer waveguides using graph approach," J. Opt. Soc. Am. A 24, 825-830 (2007). [CrossRef]
  38. W. Mayeda, Graph Theory (Wiley, 1972).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited