OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 13 — Jun. 26, 2006
  • pp: 6035–6054

Modified step-theory for investigating mode coupling mechanism in photonic crystal waveguide taper

E. H. Khoo, A. Q. Liu, J. H. Wu, J. Li, and D. Pinjala  »View Author Affiliations


Optics Express, Vol. 14, Issue 13, pp. 6035-6054 (2006)
http://dx.doi.org/10.1364/OE.14.006035


View Full Text Article

Enhanced HTML    Acrobat PDF (773 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In this paper, the mathematical model of the modified step-theory is derived based on the platform of two-dimensional photonic crystal structure that is infinitely long in third dimension. The mode coupling mechanism of photonic crystal tapers is theoretically studied using the modified step-theory. The model is verified by comparing the transmission spectrum obtained for the input/output defect coupler where it shows a good match of less than 5% discrepancy. The modified step-theory is applied to different taper structures to investigate the power loss during the transmission. The power loss at the relative position of the taper provides an explanation as to which taper designs give the highest coupling efficiency.

© 2006 Optical Society of America

OCIS Codes
(130.0130) Integrated optics : Integrated optics
(230.7380) Optical devices : Waveguides, channeled
(250.5300) Optoelectronics : Photonic integrated circuits

ToC Category:
Integrated Optics

History
Original Manuscript: March 7, 2006
Revised Manuscript: May 19, 2006
Manuscript Accepted: June 4, 2006
Published: June 26, 2006

Citation
E. H. Khoo, A. Q. Liu, J. H. Wu, J. Li, and D. Pinjala, "Modified step-theory for investigating mode coupling mechanism in photonic crystal waveguide taper," Opt. Express 14, 6035-6054 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-13-6035


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, "Photonic crystals: putting a new twist on light," Nature,  386, 143 (1997) [CrossRef]
  2. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).
  3. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, "Channel add-drop filters in photonic crystal," Opt. Express 3, 4-11 (1998). [CrossRef] [PubMed]
  4. M. Bayindir, B. Temelkuran, and E. Ozbar, "Photonic-crystal-based beam splitter," Appl. Phys. Lett. 77, 3902-3904 (2000). [CrossRef]
  5. Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, "Design of a channel drop filter by using a donor-type cavity with high-quality factor in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 82, 1341-1343 (2003). [CrossRef]
  6. S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, "Linear waveguide in photonic crystal slab," Phys. Rev. B 62, 8212-8222 (2000). [CrossRef]
  7. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High Transmission through sharp bends in Photonic Crystal Waveguide," Phys. Rev. Lett. 77, 3787-3790 (1996). [CrossRef] [PubMed]
  8. T. D. Happ, M. Kamp, and A. Forchel, "Photonic crystal tapers for ultracompact mode conversion," Opt. Lett. 26, 1102-1104 (2001). [CrossRef]
  9. S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos "Adiabatic theorem and continuous coupled mode theory for efficient taper transition," Phys. Rev. E 66, 066608 (2002). [CrossRef]
  10. P. Bienstman, S. Assefa, S. G. Johnson, J. D. Joannopoulos, G. S. Petrich, and L. A. Kolodziejski, "Taper structures for coupling into photonic crystal slab waveguide," Opt. Soc. Am. B 20, 1817-1821 (2003). [CrossRef]
  11. P. Pottier, I. Ntakis, and R. M. De La Rue, " Photonic crystal continuous taper for low-loss direct coupling into photonic crystal channel waveguides and further device functionality," Opt. Commun. 223, 339-347 (2003). [CrossRef]
  12. E. H. Khoo, A. Q. Liu, and J. H. Wu, " Nonuniform photonic crystal taper for high efficient mode coupling," Opt. Express 13, 7748-7759 (2005). [CrossRef] [PubMed]
  13. Ph. Lalanne, and A. Talneau, "Modal conversion with artificial materials for photonic-crystal waveguide," Opt. Express 10, 354-359 (2002). [PubMed]
  14. M. Palamaru, and Ph. Lalanne, "Photonic crystal waveguides: out-of-plane losses and adiabatic mode conversion," Appl. Phys. Lett. 78, 1466-1468 (2001). [CrossRef]
  15. M. Skorobogatiy, S. G. Johnson, S. A. Jacobs, and Y. Fink, "Dielectric profile variations in high-index-contrast waveguides, coupled mode theory, and perturbation expansions," Phys. Rev. E 67, 046613 (2003). [CrossRef]
  16. M. Skorobogatiy, "Modeling the impact of imperfections in high-index-contrast photonic crystal waveguides," Phys. Rev. E 70, 046609 (2004). [CrossRef]
  17. A. A Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. Martin de Sterke, "Effects of disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 60, 6118 (1999). [CrossRef]
  18. A. A Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. Martin de Sterke, "Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 62, 5711 (2000). [CrossRef]
  19. M. Koshiba, Y. Tsuji, and M. Hikari, "Time-domain beam propagation method and its application to photonic crystal circuits," J. Lightwave Technology 18, 102-110 (2000). [CrossRef]
  20. T. Fujisawa, and M. Koshiba, "Time-domain beam propagation method for nonlinear optical propagation analysis and its application to photonic Crystal circuits," J. Lightwave Technol. 22, 684-691 (2004). [CrossRef]
  21. A. F. Milton, and W. K. Burns, "Mode Conversion in planar dielectric separating waveguides," IEEE J. Quantum Electron. 11, 32-39 (1975). [CrossRef]
  22. A. R. Nelson, "Coupling optical waveguides by tapers," Appl. Opt. 14, 3012-3015 (1975). [PubMed]
  23. D. Marcuse, Theory of Dielectric Optical Waveguide (Academic Press, San Diego, 1991).
  24. O. Mitomi, K. Kasaya, and H. Miyazawa, "Design of a single-mode tapered waveguide for low-loss chip-to-fiber coupling," IEEE J. Quantum Electron. 30, 1787-1793 (1994). [CrossRef]
  25. J. David Jackson, Classical Electrodynamics (John Wiley & Sons, United States of America, 1998).
  26. A. Mekis, S. Fan, and J. D. Joannopoulos, "Bound states in photonic crystal waveguides and waveguide bends," Phys. Rev. B 58, 4809-4817 (1998). [CrossRef]
  27. M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, "Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals," Phys. Rev. B 64, 155113 (2001). [CrossRef]
  28. S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004). [CrossRef]
  29. P. Bienstman, and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. and Quantum Electron.  33, 327-341 (2001). [CrossRef]
  30. A. Lavrinenko, P. Borel, L. Frandsen, M. Thorhauge, A. Harpøth, M. Kristensen, T. Niemi, and H. Chong, "Comprehensive FDTD modelling of photonic crystal waveguide components," Opt. Express 12, 234-248 (2003). [CrossRef]

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