OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 16 — Aug. 6, 2007
  • pp: 10231–10246

Boundary integral method for the challenging problems in bandgap guiding, plasmonics and sensing

Elio Pone, Alireza Hassani, Suzanne Lacroix, Andrei Kabashin, and Maksim Skorobogatiy  »View Author Affiliations

Optics Express, Vol. 15, Issue 16, pp. 10231-10246 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (1612 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A boundary integral method [1] for calculating leaky and guided modes of microstructured optical fibers is presented. The method is rapidly converging and can handle a large number of inclusions (hundreds) of arbitrary geometries. Both, solid and hollow core photonic crystal fibers can be treated efficiently. We demonstrate that for large systems featuring closely spaced inclusions the computational intensity of the boundary integral method is significantly smaller than that of the multipole method. This is of particular importance in the case of hollow core band gap guiding fibers. We demonstrate versatility of the method by applying it to several challenging problems.

© 2007 Optical Society of America

OCIS Codes
(230.4170) Optical devices : Multilayers
(230.7370) Optical devices : Waveguides
(290.4210) Scattering : Multiple scattering
(060.4005) Fiber optics and optical communications : Microstructured fibers

ToC Category:
Photonic Crystal Fibers

Original Manuscript: May 25, 2007
Revised Manuscript: July 24, 2007
Manuscript Accepted: July 25, 2007
Published: July 30, 2007

Elio Pone, Alireza Hassani, Suzanne Lacroix, Andrei Kabashin, and Maksim Skorobogatiy, "Boundary integral method for the challenging problems in bandgap guiding, plasmonics and sensing," Opt. Express 15, 10231-10246 (2007)

Sort:  Year  |  Journal  |  Reset  


  1. Matlab implementation of the code is available at http://www.photonics.phys.polymtl.ca/codes.html
  2. P. Russell "Photonic crystal fibers," Science 299, 358-362 (2003). [CrossRef] [PubMed]
  3. A. Bjarklev, J. Broeng and A.S. Bjarklev "Photonic crystal fibers," Kluwer Academic Publishers, Boston, (2003).
  4. T.A. Burks, J.C. Knight and P.S.J. Russell "Endlessly single-mode photonic crystal fibers," Opt. Lett. 22, 961-963 (1997). [CrossRef]
  5. M.C.J. Large, L. Poladian, G.W. Barton, M.A. van Eijkelenborg, "Microstructured Polymer Optical Fibres," Springer, Sydney, (2007)
  6. A. Ferrando, E. Silvestre, J.J. Miret, P. Andres and M.V. Andres "Full vector analysis of a realistic photonic crystal fiber," Opt. Lett. 24, 276-278 (1999). [CrossRef]
  7. T.M. Monro, D.J. Richardson, N.G.R. Broderick and P.J. Bennett "Holey optical fibers: an efficient modal model," J. Lightwave Technol. 17, 1093-1102 (1999). [CrossRef]
  8. F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, "Complete analysis of the characteristics of propagation into photonic crystal fibers by the finite element method," Opt. Fiber Technol. 6, 181-191 (2000). [CrossRef]
  9. K. Saitoh,M. Koshiba, "Full-Vectorial Imaginary-Distance Beam PropagationMethod Based on a Finite Element Scheme: Application to Photonic Crystal Fibers," IEEE J. Quantum Electron. 38, 297 (2002). [CrossRef]
  10. A. Cucinotta, S. Selleri, L. Vincent and M. Zoboli, "Holey fiber analysis through the finite element method," IEEE Photon. Technol. Lett. 14, 1530-1532 (2002). [CrossRef]
  11. X. Wang, J. Lou, C. Lu, C. L. Zhao andW. T Ang, "Modeling of PCF with multiple reciprocity boundary element method," Opt. Express 12, 961-966 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-961 [CrossRef] [PubMed]
  12. N. Guan, S. Habu, K. Takenaga, K. Himeno and A. Wada "Boundary element method for analysis of holey optical fibers," J. Lightwave Technol. 21, 1787-1792 (2003). [CrossRef]
  13. T. Lu and D. Yevick, "A vectorial boundary element method analysis of integrated optical waveguides," J. Lightwave Technol. 21, 1793-1807 (2003). [CrossRef]
  14. H. Cheng,W. Crutchfield,M. Doery, and L. Greengard, "Fast, accurate integral equation methods for the analysis of photonic crystal fibers I: Theory," Opt. Express 12, 3791-3805 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-16-3791 [CrossRef] [PubMed]
  15. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke and L. C. Botten "Multipole method for microstructured optical fibers. I. Formulation," J. Opt. Soc. Am. B 19, 2322-2330 (2002). [CrossRef]
  16. B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. Martijn de Sterke, and R. C. McPhedran "Multipole method for microstructured optical fibers. II. Implementation and results," J. Opt. Soc. Am. B 19, 2331-2340 (2002). [CrossRef]
  17. S. Campbell, R. C. McPhedran, and C. Martijn de Sterke "Differential multipole method for microstructured optical fibers," J. Opt. Soc. Am. B 21, 1919-1928 (2004). [CrossRef]
  18. M. Skorobogatiy, K. Saitoh, and M. Koshiba, "Coupling between two collinear air-core Bragg fibers," J. Opt. Soc. Am. B 21, 2095-2101 (2004). [CrossRef]
  19. B. T. Kuhlmey, K. Pathmanandavel, and R. C. McPhedran, "Multipole analysis of photonic crystal fibers with coated inclusions," Opt. Express 14, 10851-10864 (2006). [CrossRef] [PubMed]
  20. S. V. Boriskina, T.M. Benson. P. Sewell and A. I. Nosich "Highly efficient full-vectorial integral equation solution for the bound, leaky and complex modes of dielectric waveguides," IEEE J. Sel. Top. Quantum Electron. 8, 1225-1231 (2002). [CrossRef]
  21. D. Colton and R. Kress "Integral equation methods in scattering theory," John Wiley & Sons, New York, (1983).
  22. R. Kress "Linear integral equations," Springer-Verlag, New York, (1989).
  23. S. V. Boriskina, P. Sewell and T. M. Benson "Accurate simulation of two-dimensional optical microcavities with uniquely solvable boundary integral equations and trigonometric Galerkin discretization," J. Opt. Soc. Am. A 21, 393-402 (2004). [CrossRef]
  24. M. Abramowitz and I. A. Stegun "Handbook of mathematical functions," Dover, New York, (1965).
  25. R. Rodriguez-Berral, F. Mesa, and F. Medina, "Systematic and efficient root finder for computing the modal spectrum of planar layered waveguides," Int. J. RF Microw. Comp. Eng. 14, 73-83 (2004). [CrossRef]
  26. M. S. Alam, K. Saitoh, and M. Koshiba "High group birefringence in air-core photonic bandgap fibers," Opt. Lett. 30, 824-826 (2005). [CrossRef] [PubMed]

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