OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 23 — Nov. 13, 2006
  • pp: 11128–11141

Full-vectorial finite element method in a cylindrical coordinate system for loss analysis of photonic wire bends

Kuniaki Kakihara, Naoya Kono, Kunimasa Saitoh, and Masanori Koshiba  »View Author Affiliations

Optics Express, Vol. 14, Issue 23, pp. 11128-11141 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (313 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



This paper presents a new full-vectorial finite-element method in a local cylindrical coordinate system, to effectively analyze bending losses in photonic wires. The discretization is performed in the cross section of a three-dimensional curved waveguide, using hybrid edge/nodal elements. The solution region is truncated by anisotropic, perfectly matched layers in the cylindrical coordinate system, to deal properly with leaky modes of the waveguide. This approach is used to evaluate bending losses in silicon wire waveguides. The numerical results of the present approach are compared with results calculated with an equivalent straight waveguide approach and with reported experimental data. These comparisons together demonstrate the validity of the present approach based on the cylindrical coordinate system and also clarifies the limited validity of the equivalent straight waveguide approximation.

© 2006 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(130.0130) Integrated optics : Integrated optics
(230.7370) Optical devices : Waveguides

ToC Category:
Integrated Optics

Original Manuscript: August 10, 2006
Revised Manuscript: October 30, 2006
Manuscript Accepted: November 1, 2006
Published: November 13, 2006

Kuniaki Kakihara, Naoya Kono, Kunimasa Saitoh, and Masanori Koshiba, "Full-vectorial finite element method in a cylindrical coordinate system for loss analysis of photonic wire bends," Opt. Express 14, 11128-11141 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. 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]
  2. B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998). [CrossRef]
  3. K. K. Lee, D. R. Lim, L. C. Kimerling, J. Shin, and F. Cerrina, "Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction," Opt. Lett. 26, 1888-1890 (2001). [CrossRef]
  4. C. Li, N. Ma, and A. W. Poon, "Waveguide-coupled octagonal microdisk channel add-drop filters," Opt. Lett. 29, 471-473 (2004). [CrossRef] [PubMed]
  5. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431, 1081-1084 (2004). [CrossRef] [PubMed]
  6. T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Top. Quantum Electron. 11, 232-240 (2005). [CrossRef]
  7. K. Sasaki, F. Ohno, A. Motegi, and T. Baba, "Arrayed waveguide grating of 70×60 μm2 size based on Si photonic wire waveguides," Electron. Lett. 41, 801-802 (2005). [CrossRef]
  8. R. L. Espinola, J. I. Dadap, R. M. OsgoodJr., S. J. McNab, and Y. A. Vlasov, "C-band wavelength conversion in silicon photonic wire waveguides," Opt. Express 13, 4341-4349 (2005). [CrossRef] [PubMed]
  9. G. Roelkens, J. Brouckaert, D. Taillaert, P. Dumon, W. Bogaerts, D. Van Thourhout, R. Baets, R. Nötzel, and M. Smit, "Integration of InP/InGaAsP photodetectors onto silicon-on-insulator waveguide circuits," Opt. Express 13, 10102-10108 (2005). [CrossRef] [PubMed]
  10. A. Sakai, G. Hara, and T. Baba, "Propagation characteristics of ultrahigh-Δ optical waveguide on silicon-on-insulator substrate," Jpn. J. Appl. Phys. 40, L383-L385 (2001). [CrossRef]
  11. Y. A. Vlasov and S. J. McNab, "Losses in single-mode silicon-on-insulator strip waveguides and bends," Opt. Express 12, 1622-1631 (2004). [CrossRef] [PubMed]
  12. R. L. Espinola, R. U. Ahmad, F. Pizzuto, M. J. Steel, and R. M. Osgood, Jr., "A study of high-index-contrast 90° waveguide bend structures," Opt. Express 8, 517-528 (2001). [CrossRef] [PubMed]
  13. A. Sakai, T. Fukazawa, and T. Baba, "Estimation of polarization crosstalk at a micro-bend in Si-photonic wire waveguide," J. Lightwave Technol. 22, 520-525 (2004). [CrossRef]
  14. A. Jiang, S. Shi, G. Jin, and D. W. Prather, "Performance analysis of three dimensional high index contrast dielectric waveguides," Opt. Express 12, 633-643 (2004). [CrossRef] [PubMed]
  15. E. Cassan, L. Vivien, and S. Laval, "Polarization-independent 90°-turns in single-mode micro-waveguides on silicon-on-insulator wafers for telecommunication wavelengths," Opt. Commun. 235, 83-88 (2004). [CrossRef]
  16. S. Kim and A. Gopinath, "Vector analysis of optical dielectric waveguide bends using finite-difference method," J. Lightwave Technol. 14, 2085-2092 (1996). [CrossRef]
  17. N. N. Feng, G. R. Zhou, C. Xu, and W. P. Huang, "Computation of full-vector modes for bending waveguide using cylindrical perfectly matched layers," J. Lightwave Technol. 20, 1976-1980 (2002). [CrossRef]
  18. D. Dai and S. He, "Analysis of characteristics of bent rib waveguides," J. Opt. Soc. Am. A 21, 113-121 (2004). [CrossRef]
  19. T. Yamamoto and M. Koshiba, "Numerical analysis of curvature loss in optical waveguides by the finite-element method," J. Lightwave Technol. 11, 1579-1583 (1993). [CrossRef]
  20. F. A. Malek, S. S. A. Obayya, B. M. A. Rahman, J. B. Davies, F. A. Fernandez, J. M. Heaton, and K. T. V. Grattan, "Full vectorial finite-element analysis of sharp optical waveguide corners," IEEE Photon. Technol. Lett. 14, 1527-1529 (2002). [CrossRef]
  21. Y. Tsuji and M. Koshiba, "Complex modal analysis of curved optical waveguides using a full-vectorical finite element method with perfectly matched layer boundary conditions," Electromagnetics 24, 39-48 (2004). [CrossRef]
  22. S. S. A. Obayya, B. M. A. Rahman, and K. T. V. Grattan, "Full vectorial finite element modal solution of curved optical waveguides," Laser Phys. Lett. 2, 131-136 (2004). [CrossRef]
  23. W. W. Lui, C. L. Xu, T. Hirono, K. Yokoyama, and W. P. Huang, "Full-vectorial wave propagation in semiconductor optical bending waveguides and equivalent straight waveguide approximations," J. Lightwave Technol. 16, 910-914 (1998). [CrossRef]
  24. J. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comp. Phys. 114, 185-200 (1994). [CrossRef]
  25. F. L. Teixeira and W. C. Chew, "PML-FDTD in cylindrical and spherical grids," IEEE Microw. Guid. Wave Lett. 7, 285-287 (1997). [CrossRef]
  26. F. L. Teixeira and W. C. Chew, "Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates," IEEE Microw. Guid. Wave Lett. 7, 371-373 (1997). [CrossRef]
  27. F. L. Teixeira and W. C. Chew, "General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media," IEEE Microw. Guid. Wave Lett. 8, 223-225 (1998). [CrossRef]
  28. M. Koshiba and Y. Tsuji, "Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems," J. Lightwave Technol. 18, 737-743 (2000). [CrossRef]
  29. Y. Cheng, W. Lin, and Y. Fujii, "Local field analysis of bent graded-index planar waveguides," J. Lightwave Technol. 8, 1461-1469 (1990). [CrossRef]
  30. W. C. Chew and W. Weedon, "A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates," Microw. Opt. Technol. Lett. 7, 599-604 (1994). [CrossRef]
  31. J. Jin, The Finite Element Method in Electromagnetics (John Wiley & Sons, Inc., 1993), Chap. 4.
  32. I. S. Duff and J. K. Reid, "The multifrontal solution of indefinite sparse symmetric linear equations," ACM Trans. Math. Softw. 9, 302-325 (1983). [CrossRef]
  33. Y. Tsuchida, K. Saitoh, and M. Koshiba, "Design and characterization of single-mode holey fibers with low bending losses," Opt. Express 13, 4770-4779 (2005). [CrossRef] [PubMed]
  34. S. Mokhov, R. El-Ganainy, and D. N. Christodoulides, "Power circulation via negative energy-flux wormholes in optical nanowaveguides," Opt. Express 14, 3255-3262 (2006). [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