OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 18 — Sep. 3, 2007
  • pp: 11042–11060

Theoretical and computational concepts for periodic optical waveguides

G. Lecamp, J. P. Hugonin, and P. Lalanne  »View Author Affiliations

Optics Express, Vol. 15, Issue 18, pp. 11042-11060 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (922 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present a general, rigorous, modal formalism for modeling light propagation and light emission in three-dimensional (3D) periodic waveguides and in aggregates of them. In essence, the formalism is a generalization of well-known modal concepts for translation-invariant waveguides to situations involving stacks of periodic waveguides. By surrounding the actual stack by perfectly-matched layers (PMLs) in the transverse directions, reciprocity considerations lead to the derivation of Bloch-mode orthogonality relations in the sense of E×H products, to the normalization of these modes, and to the proof of the symmetrical property of the scattering matrix linking the Bloch modes. The general formalism, which rigorously takes into account radiation losses resulting from the excitation of radiation Bloch modes, is implemented with a Fourier numerical approach. Basic examples of light scattering like reflection, transmission and emission in periodic-waveguides are accurately resolved.

© 2007 Optical Society of America

OCIS Codes
(130.2790) Integrated optics : Guided waves
(260.2110) Physical optics : Electromagnetic optics
(350.7420) Other areas of optics : Waves

ToC Category:
Physical Optics

Original Manuscript: March 6, 2007
Revised Manuscript: May 16, 2007
Manuscript Accepted: May 16, 2007
Published: August 20, 2007

G. Lecamp, J. P. Hugonin, and P. Lalanne, "Theoretical and computational concepts for periodic optical waveguides," Opt. Express 15, 11042-11060 (2007)

Sort:  Year  |  Journal  |  Reset  


  1. B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, E. Seiferth, D. Gill, V. Van, O. King and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004). [CrossRef]
  2. J. D. Joannopoulos, R. Meade and J. Winn, Photonic crystals: molding the flow of light (Princeton University Press NJ, 1995).
  3. S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999). [CrossRef]
  4. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001). [CrossRef] [PubMed]
  5. M. Soljacic and J. D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals," Nat. Mat. 3, 211-219 (2004). [CrossRef]
  6. Y. A. Vlasov, M. O'Boyle, H. F. Hamann and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005). [CrossRef] [PubMed]
  7. A. W. Snyder and J. D. Love, Optical waveguide theory (Chapman and Hall NY, 1983).
  8. C. Vassallo, Optical waveguide concepts (Elsevier Amsterdam, 1991).
  9. R. Scarmozzino, A. Gopinath, R. Pregla and S. Helfert, "Numerical techniques for modeling guided-wave photonic devices," IEEE J. Sel. Top. Quantum Electron. 6, 150-162 (2000). [CrossRef]
  10. P. Bienstman, Rigorous and efficient modeling of wavelength scale photonic components (Gent University PhD thesis in English, 2001).
  11. P. Bienstman, "Two-stage mode finder for waveguides with a 2D cross-section," Opt. Quantum Electron. 36, 5-14 (2004). [CrossRef]
  12. E. Silberstein, P. Lalanne, J. P. Hugonin and Q. Cao, "Use of grating theories in integrated optics," J. Opt. Soc. Am. A 18, 2865-2875 (2001). [CrossRef]
  13. C. Ciminelli, F. Peluso and M. N. Armenise, "Modeling and design of two-dimensional guided-wave photonic band-gap devices," J. Lightwave Technol. 23, 886-901 (2005). [CrossRef]
  14. J. M. Elson, "Scattering losses from planar waveguides with material inhomogeneity," Waves Random Media 13, 95-105 (2003). [CrossRef]
  15. 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 transitions in photonic crystals," Phys. Rev. E 66, 066608 (2002). [CrossRef]
  16. G. Lecamp, P. Lalanne, J. P. Hugonin and J. M. Gerard, "Energy transfer through laterally confined Bragg mirrors and its impact on pillar microcavities," IEEE J. Quantum Electron. 41, 1323-1329 (2005). [CrossRef]
  17. P. Lalanne and J. P. Hugonin, "Bloch-wave engineering for high-Q, small-V microcavities," IEEE J. Quantum Electron. 39, 1430-1438 (2003). [CrossRef]
  18. L. C. Botten, T. P. White, A. A. Asatryan, T. N. Langtry, C. M. de Sterke and R. C. McPhedran, "Bloch mode scattering matrix methods for modeling extended photonic crystal structures. I. Theory," Phys. Rev. E 70, 056606 (2004). [CrossRef]
  19. K. Dossou, M. A. Byrne and L. C. Botten, "Finite element computation of grating scattering matrices and application to photonic crystal band calculations," J. Comput. Phys. 219, 120-143 (2006). [CrossRef]
  20. B. Gralak, S. Enoch and G. Tayeb, "From scattering or impedance matrices to Bloch modes of photonic crystals," J. Opt. Soc. Am. A 19, 1547-1554 (2002). [CrossRef]
  21. D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002). [CrossRef]
  22. S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-190 (2001). [CrossRef] [PubMed]
  23. P. Lalanne, "Electromagnetic analysis of photonic crystal waveguides operating above the light cone," IEEE J. Quantum Electron. 38, 800-804 (2002). [CrossRef]
  24. S. F. Helfert, "Determination of Floquet modes in asymmetric periodic structures," Opt. Quantum Electron. 37, 185-197 (2005). [CrossRef]
  25. A. Chutinan and S. Noda, "Waveguides and waveguide bends in two-dimensional photonic crystal slabs," Phys. Rev. B 62, 4488-4492 (2000). [CrossRef]
  26. L. C. Andreani and D. Gerace, "Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method," Phys. Rev. B 73, 235114 (2006). [CrossRef]
  27. S. Hughes, "Enhanced single-photon emission from quantum dots in photonic crystal waveguides and nanocavities," Opt. Lett. 29, 2659-2661 (2004). [CrossRef] [PubMed]
  28. S. Hughes, L. Ramunno, J. F. Young and J. E. Sipe, "Extrinsic optical scattering loss in photonic crystal waveguides: Role of fabrication disorder and photon group velocity," Phys. Rev. Lett. 94, 033903 (2005). [CrossRef] [PubMed]
  29. D. Gerace and L. C. Andreani, "Effects of disorder on propagation losses and cavity Q-factors in photonic crystal slabs," Photon. Nanostruct. Fundam. Appl. 3, 120-128 (2005). [CrossRef]
  30. R. K. Chang and A. J. Campillo, Optical processes in microcavities (World Scientific London, 1996). [CrossRef]
  31. W. C. Chew and W. H. Weedon, "A 3D perfectly matched medium from modified Maxwells equations with stretched coordinates," Microwave Opt. Technol. Lett. 7, 599-604 (1994). [CrossRef]
  32. Z. S. Sacks, D. M. Kingsland, R. Lee and J. F. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition," IEEE Trans. Antennas Propag. 43, 1460-1463 (1995). [CrossRef]
  33. W. Kuang, W. J. Kim, A. Mock and J. O'Brien, "Propagation loss of line-defect photonic crystal slab waveguides," IEEE J. Sel. Top. Quantum Electron. 12, 1183-1195 (2006). [CrossRef]
  34. Y. Xu, R. K. Lee and A. Yariv, "Quantum analysis and the classical analysis of spontaneous emission in a microcavity," Phys. Rev. A 61, 033807 (2000). [CrossRef]
  35. R. C. McPhedran, L. C. Botten, J. McOrist, A. A. Asatryan, C. M. de Sterke and N. A. Nicorovici, "Density of states functions for photonic crystals," Phys. Rev. E 69, 016609 (2004). [CrossRef]
  36. J. P. Hugonin and P. Lalanne, "Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization," J. Opt. Soc. Am. A 22, 1844-1849 (2005). [CrossRef]
  37. M. G. Moharam, E. B. Grann, D. A. Pommet and T. K. Gaylord, "Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings," J. Opt. Soc. Am. A 12, 1068-1076 (1995). [CrossRef]
  38. L. F. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings," J. Opt. Soc. Am. A 13, 1024-1035 (1996). [CrossRef]
  39. Q. Cao, P. Lalanne and J. P. Hugonin, "Stable and efficient Bloch-mode computational method for one-dimensional grating waveguides," J. Opt. Soc. Am. A 19, 335-338 (2002). [CrossRef]
  40. S. F. Helfert, "Numerical stable determination of Floquet-modes and the application to the computation of band structures," Opt. Quantum Electron. 36, 87-107 (2004). [CrossRef]
  41. C. Sauvan, P. Lalanne, J. C. Rodier, J. P. Hugonin and A. Talneau, "Accurate modeling of line-defect photonic crystal waveguides," IEEE Photon. Technol. Lett. 15, 1243-1245 (2003). [CrossRef]
  42. C. Sauvan, P. Lalanne and J. P. Hugonin, "Slow-wave effect and mode-profile matching in photonic crystal microcavities," Phys. Rev. B 71, 165118 (2005). [CrossRef]
  43. T. Baba, T. Hamano, F. Koyama and K. Iga, "Spontaneous emission factor of a microcavity DBR surface-emitting laser," IEEE J. Quantum Electron. 27, 1347-1358 (1991). [CrossRef]
  44. G. Lecamp, J. P. Hugonin and P. Lalanne, "Remarkably large spontaneous emission β-factor in photonic crystal waveguides," Phys. Rev. Lett. 99, 023902 (2007). [CrossRef] [PubMed]
  45. A. Baudrion, J. Weeber, A. Dereux, G. Lecamp, P. Lalanne, S. Bozhevolnyi, "Influence of the filling factor on the spectral properties of plasmonic crystals," Phys. Rev. B. 74, 125406 (2006). [CrossRef]
  46. J. C. Chen and K. Li, "Quartic perfectly matched layers for dielectric waveguides and gratings," Microwave Opt. Technol. Lett. 10, 319-323 (1995). [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.

Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited