OSA's Digital Library

Journal of Lightwave Technology

Journal of Lightwave Technology


  • Vol. 24, Iss. 6 — Jun. 1, 2006
  • pp: 2442–

Optical Properties of Deep Lamellar Gratings: A Coupled Bloch-Mode Insight

Philippe Lalanne, Jean Paul Hugonin, and Pierre Chavel

Journal of Lightwave Technology, Vol. 24, Issue 6, pp. 2442- (2006)

View Full Text Article

Acrobat PDF (346 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

  • Export Citation/Save Click for help


A coupled-Bloch-mode model for explaining various optical properties of strongly modulated subwavelength lamellar gratings is proposed. The model evidences the key role played by propagative Bloch modes, which bounce inside the grating and couple at the grating interfaces. Many optical properties of these gratings, such as their broadband reflectance, their polarization effect, and the presence of sharp anomalies, are understood as resulting from vertical resonances of the coupled-resonator modes. The approach provides a new insight on the physical mechanisms or optical behaviors observed, which is different from the classical study of the poles and zeros of the scattering operator.

© 2006 IEEE

Philippe Lalanne, Jean Paul Hugonin, and Pierre Chavel, "Optical Properties of Deep Lamellar Gratings: A Coupled Bloch-Mode Insight," J. Lightwave Technol. 24, 2442- (2006)

Sort:  Journal  |  Reset


  1. Y. Kanamori, K. Hane, H. Sai and H. Yugami, "100 nm period silicon antireflection structures fabricated using a porous alumina membrane mask", Appl. Phys. Lett., vol. 78, no. 2, pp. 142-143, Jan. 2001.
  2. H. Kikuta, Y. Ohira and K. Iwata, "Achromatic quarter-wave plates using the dispersion of form birefringence", Appl. Opt., vol. 36, no. 7, pp. 1566-1572, Mar. 1997.
  3. P. C. Deguzman and G. P. Nordin, "Stacked subwavelength gratings as circular polarization filters", Appl. Opt., vol. 40, no. 31, pp. 5731-5737, Nov. 2001.
  4. L. Pajewski, R. Borghi, G. Schettini, F. Frezza and M. Santarsiero, "Design of a binary grating with subwavelength features that acts as a polarizating beam splitter", Appl. Opt., vol. 40, no. 32, pp. 5898-5905, Nov. 2001.
  5. D. Delbeke, R. Baets and P. Muys, "Polarization-selective beam splitter based on highly efficient simple binary diffraction grating", Appl. Opt., vol. 43, no. 33, pp. 6157-6165, Nov. 2004.
  6. T. Glaser, S. Schröter, H. Bartelt, H. J. Fuchs and E. B. Kley, "Diffractive optical isolator made of high-efficiency dielectric gratings only", Appl. Opt., vol. 41, no. 18, pp. 3558-3566, Jun. 2002.
  7. R. Baets, B. Demeulenaere, B. Dhoedt and S. Goeman, "Optical system with a dielectric subwavelength structure having high reflectivity and polarization selectivity", U.S. Patent 6 191 890, Feb. 20, 2001.
  8. C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain and Y. Suzuki, "Broad-band mirror using a subwavelength grating", IEEE Photon. Technol. Lett., vol. 16, no. 7, pp. 1676-1678, Jul. 2004.
  9. P. Lalanne, S. Astilean, P. Chavel, E. Cambril and H. Launois, "Design and fabrication of blazed-binary diffractive elements with sampling periods smaller than the structural cutoff", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 16, no. 5, pp. 1143-1156, May 1999.
  10. H. Lajunen, L. Tervo and J. Turunen, "High-efficiency broadband diffractive elements based on polarization gratings", Opt. Lett., vol. 29, no. 8, pp. 803-805, Apr. 2004.
  11. Y. Din and R. Magnusson, "Resonant leaky-mode spectral-band engineering and device applications", Opt. Express, vol. 12, no. 23, pp. 5661-5674, Nov. 2004.
  12. 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. Amer. A, Opt. Image Sci., vol. 12, no. 5, pp. 1068-1076, May 1995.
  13. P. Lalanne and G. M. Morris, "Highly improved convergence of the coupled-wave method for TM polarization", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 13, no. 4, pp. 779-784, Apr. 1996.
  14. G. Granet and B. Guizal, "Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 13, no. 5, pp. 1019-1023, May 1996.
  15. S. T. Peng, T. Tamir and H. L. Bertoni, "Theory of periodic dielectric waveguides", IEEE Trans. Microw. Theory Tech., vol. MTT-23, no. 1, pp. 123-133, Jan. 1975.
  16. E. Popov, "Light diffraction by relief gratings", Prog. Opt., vol. 31, pp. 141-187, 1993.
  17. M. Nevière, E. Popov and R. Reinisch, "Electromagnetic resonances in linear and nonlinear optics: Phenomenological study of grating behavior through the poles and zeros of the scattering operator", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 12, no. 3, pp. 513-523, Mar. 1995.
  18. D. Rosenblatt, A. Sharon and A. A. Friesem, "Resonant grating waveguide structures", IEEE J. Quantum Electron., vol. 33, no. 11, pp. 2038-2059, Nov. 1997.
  19. A. L. Fehrembach and A. Sentenac, "Study of waveguide grating eigenmodes for unpolarized filtering applications", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 20, no. 3, pp. 481-488, Mar. 2003.
  20. D. K. Jacob, S. C. Dunn and M. G. Moharam, "Normally incident resonant grating reflection filters for efficient narrow-band spectral filtering of finite beams", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 18, no. 9, pp. 2109-2120, Sep. 2001.
  21. V. N. Astratov, I. S. Culshaw, R. M. Stevenson, D. M. Whittaker, M. S. Skolnick, T. F. Krauss and R. M. De La Rue, "Resonant coupling of near-infrared radiation to photonic band structure waveguides", J. Lightw. Technol., vol. 17, no. 11, pp. 2050-2057, Nov. 1999.
  22. D. L. Brundrett, E. N. Glytsis, T. K. Gaylord and J. M. Bendickson, "Effects of modulation strength in guided-mode resonant subwavelength gratings at normal incidence", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 17, no. 7, pp. 1221-1230, Jul. 2000.
  23. D. L. Brundrett, E. N. Glytsis and T. K. Gaylord, "Homogeneous layer models for high-spatial-frequency dielectric surface-relief gratings: Conical diffraction and antireflection designs", Appl. Opt., vol. 33, no. 13, pp. 2695-2706, May 1994.
  24. P. Lalanne and D. Lalanne, "On the effective medium theory of subwavelength periodic structures", J. Mod. Opt., vol. 43, no. 10, pp. 2063-2085, Oct. 1996.
  25. A. A. Krokhin, P. Halevi and J. Arriaga, "Long-wavelength limit (homogenization) for two-dimensional photonic crystals", Phys. Rev. B. Condens. Matter, vol. 65, no. 11, p. 115208, Mar. 2002.
  26. J. M. Pottage, E. Silvestre and P. S. J. Russell, "Vertical-cavity surface-emitting resonances in photonic crystal films", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 18, no. 2, pp. 442-447, Feb. 2001.
  27. W. Suh, Z. Wang and S. Fan, "Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities", IEEE J. Quantum Electron., vol. 40, no. 10, pp. 1511-1518, Oct. 2004.
  28. T. Clausnitzer, T. Kämpfe, E.-B. Kley, A. Tünnermann, U. Peschel, A. V. Tishchenko and O. Parriaux, "An intelligible explanation of highly-efficient diffraction in deep dielectric rectangular transmission gratings", Opt. Express, vol. 13, no. 26, pp. 10448-10456, Dec. 2004.
  29. F. J. Garcia-Vidal, L. Martin-Moreno and J. B. Pendry, "Surfaces with holes in them: New plasmonic metamaterials", J. Opt. A, Pure Appl. Opt., vol. 7, no. 2, pp. S97-S101, Feb. 2005.
  30. J. B. Pendry, L. Martin-Moreno and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces", Science, vol. 305, no. 5685, pp. 847-848, Aug. 2004.
  31. P. Lalanne, C. Sauvan, J. C. Rodier and J. P. Hugonin, "Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures", Phys. Rev. B, Condens. Matter, vol. 68, no. 12, p. 125404, Sep. 2003.
  32. P. Lalanne, J. C. Rodier and J. P. Hugonin, "Surface plasmons of metallic surfaces perforated by nanohole arrays", J. Opt. A, Pure Appl. Opt., vol. 7, no. 8, pp. 422-426, Aug. 2005.
  33. Q. Cao, P. Lalanne and J. P. Hugonin, "Stable and efficient Bloch-mode computational method for one-dimensional grating waveguide", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 19, no. 2, pp. 335-338, Feb. 2002.
  34. P. Vincent and M. Nevière, "Corrugated dielectric waveguide: A numerical study of the second-order stop bands", Appl. Phys., vol. 20, no. 4, pp. 345-351, Dec. 1979.
  35. X. Letartre, J. Mouette, J. L. Leclercq, P. R. Romeo, C. Seassaland and P. Viktorovitch, "Switching devices with spatial and spectral resolution combining photonic crystal and MOEMS structures", J. Lightw. Technol., vol. 21, no. 7, pp. 1691-1699, Jul. 2003.
  36. J. Mouette, C. Seassal, X. Letartre, P. Rojo-Romeo, J. L. Leclercq, P. Regreny and P. Viktorovitch, "Very low threshold vertical emitting laser operation in InP graphite photonic crystal slab on silicon", Electron. Lett., vol. 39, no. 6, pp. 526-528, Mar. 2003.
  37. P. Lalanne and D. Lemercier-Lalanne, "Depth dependence of the effective properties of subwavelength gratings", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 14, no. 2, pp. 450-458, Feb. 1997.
  38. E. Popov, L. Mashev and D. Maystre, "Theoretical study of the anomalies of coated dielectric gratings", Opt. Acta, vol. 33, no. 5, pp. 607-619, May 1986.
  39. H. A. Haus, Waves and Fields in Optoelectronics, London: U.K.: Prentice-Hall, 1984.

Cited By

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