OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 11 — Nov. 1, 2001
  • pp: 2865–2875

Use of grating theories in integrated optics

Eric Silberstein, Philippe Lalanne, Jean-Paul Hugonin, and Qing Cao  »View Author Affiliations

JOSA A, Vol. 18, Issue 11, pp. 2865-2875 (2001)

View Full Text Article

Enhanced HTML    Acrobat PDF (527 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Recently [Opt. Lett. 25, 1092 (2000)], two of the present authors proposed extending the domain of applicability of grating theories to aperiodic structures, especially the diffraction structures that are encountered in integrated optics. This extension was achieved by introduction of virtual periodicity and incorporation of artificial absorbers at the boundaries of the elementary cells of periodic structures. Refinements and extensions of that previous research are presented. Included is a thorough discussion of the effect of the absorber quality on the accuracy of the computational results, with highly accurate computational results being achieved with perfectly matched layer absorbers. The extensions are concerned with the diversity of diffraction waveguide problems to which the method is applied. These problems include two-dimensional classical problems such as those involving Bragg mirrors and grating couplers that may be difficult to model because of the length of the components and three-dimensional problems such as those involving integrated diffraction gratings, photonic crystal waveguides, and waveguide airbridge microcavities. Rigorous coupled-wave analysis (also called the Fourier modal method) is used to support the analysis, but we believe that the approach is applicable to other grating theories. The method is tested both against available numerical data obtained with finite-difference techniques and against experimental data. Excellent agreement is obtained. A comparison in terms of convergence speed with the finite-difference modal method that is widely used in waveguide theory confirms the relevancy of the approach. Consequently, a simple, efficient, and stable method that may also be applied to waveguide and grating diffraction problems is proposed.

© 2001 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1960) Diffraction and gratings : Diffraction theory
(050.1970) Diffraction and gratings : Diffractive optics

Original Manuscript: January 25, 2001
Revised Manuscript: May 8, 2001
Manuscript Accepted: May 9, 2001
Published: November 1, 2001

Eric Silberstein, Philippe Lalanne, Jean-Paul Hugonin, and Qing Cao, "Use of grating theories in integrated optics," J. Opt. Soc. Am. A 18, 2865-2875 (2001)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. T. Itoh, ed., Numerical Techniques for Microwave and Millimeter-Wave Passive Structures (Wiley, New York, 1989).
  2. L. Li, “Recent advances and present limitations of the electromagnetic theory of diffraction gratings,” in Diffractive Optics and Micro-Optics, 2000 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), pp. 2–4.
  3. M. G. Moharam, E. B. Grann, D. A. Pommet, 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]
  4. F. Montiel, M. Nevière, “Differential theory of gratings: extension to deep gratings of arbitrary profile and permittivity through the R-matrix propagation algorithm,” J. Opt. Soc. Am. A 11, 3241–3250 (1994). [CrossRef]
  5. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 1995), Chap. 7.
  6. Ph. Lalanne, E. Silberstein, “Fourier-modal method applied to waveguide computational problems,” Opt. Lett. 25, 1092–1094 (2000). [CrossRef]
  7. Ph. Lalanne, G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996). [CrossRef]
  8. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758–2767 (1997). [CrossRef]
  9. See, for instance, L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1035 (1996). [CrossRef]
  10. G. Granet, B. Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A 13, 1019–1023 (1996). [CrossRef]
  11. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996). [CrossRef]
  12. E. Popov, M. Nevière, “Grating theory: new equations in Fourier space leading to fast converging results for TM polarization,” J. Opt. Soc. Am. A 17, 1773–1784 (2000). [CrossRef]
  13. Ph. Lalanne, “Effective properties and band structure of lamellar subwavelength crystals: plane-wave method revisited,” Phys. Rev. B 58, 9801–9807 (1998). [CrossRef]
  14. Ph. Lalanne, J. P. Hugonin, “Numerical performance of finite-difference modal methods for the electromagnetic analysis of one-dimensional lamellar gratings,” J. Opt. Soc. Am. A 17, 1033–1042 (2000). [CrossRef]
  15. J. P. Bérenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994). [CrossRef]
  16. See, for instance, E. A. Marengo, C. M. Rappaport, E. L. Miller, “Optimum PML ABC conductivity profile in FDTD,” IEEE Trans. Magn. 35, 1506–1509 (1999). [CrossRef]
  17. S. F. Helfert, R. Pregla, “Efficient analysis of periodic structures,” J. Lightwave Technol. 16, 1694–1702 (1998). [CrossRef]
  18. R. Pregla, W. Pasher, “The method of lines,” in Numerical Techniques for Microwave and Millimeter Wave Passive Structure, T. Itoh, ed. (Wiley, New York, 1989), pp. 381–446.
  19. Ph. Lalanne, M. P. Jurek, “Computation of the near-field pattern with the coupled-wave method for TM polarization,” J. Mod. Opt. 45, 1357–1374 (1998). [CrossRef]
  20. D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, C. Jouanin, “Quantitative measurement of transmission, reflection and diffraction of two-dimensional photonic bandgap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997). [CrossRef]
  21. M. S. D. Smith, K. A. McGreer, “Diffraction gratings utilizing total internal reflection facets in Littrow configuration,” IEEE Photon. Technol. Lett. 11, 84–86 (1999). [CrossRef]
  22. J. B. D. Soole, A. Scherer, H. P. LeBlanc, N. C. Andreadakis, R. Bhat, M. A. Kosa, “Monolithic InP/InGaAsP/InP grating spectrometer for the 1.48–1.56 µm wavelength range,” Appl. Phys. Lett. 58, 1949–1951 (1991). [CrossRef]
  23. Ph. Lalanne, H. Benisty, “Out-of-plane losses of two-dimensional photonic crystal waveguides: electromagnetic analysis,” J. Appl. Phys. 89, 1512–1514 (2001). [CrossRef]
  24. D. J. Ripin, K. Y. Lim, G. S. Petrich, P. R. Villeneuve, S. Fan, E. R. Thoen, J. D. Joannopoulos, E. P. Ippen, L. A. Kolodziejski, “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–1580 (2000). [CrossRef]
  25. Ph. Lalanne, D. Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2086 (1996). [CrossRef]
  26. M. Aubourg, S. Verdeyme, P. Guillon, “Finite element software for microwave engineering,” in Microwave Passive Devices, T. Itoh, G. Pelosi, P. P. Silvester, eds. (Wiley, New York, 1996), Chap. 1.
  27. C. H. Henry, B. H. Verbeek, “Solution of the scalar wave equation for arbitrarily shaped dielectric waveguides by two-dimensional Fourier analysis,” J. Lightwave Technol. 7, 308–313 (1989). [CrossRef]
  28. J. Rodriguez, R. D. Crespo, S. Fernandez, J. Pandavenes, J. Olivares, S. Carrasco, I. Ibanez, J. M. Virgos, “Radiation losses on discontinuities in integrated optical waveguides,” Opt. Eng. 38, 1896–1906 (1999). [CrossRef]
  29. P. Vahihama, J. Turunen, Diffractive Optics and Micro-Optics, Vol. 10 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1998), p. 69.

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