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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 4, Iss. 1 — Jan. 1, 1987
  • pp: 60–65

Analysis of waveguide gratings: a comparison of the results of Rouard’s method and coupled-mode theory

L. A. Weller-Brophy and D. G. Hall  »View Author Affiliations

JOSA A, Vol. 4, Issue 1, pp. 60-65 (1987)

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Recently we introduced a new computational tool for the analysis of waveguide diffraction gratings based on Rouard’s method, a recursive technique used in thin-film coating design. In this paper we compare the reflectivities predicted by Rouard’s method with those found by using the ideal mode expansion of coupled-mode theory for both periodic and aperiodic gratings. We find empirically that the two methods are in excellent agreement, with typical differences in reflectivity of less than 1%.

© 1987 Optical Society of America

Original Manuscript: June 26, 1986
Manuscript Accepted: August 21, 1986
Published: January 1, 1987

L. A. Weller-Brophy and D. G. Hall, "Analysis of waveguide gratings: a comparison of the results of Rouard’s method and coupled-mode theory," J. Opt. Soc. Am. A 4, 60-65 (1987)

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  1. Throughout this paper we compare the results of Rouard’s method with those of an ideal mode expansion of coupled-mode theory.2–4 The coupled-mode-theory results are derived by using a synchronous approximation resulting in the general coupled equations given by Eqs. (5a) and (5b) in the text.5
  2. A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973). [CrossRef]
  3. H. Kogelnik, in Integrated Optics, Vol. 7 of Topics in Applied Physics, T. Tamir, ed. (Springer-Verlag, New York, 1975), pp. 66–79. [CrossRef]
  4. D. Marcuse, Theory of Dielecteic Optical Waveguides (Academic, New York, 1974), pp. 95–126 and 132–145.
  5. H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Syst. Tech. J. 55, 109–126 (1976).
  6. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  7. T. Fukuzawa, M. Nakamura, “Mode coupling in thin-film chirped gratings,” Opt. Lett. 4, 343–345 (1979). [CrossRef] [PubMed]
  8. C. S. Hong, J. B. Shellan, A. C. Livanos, A. Yariv, A. Katzir, “Broad-band grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 31, 276–278 (1977). [CrossRef]
  9. J. B. Shellan, C. S. Hong, A. Yariv, “Theory of chirped gratings in broad band filters,” Opt. Commun. 23, 398–400 (1977). [CrossRef]
  10. L. A. Weller-Brophy, D. G. Hall, “Analysis of waveguide gratings: application of Rouard’s method,” J. Opt. Soc. Am. A 2, 863–871 (1985). [CrossRef]
  11. M. P. Rouard, “Etudes des propriétés optiques des lames métalliques trés minces,” Ann. Phys. (Paris) Ser. II 7, 291–384 (1937).
  12. IMSL Library User’s Manual, Ed. 9.2 (IMSL, Houston, Tex., 1984), Chap. D, pp. DVERK-1–DVERK-9.
  13. We will consider only TE–TE coupling in the examples presented in this paper and will use the TE–TE coupling coefficient derived by Wagatsuma using a coupled-mode analysis.14,15 It should be noted that there is little agreement among the coupling coefficients presented in the literature, a point that has been discussed by several authors.16–19 Consequently, a judicious choice of coupling coefficient is required in order to obtain the most accurate predictions of the grating response characteristics.
  14. K. Wagatsuma, H. Sakaki, S. Saito, “Mode conversion and optical filtering of obliquely incident waves in corrugated waveguide filters,” IEEE J. Quantum Electron. QE-15, 632–637 (1979). [CrossRef]
  15. K. Wagatsuma, K. Yokoyama, H. Sakaki, S. Saito, “Mode couplings in corrugated-waveguide optical demultiplexers,” presented at the Fifth European Conference on Optical Communication, Amsterdam, September 1979.
  16. R. W. Gruhlke, D. G. Hall, “Comparison of two approaches to the waveguide scattering problem: TM polarization,” Appl. Opt. 23, 127–133 (1984). [CrossRef] [PubMed]
  17. W. Streifer, D. R. Scifres, R. D. Burnham, “Coupling coefficients for DFB single- and double-heterostructure diode lasers,” IEEE J. Quantum Electron. QE-11, 867–873 (1975). [CrossRef]
  18. G. I. Stegeman, D. Sarid, J. J. Burke, D. G. Hall, “Scattering of guided waves by surface periodic gratings for arbitrary angles of incidence: perturbation theory and implications to normal-mode analysis,”J. Opt. Soc. Am. 71, 1497–1507 (1981). [CrossRef]
  19. L. A. Weller-Brophy, D. G. Hall, “Waveguide diffraction gratings in integrated optics,” in Integrated Optical Circuit Engineering II, S. Sriram, ed., Proc. Soc. Photo-Opt. Instrum. Eng.578, 173–177 (1985). [CrossRef]

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