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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 12, Iss. 5 — May. 1, 1995
  • pp: 1068–1076

Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings

M. G. Moharam, Eric B. Grann, Drew A. Pommet, and T. K. Gaylord  »View Author Affiliations


JOSA A, Vol. 12, Issue 5, pp. 1068-1076 (1995)
http://dx.doi.org/10.1364/JOSAA.12.001068


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Abstract

The rigorous coupled-wave analysis technique for describing the diffraction of electromagnetic waves by periodic grating structures is reviewed. Formulations for a stable and efficient numerical implementation of the analysis technique are presented for one-dimensional binary gratings for both TE and TM polarization and for the general case of conical diffraction. It is shown that by exploitation of the symmetry of the diffraction problem a very efficient formulation, with up to an order-of-magnitude improvement in the numerical efficiency, is produced. The rigorous coupled-wave analysis is shown to be inherently stable. The sources of potential numerical problems associated with underflow and overflow, inherent in digital calculations, are presented. A formulation that anticipates and preempts these instability problems is presented. The calculated diffraction efficiencies for dielectric gratings are shown to converge to the correct value with an increasing number of space harmonics over a wide range of parameters, including very deep gratings. The effect of the number of harmonics on the convergence of the diffraction efficiencies is investigated. More field harmonics are shown to be required for the convergence of gratings with larger grating periods, deeper gratings, TM polarization, and conical diffraction.

© 1995 Optical Society of America

Citation
M. G. Moharam, Eric B. Grann, Drew 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)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-12-5-1068


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References

  1. M. G. Moharam and T. K. Gaylord, "Rigorous coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Am. 71, 811–818 (1981). [CrossRef]
  2. M. G. Moharam and T. K. Gaylord, "Rigorous coupled-wave analysis of planar grating diffraction—E-mode polarization and losses," J. Opt. Soc. Am. 73, 451–455 (1983). [CrossRef]
  3. M. G. Moharam and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings," J. Opt. Soc. Am. 72, 1385–1392 (1982). [CrossRef]
  4. M. G. Moharam and T. K. Gaylord, "Three-dimensional vector coupled-wave analysis of planar grating diffraction," J. Opt. Soc. Am. 73, 1105–1112 (1983). [CrossRef]
  5. W. E. Baird, M. G. Moharam, and T. K. Gaylord, "Diffraction characteristics of planar absorption gratings," Appl. Phys. B 32, 15–20 (1983). [CrossRef]
  6. M. G. Moharam and T. K. Gaylord, "Rigorous coupled-wave analysis of metallic surface-relief gratings," J. Opt. Soc. Am. A 3, 1780–1796 (1986). [CrossRef]
  7. M. G. Moharam, "Diffraction analysis of multiplexed holographic gratings," in Digest of Topical Meeting on Holography (Optical Society of America, Washington, D.C., 1986), pp. 100–103.
  8. M. G. Moharam, "Coupled-wave analysis of two-dimensional gratings," in Holographic Optics: Design and Applications, I. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 883, 8–11 (1988). [CrossRef]
  9. E. N. Glytsis and T. K. Gaylord, "Rigorous three-dimensional coupled-wave diffraction analysis of single and cascaded anisotropic gratings," J. Opt. Soc. Am. A. 4, 2061–2080 (1987). [CrossRef]
  10. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, "Stable implementation of the rigorous coupledwave analysis for surface-relief dielectric gratings: enhanced transmittance matrix approach," J. Opt. Soc. Am. A 12, 1077–1086 (1995). [CrossRef]
  11. L. Li and C. W. Haggans, "Convergence of the coupled-wave method for metallic lamellar diffraction gratings," J. Opt. Soc. Am. A 10, 1184–1187 (1993). [CrossRef]

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