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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 13, Iss. 5 — May. 1, 1996
  • pp: 993–1005

Resonant scattering from two-dimensional gratings

Song Peng and G. Michael Morris  »View Author Affiliations

JOSA A, Vol. 13, Issue 5, pp. 993-1005 (1996)

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A theoretical investigation of resonant scattering from two-dimensional gratings is presented. Abrupt changes of diffraction efficiency over a small parameter range have been observed by rigorous coupled-wave analysis. The peak reflection or transmission efficiencies can approach unity. This phenomenon is explained in terms of the coupling between the incident plane wave and guided modes that can be supported by the two-dimensional-grating waveguide structure. Because of the double periodicity, the incident field can be coupled into any direction in the grating plane. The guided modes supported by two-dimensional gratings are found by rigorous solution of the homogeneous problem associated with the scattering (inhomogeneous) problem. The complex propagation constants for the guided modes provide estimates of both the resonance angle and width. In addition, to illustrate the implication of the radical change in the phase and amplitude of the propagating waves, we report a study of finite-beam diffraction in the resonant scattering region. Applications for the structures include polarization-independent narrow-band filters and bandwidth-tunable filters. It is shown that, because of the double resonance, the polarization-independent narrow-band filters have a large angular tolerance.

© 1996 Optical Society of America

Original Manuscript: June 13, 1995
Revised Manuscript: October 20, 1995
Manuscript Accepted: November 21, 1995
Published: May 1, 1996

Song Peng and G. Michael Morris, "Resonant scattering from two-dimensional gratings," J. Opt. Soc. Am. A 13, 993-1005 (1996)

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  1. R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396–402 (1902).
  2. L. Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. London Ser. A 79, 399–416 (1907). [CrossRef]
  3. A. Hessel, A. A. Oliner, “A new theory of Wood’s anomalies on optical gratings,” Appl. Opt. 4, 1275–1297 (1965). [CrossRef]
  4. N. Nevière, R. Petit, M. Cadilhac, “About the theory of optical grating coupler-waveguide systems,” Opt. Commun. 8, 113–117 (1973). [CrossRef]
  5. M. Nevière, R. Petit, M. Cadilhac, “Systematic study of resonances of holographic thin film couplers,” Opt. Commun. 9, 48–53 (1973). [CrossRef]
  6. E. Popov, L. Mashev, D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986). [CrossRef]
  7. H. L. Bertoni, L.-H. S. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antennas Propag. 37, 78–83 (1989). [CrossRef]
  8. L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985). [CrossRef]
  9. M. T. Gale, K. Knop, R. Morf, “Zero-order diffractive microstructures for security applications,” in Optical Security and Anticounterfeiting Systems, W. Fagan, ed., Proc. SPIE1210, 83–89 (1990). [CrossRef]
  10. S. S. Wang, R. Magnusson, J. S. Bagby, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 7, 1470–1474 (1990). [CrossRef]
  11. S. S. Wang, R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. 19, 919–921 (1994). [CrossRef] [PubMed]
  12. R. Ulrich, “Modes of propagation on an open periodic waveguide for the far infrared,” in Proceedings of the Symposium on Optical and Acoustical Micro-Electronics (Polytechnic Press, New York, 1974), pp. 359–376.
  13. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980), pp. 123–157.
  14. P. Vincent, “A finite-different method for dielectric and conducting crossed gratings,” Opt. Commun. 26, 293–296 (1978). [CrossRef]
  15. M. G. Moharam, T. K. Gaylord, “Coupled-wave analysis of two-dimensional gratings,” in Holographic Optics: Design and Applications, I. Cindrich, ed., Proc. SPIE883, 8–11 (1986). [CrossRef]
  16. G. H. Derrick, R. C. McPhedran, D. Maystrey, M. Nevière, “Crossed gratings: a theory and its applications,” Appl. Phys. 18, 39–52 (1979). [CrossRef]
  17. O. P. Bruno, F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries. III. Doubly periodic gratings,” J. Opt. Soc. Am. A 10, 2551–2562 (1993). [CrossRef]
  18. P. St. J. Russell, “Power conservation and field structures in uniform dielectric gratings,” J. Opt. Soc. Am. A 1, 293–299 (1984). [CrossRef]
  19. S. Peng, G. M. Morris, “Efficient implementation of rigorous coupled-wave analysis for surface-relief gratings,” J. Opt. Soc. Am. A 12, 1087–1096 (1995). [CrossRef]
  20. N. Chateau, J. Hugonin, “Algorithm for the rigorous coupled-wave analysis of grating diffraction,” J. Opt. Soc. Am. A 11, 1321–1331 (1994). [CrossRef]
  21. L. Li, “Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity,” J. Opt. Soc. Am. A 10, 2581–2591 (1993). [CrossRef]
  22. J. Chilwell, I. Hodgkinson, “Thin-films field-transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguides,” J. Opt. Soc. Am. A 1, 742–753 (1984). [CrossRef]
  23. P. Vincent, M. Nevière, “Corrugated dielectric waveguides: a numerical study of the second-order stop bands,” Appl. Phys. 20, 345–351 (1979). [CrossRef]
  24. M. Nevière, E. Popov, 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. Am. A 12, 513–523 (1995). [CrossRef]
  25. S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975). [CrossRef]
  26. K. C. Chang, V. Shah, T. Tamir, “Scattering and guiding of waves by dielectric grating with arbitrary profiles,” J. Opt. Soc. Am. 70, 804–813 (1980). [CrossRef]
  27. S. T. Peng, “Rigorous formulation of scattering and guidance by dielectric grating waveguides: general case of oblique incidence,” J. Opt. Soc. Am. A 6, 1869–1883 (1989). [CrossRef]
  28. S. Zhang, T. Tamir, “Spatial modifications of Gaussian beams diffracted by reflection gratings,” J. Opt. Soc. Am. A 6, 1368–1381 (1989). [CrossRef]
  29. C. W. Hsue, T. Tamir, “Lateral displacement and distortion of beams incident upon a transmitting-layer configuration,” J. Opt. Soc. Am. A 2, 978–988 (1985). [CrossRef]
  30. V. Shah, T. Tamir, “Absorption and lateral shift of beams incident upon lossy multilayered media,” J. Opt. Soc. Am. 73, 37–44 (1983). [CrossRef]
  31. T. Tamir, H. L. Bertoni, “Lateral displacement of optical beams at multilayered and periodic structures,” J. Opt. Soc. Am. 61, 1397–1413 (1971). [CrossRef]
  32. G. A. Evans, N. W. Carlson, J. M. Hammer, S. L. Palfrey, R. Amantea, L. A. Carr, F. Z. Hawrylo, E. A. James, C. J. Kaiser, J. B. Kirk, W. F. Reichert, “Two-dimensional coherent laser arrays using grating surface emission,” IEEE J. Quantum Electron. 25, 1525–1538 (1989). [CrossRef]
  33. S. S. Wang, R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32, 2606–2613 (1993). [CrossRef] [PubMed]

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