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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 70, Iss. 7 — Jul. 1, 1980
  • pp: 804–813

Scattering and guiding of waves by dielectric gratings with arbitrary profiles

K. C. Chang, V. Shah, and T. Tamir  »View Author Affiliations


JOSA, Vol. 70, Issue 7, pp. 804-813 (1980)
http://dx.doi.org/10.1364/JOSA.70.000804


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Abstract

Based on an exact solution of the pertinent boundary-value problem, a method is presented for finding the electromagnetic fields scattered or guided by lossy dielectric gratings having arbitrary profiles. This method unifies the treatment of both perpendicular (TE) and parallel (TM) polarizations by expressing the fields in terms of two coupled first-order differential equations. Their solution is obtained by resorting to difference equations in conjunction with the algorithm of Adams—Moulton, which easily leads to accurate results for a large variety of practical problems. To illustrate the application of this approach, quantitative results are presented for the scattering of plane waves by lossy corrugated structures and for the guiding of (leaky) surface waves by triangular gratings with symmetric or asymmetric profiles.

© 1980 Optical Society of America

Citation
K. C. Chang, V. Shah, and T. Tamir, "Scattering and guiding of waves by dielectric gratings with arbitrary profiles," J. Opt. Soc. Am. 70, 804-813 (1980)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-70-7-804


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References

  1. A. R. Neureuther and K. Zaki, "Numerical methods for the analysis of scattering from nonplanar and periodic structures," Alta Freq. 38, 282–285 (1969).
  2. P. M. van den Berg, "Rigorous diffraction theory of optical reflection and transmission gratings," Thesis, Delft University of Technolgy, The Netherlands, Report No. 1971-16, 1971 (unpublished).
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  11. K. C. Chang, "Surface-wave scattering by dielectric gratings with arbitrary profiles," Ph.D. thesis, Polytechnic Institute of New York, Brooklyn, N.Y., 1979 (unpublished).
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  13. K. C. Chang and T. Tamir, "Simplified approach to surface-wave scattering by blazed dielectric gratings," Appl. Opt. 19, 282–288 (1980).
  14. For surface waves, the sign is chosen as in the case of the scattering problem. For leaky waves, the same rule holds except that if n < 0 and βn β 0, the sign must usually be chosen so that the imaginary part of k(u)znis negative. The reader should refer for a detailed discussion of this aspect to Antenna Theory, edited by R. E. Collin and F. J. Zucker (McGraw-Hill, New York, 1969), Sec. 19.10, pp. 203–208.
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  16. Reference 15, p. 116.
  17. M. Nevière (personal communication).
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  20. V. Shah and T. Tamir, "Brewster phenomena in lossy structures," Opt. Commun. 23, 113–117 (1977).
  21. T. Tamir and S. T. Peng, "Analysis and design of grating couplers," Appl. Phys. 14, 235–254 (1977).

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