Abstract

In a recent paper [J. Opt. Soc. Am. A 16, 113 (1999)] a thin-element approximation of diffractive optical elements was used to describe diffraction of oblique incident wave fronts. This expression motivated by a ray optical analysis is shown to be incorrect. I discuss how the thin-element approximation can be generalized to arbitrary diffraction geometries. This includes an intuitive interpretation of the results.

© 2000 Optical Society of America

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References

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  1. J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, “Metallic surface-relief on-axis and off-axis focusing diffractive cylindrical mirrors,” J. Opt. Soc. Am. A 16, 113–130 (1999).
    [CrossRef]
  2. B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), Chap. 2, pp. 55–63.
  3. W. Singer, K.-H. Brenner, “Transition of the scalar field at a surface in the generalized Kirchhoff diffraction theory,” J. Opt. Soc. Am. A 12, 1913–1919 (1995).
    [CrossRef]
  4. M. Testorf, “Perturbation theory as a unified approach to design diffractive optical elements,” J. Opt. Soc. Am. A 16, 1115–1123 (1999).
    [CrossRef]
  5. P. C. Waterman, “Scattering by periodic surfaces,” J. Acoust. Soc. Am. 57, 791–802 (1975).
    [CrossRef]
  6. A. Ishimaru, Electrodynamic Wave Propagation, Radiation, and Scattering (Prentice-Hall, Englewood Cliffs, N. J., 1991), Chap. 6.3, pp. 156–157.
  7. K.-H. Brenner, W. Singer, “Light propagation through microlenses: a new simulation method,” Appl. Opt. 32, 4984–4988 (1993).
    [CrossRef] [PubMed]

1999

1995

1993

1975

P. C. Waterman, “Scattering by periodic surfaces,” J. Acoust. Soc. Am. 57, 791–802 (1975).
[CrossRef]

Bendickson, J. M.

Brenner, K.-H.

Gaylord, T. K.

Glytsis, E. N.

Ishimaru, A.

A. Ishimaru, Electrodynamic Wave Propagation, Radiation, and Scattering (Prentice-Hall, Englewood Cliffs, N. J., 1991), Chap. 6.3, pp. 156–157.

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), Chap. 2, pp. 55–63.

Singer, W.

Teich, M. C.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), Chap. 2, pp. 55–63.

Testorf, M.

Waterman, P. C.

P. C. Waterman, “Scattering by periodic surfaces,” J. Acoust. Soc. Am. 57, 791–802 (1975).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Geometry of diffraction at a reflecting step profile.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

ϕ(x)=2πλ h(x)Λ,
u˜(ν)=C[β(i), β]- exp(-i2π{[β-β(i)]h(x, y)+[ν-ν(i)]x})d x,
Λ=-2 cos α,
Λ=-(cos α+cos α).
Λ=n1 cos α-n2 cos α.

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