Abstract

The reflection efficiencies for the various orders of diffraction produced by a grating are calculated under the following assumptions. The grating is for the most part flat, but with a fraction ε of the periodicity interval <i>a</i> described by a profile function <i>z</i>= ƒ(<i>x</i>). The reflection and transmission efficiencies are calculated as a series expansion in ε. Numerical calculations have been performed for the case of ultrasoft x rays incident at near grazing angles, using a complex index of refraction η = 1-δ<sub>0</sub>λ<sup>2</sup>+<i>i</i>β<sub>0</sub>λ<sup>3.25</sup> or tabulated values. No effects of shadowing by the grating profile have been considered, and the numerical work has been done for a symmetrical triangular trench incised in the flat surface.

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  1. J. W. Strutt (Lord Rayleigh), The Theory of Sound (Dover Publications, Inc., New York, 1896), Vol. II, Sec. 272a.
  2. See, for example: W. C. Meecham, J. Appl. Phys. 27, 361 (1956), or I. Abubakar, Proc. Cambridge Phil. Soc. 59, 231 (1963). Compare also: G. Sprague, D. H. Tomboulian, and D. E. Bedo, J. Opt. Soc. Am. 45, 756 (1955). The results of this last paper, when applied to a situation with the parameters of our surface, are at considerable variance with the results obtained herein.
  3. C. Eckart, Phys. Rev. 44, 12 (1933).
  4. B. A. Lippman, J. Opt. Soc. Am. 43, 408 (1953).
  5. B . L. Henke and J. C. Miller, "Ultrasoft X-Ray Interaction Coefficients," Tech. Rept. No. 3, Ultrasoft X-ray Physics Contract No. AF 49(638)-394 AFOSR, August 1959.
  6. A. P. Lukiriskii and E. P. Savinov, Opt. Spectry. 14, 147 (1963) [Opt. i Spektroskopiya 14, 285 (1963)].
  7. See, for example, the gratings reported upon by H. A. Kirkpatrick, J. Quant. Spectry. Radiative Transfer 2, 715–724 (1962). A private communication from this author also suggests that the values quoted are within the bounds of actual grating parameters.

Eckart, C.

C. Eckart, Phys. Rev. 44, 12 (1933).

Henke, B . L.

B . L. Henke and J. C. Miller, "Ultrasoft X-Ray Interaction Coefficients," Tech. Rept. No. 3, Ultrasoft X-ray Physics Contract No. AF 49(638)-394 AFOSR, August 1959.

Kirkpatrick, H. A.

See, for example, the gratings reported upon by H. A. Kirkpatrick, J. Quant. Spectry. Radiative Transfer 2, 715–724 (1962). A private communication from this author also suggests that the values quoted are within the bounds of actual grating parameters.

Lippman, B. A.

B. A. Lippman, J. Opt. Soc. Am. 43, 408 (1953).

Lukiriskii, A. P.

A. P. Lukiriskii and E. P. Savinov, Opt. Spectry. 14, 147 (1963) [Opt. i Spektroskopiya 14, 285 (1963)].

Meecham, W. C.

See, for example: W. C. Meecham, J. Appl. Phys. 27, 361 (1956), or I. Abubakar, Proc. Cambridge Phil. Soc. 59, 231 (1963). Compare also: G. Sprague, D. H. Tomboulian, and D. E. Bedo, J. Opt. Soc. Am. 45, 756 (1955). The results of this last paper, when applied to a situation with the parameters of our surface, are at considerable variance with the results obtained herein.

Miller, J. C.

B . L. Henke and J. C. Miller, "Ultrasoft X-Ray Interaction Coefficients," Tech. Rept. No. 3, Ultrasoft X-ray Physics Contract No. AF 49(638)-394 AFOSR, August 1959.

Savinov, E. P.

A. P. Lukiriskii and E. P. Savinov, Opt. Spectry. 14, 147 (1963) [Opt. i Spektroskopiya 14, 285 (1963)].

Strutt, J. W.

J. W. Strutt (Lord Rayleigh), The Theory of Sound (Dover Publications, Inc., New York, 1896), Vol. II, Sec. 272a.

Other

J. W. Strutt (Lord Rayleigh), The Theory of Sound (Dover Publications, Inc., New York, 1896), Vol. II, Sec. 272a.

See, for example: W. C. Meecham, J. Appl. Phys. 27, 361 (1956), or I. Abubakar, Proc. Cambridge Phil. Soc. 59, 231 (1963). Compare also: G. Sprague, D. H. Tomboulian, and D. E. Bedo, J. Opt. Soc. Am. 45, 756 (1955). The results of this last paper, when applied to a situation with the parameters of our surface, are at considerable variance with the results obtained herein.

C. Eckart, Phys. Rev. 44, 12 (1933).

B. A. Lippman, J. Opt. Soc. Am. 43, 408 (1953).

B . L. Henke and J. C. Miller, "Ultrasoft X-Ray Interaction Coefficients," Tech. Rept. No. 3, Ultrasoft X-ray Physics Contract No. AF 49(638)-394 AFOSR, August 1959.

A. P. Lukiriskii and E. P. Savinov, Opt. Spectry. 14, 147 (1963) [Opt. i Spektroskopiya 14, 285 (1963)].

See, for example, the gratings reported upon by H. A. Kirkpatrick, J. Quant. Spectry. Radiative Transfer 2, 715–724 (1962). A private communication from this author also suggests that the values quoted are within the bounds of actual grating parameters.

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