Abstract

The reflection efficiency of a lightly ruled glass grating, mainly in relation to its short-wavelength limit in the soft x-ray region, is discussed on the basis of the Rayleigh-Fano theory, which deals with Wood’s anomalies of optical gratings. The reflectances of waves diffracted by a glass grating are calculated under appropriately assumed conditions and the locations of the abrupt enhancement of reflection are derived. Theoretical predictions have been confirmed by a simulated experiment performed in the visible region.

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  1. G. Sprague, D. H. Tomboulian, and D. E. Bedo, J. Opt. Soc. Am. 45, 756 (1955); G. W. Stroke, in Encyclopedia of Physics 29, S. Flügge Ed. (Springer-Verlag, Berlin, 1967), pp. 603-6.
  2. J. C. Miller, J. Opt. Soc. Am. 54, 353 (1964).
  3. P. Jaeglé, Compt. Rend. 259, 533, 4556 (1964); Thèses, Contribution à la Spectrographie dans l’Ultraviolet de la Région de Holweck (Université de Paris, 1965).
  4. A. P. Lukirskii and E. P. Savinov, Opt. Spektrosk. [Opt. Spektrosc.] 14, 147 (1963).
  5. T. Sagawa, Sci. Rept. Tôhoku Univ. (I) 16, 119 (1962).
  6. T. Sagawa, Y. Iguchi, M. Sasanuma, A. Ejiri, S. Fujiwara, M. Yokota, S. Yamaguchi, M. Nakamura, T. Sasaki, and T. Oshio, J. Phys. Soc. Japan 21, 2602 (1966).
  7. Lord Rayleigh, Proc. Roy. Soc. (London) A79, 399 (1907).
  8. U. Fano, Ann. Phys. 32, 393 (1938).
  9. R. W. Wood, Phil. Mag. 4, 396 (1902); Phys. Rev. 48, 928 (1935).
  10. A. Hessel and A. A. Oliner, Appl. Opt. 4, 1275 (1965).
  11. S. Fujiwara and Y. Iguchi, J. Opt. Soc. Am. 58, 361 (1968). 1189
  12. In our expressions of boundary conditions, we assume that the whole grating surface is illuminated and that no part is shadowed by another part.
  13. The P and S components correspond to the components of the incident light with its electric vector parallel and perpendicular to the grooves, respectively.
  14. The spectral reflectances for the P component are almost the same as those of the S component, because the refractive index of glass is nearly equal to one in the soft x-ray region.
  15. G. Toraldo di Francia, La diffrazione della Luce (Edizioni Scientifiche Einaudi, Torino, Italia, 1958), p. 164; also, in La Théorie des Images Optiques, P. Fleury, A. Maréchal, C. Anglande, Eds. (Éditions de la Revue d’Optique, Paris, 1949), p. 205.
  16. When a beam of soft x rays is incident from vacuum side on a glass grating, the total reflection phenomenon can occur, since the refractive index of glass is less than one in the soft x-ray region.
  17. The reflectances are normalized at the second enhancing angle; that is, at ϑc, 0 for n>0 and ϑc, n for n<0.

Bedo, D. E.

G. Sprague, D. H. Tomboulian, and D. E. Bedo, J. Opt. Soc. Am. 45, 756 (1955); G. W. Stroke, in Encyclopedia of Physics 29, S. Flügge Ed. (Springer-Verlag, Berlin, 1967), pp. 603-6.

Ejiri, A.

T. Sagawa, Y. Iguchi, M. Sasanuma, A. Ejiri, S. Fujiwara, M. Yokota, S. Yamaguchi, M. Nakamura, T. Sasaki, and T. Oshio, J. Phys. Soc. Japan 21, 2602 (1966).

Fano, U.

U. Fano, Ann. Phys. 32, 393 (1938).

Francia, G. Toraldo di

G. Toraldo di Francia, La diffrazione della Luce (Edizioni Scientifiche Einaudi, Torino, Italia, 1958), p. 164; also, in La Théorie des Images Optiques, P. Fleury, A. Maréchal, C. Anglande, Eds. (Éditions de la Revue d’Optique, Paris, 1949), p. 205.

Fujiwara, S.

S. Fujiwara and Y. Iguchi, J. Opt. Soc. Am. 58, 361 (1968). 1189

T. Sagawa, Y. Iguchi, M. Sasanuma, A. Ejiri, S. Fujiwara, M. Yokota, S. Yamaguchi, M. Nakamura, T. Sasaki, and T. Oshio, J. Phys. Soc. Japan 21, 2602 (1966).

Hessel, A.

A. Hessel and A. A. Oliner, Appl. Opt. 4, 1275 (1965).

Iguchi, Y.

S. Fujiwara and Y. Iguchi, J. Opt. Soc. Am. 58, 361 (1968). 1189

T. Sagawa, Y. Iguchi, M. Sasanuma, A. Ejiri, S. Fujiwara, M. Yokota, S. Yamaguchi, M. Nakamura, T. Sasaki, and T. Oshio, J. Phys. Soc. Japan 21, 2602 (1966).

Jaeglé, P.

P. Jaeglé, Compt. Rend. 259, 533, 4556 (1964); Thèses, Contribution à la Spectrographie dans l’Ultraviolet de la Région de Holweck (Université de Paris, 1965).

Lukirskii, A. P.

A. P. Lukirskii and E. P. Savinov, Opt. Spektrosk. [Opt. Spektrosc.] 14, 147 (1963).

Miller, J. C.

J. C. Miller, J. Opt. Soc. Am. 54, 353 (1964).

Nakamura, M.

T. Sagawa, Y. Iguchi, M. Sasanuma, A. Ejiri, S. Fujiwara, M. Yokota, S. Yamaguchi, M. Nakamura, T. Sasaki, and T. Oshio, J. Phys. Soc. Japan 21, 2602 (1966).

Oliner, A. A.

A. Hessel and A. A. Oliner, Appl. Opt. 4, 1275 (1965).

Oshio, T.

T. Sagawa, Y. Iguchi, M. Sasanuma, A. Ejiri, S. Fujiwara, M. Yokota, S. Yamaguchi, M. Nakamura, T. Sasaki, and T. Oshio, J. Phys. Soc. Japan 21, 2602 (1966).

Rayleigh, Lord

Lord Rayleigh, Proc. Roy. Soc. (London) A79, 399 (1907).

Sagawa, T.

T. Sagawa, Sci. Rept. Tôhoku Univ. (I) 16, 119 (1962).

T. Sagawa, Y. Iguchi, M. Sasanuma, A. Ejiri, S. Fujiwara, M. Yokota, S. Yamaguchi, M. Nakamura, T. Sasaki, and T. Oshio, J. Phys. Soc. Japan 21, 2602 (1966).

Sasaki, T.

T. Sagawa, Y. Iguchi, M. Sasanuma, A. Ejiri, S. Fujiwara, M. Yokota, S. Yamaguchi, M. Nakamura, T. Sasaki, and T. Oshio, J. Phys. Soc. Japan 21, 2602 (1966).

Sasanuma, M.

T. Sagawa, Y. Iguchi, M. Sasanuma, A. Ejiri, S. Fujiwara, M. Yokota, S. Yamaguchi, M. Nakamura, T. Sasaki, and T. Oshio, J. Phys. Soc. Japan 21, 2602 (1966).

Savinov, E. P.

A. P. Lukirskii and E. P. Savinov, Opt. Spektrosk. [Opt. Spektrosc.] 14, 147 (1963).

Sprague, G.

G. Sprague, D. H. Tomboulian, and D. E. Bedo, J. Opt. Soc. Am. 45, 756 (1955); G. W. Stroke, in Encyclopedia of Physics 29, S. Flügge Ed. (Springer-Verlag, Berlin, 1967), pp. 603-6.

Tomboulian, D. H.

G. Sprague, D. H. Tomboulian, and D. E. Bedo, J. Opt. Soc. Am. 45, 756 (1955); G. W. Stroke, in Encyclopedia of Physics 29, S. Flügge Ed. (Springer-Verlag, Berlin, 1967), pp. 603-6.

Wood, R. W.

R. W. Wood, Phil. Mag. 4, 396 (1902); Phys. Rev. 48, 928 (1935).

Yamaguchi, S.

T. Sagawa, Y. Iguchi, M. Sasanuma, A. Ejiri, S. Fujiwara, M. Yokota, S. Yamaguchi, M. Nakamura, T. Sasaki, and T. Oshio, J. Phys. Soc. Japan 21, 2602 (1966).

Yokota, M.

T. Sagawa, Y. Iguchi, M. Sasanuma, A. Ejiri, S. Fujiwara, M. Yokota, S. Yamaguchi, M. Nakamura, T. Sasaki, and T. Oshio, J. Phys. Soc. Japan 21, 2602 (1966).

Other (17)

G. Sprague, D. H. Tomboulian, and D. E. Bedo, J. Opt. Soc. Am. 45, 756 (1955); G. W. Stroke, in Encyclopedia of Physics 29, S. Flügge Ed. (Springer-Verlag, Berlin, 1967), pp. 603-6.

J. C. Miller, J. Opt. Soc. Am. 54, 353 (1964).

P. Jaeglé, Compt. Rend. 259, 533, 4556 (1964); Thèses, Contribution à la Spectrographie dans l’Ultraviolet de la Région de Holweck (Université de Paris, 1965).

A. P. Lukirskii and E. P. Savinov, Opt. Spektrosk. [Opt. Spektrosc.] 14, 147 (1963).

T. Sagawa, Sci. Rept. Tôhoku Univ. (I) 16, 119 (1962).

T. Sagawa, Y. Iguchi, M. Sasanuma, A. Ejiri, S. Fujiwara, M. Yokota, S. Yamaguchi, M. Nakamura, T. Sasaki, and T. Oshio, J. Phys. Soc. Japan 21, 2602 (1966).

Lord Rayleigh, Proc. Roy. Soc. (London) A79, 399 (1907).

U. Fano, Ann. Phys. 32, 393 (1938).

R. W. Wood, Phil. Mag. 4, 396 (1902); Phys. Rev. 48, 928 (1935).

A. Hessel and A. A. Oliner, Appl. Opt. 4, 1275 (1965).

S. Fujiwara and Y. Iguchi, J. Opt. Soc. Am. 58, 361 (1968). 1189

In our expressions of boundary conditions, we assume that the whole grating surface is illuminated and that no part is shadowed by another part.

The P and S components correspond to the components of the incident light with its electric vector parallel and perpendicular to the grooves, respectively.

The spectral reflectances for the P component are almost the same as those of the S component, because the refractive index of glass is nearly equal to one in the soft x-ray region.

G. Toraldo di Francia, La diffrazione della Luce (Edizioni Scientifiche Einaudi, Torino, Italia, 1958), p. 164; also, in La Théorie des Images Optiques, P. Fleury, A. Maréchal, C. Anglande, Eds. (Éditions de la Revue d’Optique, Paris, 1949), p. 205.

When a beam of soft x rays is incident from vacuum side on a glass grating, the total reflection phenomenon can occur, since the refractive index of glass is less than one in the soft x-ray region.

The reflectances are normalized at the second enhancing angle; that is, at ϑc, 0 for n>0 and ϑc, n for n<0.

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