Abstract

The invariance of the direction of a given order diffracted by a grating used in conical diffraction (i.e., in off-plane mounting) when the grating is rotated about a suitable direction is established. The extension of this property to crossed gratings (2-D gratings) is demonstrated. An explanation of this amazing property is given in terms of Fermat's principle and applies to any reflecting surface.

© 1985 Optical Society of America

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References

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  1. D. Maystre, M. Neviere, R. Petit, “Experimental Verifications and Applications of the Theory,” in Electromagnetic Theory of Gratings, R. Petit, Ed. (Springer, Berlin, 1980), pp. 159–225.
    [CrossRef]
  2. W. Werner, “X-ray Efficiencies of Blazed Gratings in Extreme Off-Plane Mountings,” Appl. Opt. 16, 2078 (1977).
    [CrossRef] [PubMed]
  3. M. Neviere, D. Maystre, W. R. Hunter, “Use of Classical and Conical Diffraction Mountings for XUV Gratings,” J. Opt. Soc. Am. 68, 1106 (1967).
    [CrossRef]
  4. P. Vincent, M. Neviere, D. Mastre, “X-ray Gratings: the GMS Mounts,” Appl. Opt. 18, 1780 (1979).
    [CrossRef] [PubMed]
  5. W. Cash, “Echelle Spectrographs at Grazing Incidence,” Appl. Opt. 21, 710 (1982).
    [CrossRef] [PubMed]
  6. D. Maystre, “Integral Methods,” in Electromagnetic Theory of Gratings, R. Petit, Ed. (Springer, Berlin, 1980), p. 87.
  7. D. Maystre, M. Neviere, “Electromagnetic Theory of Crossed Gratings,” J. Opt. 9, 301 (1978).
    [CrossRef]
  8. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), p. 281.

1982 (1)

1979 (1)

1978 (1)

D. Maystre, M. Neviere, “Electromagnetic Theory of Crossed Gratings,” J. Opt. 9, 301 (1978).
[CrossRef]

1977 (1)

1967 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), p. 281.

Cash, W.

Hunter, W. R.

Mastre, D.

Maystre, D.

D. Maystre, M. Neviere, “Electromagnetic Theory of Crossed Gratings,” J. Opt. 9, 301 (1978).
[CrossRef]

M. Neviere, D. Maystre, W. R. Hunter, “Use of Classical and Conical Diffraction Mountings for XUV Gratings,” J. Opt. Soc. Am. 68, 1106 (1967).
[CrossRef]

D. Maystre, M. Neviere, R. Petit, “Experimental Verifications and Applications of the Theory,” in Electromagnetic Theory of Gratings, R. Petit, Ed. (Springer, Berlin, 1980), pp. 159–225.
[CrossRef]

D. Maystre, “Integral Methods,” in Electromagnetic Theory of Gratings, R. Petit, Ed. (Springer, Berlin, 1980), p. 87.

Neviere, M.

P. Vincent, M. Neviere, D. Mastre, “X-ray Gratings: the GMS Mounts,” Appl. Opt. 18, 1780 (1979).
[CrossRef] [PubMed]

D. Maystre, M. Neviere, “Electromagnetic Theory of Crossed Gratings,” J. Opt. 9, 301 (1978).
[CrossRef]

M. Neviere, D. Maystre, W. R. Hunter, “Use of Classical and Conical Diffraction Mountings for XUV Gratings,” J. Opt. Soc. Am. 68, 1106 (1967).
[CrossRef]

D. Maystre, M. Neviere, R. Petit, “Experimental Verifications and Applications of the Theory,” in Electromagnetic Theory of Gratings, R. Petit, Ed. (Springer, Berlin, 1980), pp. 159–225.
[CrossRef]

Petit, R.

D. Maystre, M. Neviere, R. Petit, “Experimental Verifications and Applications of the Theory,” in Electromagnetic Theory of Gratings, R. Petit, Ed. (Springer, Berlin, 1980), pp. 159–225.
[CrossRef]

Vincent, P.

Werner, W.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), p. 281.

Appl. Opt. (3)

J. Opt. (1)

D. Maystre, M. Neviere, “Electromagnetic Theory of Crossed Gratings,” J. Opt. 9, 301 (1978).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (3)

D. Maystre, “Integral Methods,” in Electromagnetic Theory of Gratings, R. Petit, Ed. (Springer, Berlin, 1980), p. 87.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), p. 281.

D. Maystre, M. Neviere, R. Petit, “Experimental Verifications and Applications of the Theory,” in Electromagnetic Theory of Gratings, R. Petit, Ed. (Springer, Berlin, 1980), pp. 159–225.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Description of the grating and notations.

Fig. 2
Fig. 2

Geometrical invariance property.

Fig. 3
Fig. 3

Interpretation of the invariance property in terms of geometrical optics; the angle of incidence i is defined with respect to Δ.

Equations (9)

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

k n x = k x + n K
k n y = k 2 k n x 2 k n z 2 ,
k n z = k z .
( k n k ) x ̂ = n K ,
( k n k ) z ̂ = 0 .
k n x = k x + n K 1 with K 1 = ( 2 π ) / ( d 1 ) ,
k n y = k 2 k n x 2 k n z 2
k n z = k z + n K 2 with K 2 = ( 2 π ) / ( d 2 ) .
( k n k ) x ̂ = n K 1 , ( k n k ) z ̂ = n K 2 .

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