Abstract

Using electromagnetic theory, we first establish that a triangular-groove dielectric grating can be optimized to concentrate all the transmitted energy into only one transmitted order. This is done by evaporating an infinitely thin layer of a perfectly conducting metal on the small facet of the grooves. The +1-order transmitted efficiency then approaches 96%, the difference from 100% being due to only the Fresnel normal reflection on the large facet. Second, a similar study is conducted with an antireflection coating added to the large facet. A diffraction efficiency of 100% is then theoretically obtained.

© 1990 Optical Society of America

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References

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  1. R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
    [CrossRef]
  2. M. C. Hutley, Diffraction Gratings, N. H. March, H. N. Daglish, eds. (Academic, New York, 1982).
  3. A. Baranne, “The large pupil case: the Essefem multislit spectrograph,” presented at Summer Workshop on Instrumentation for Ground Based Optical Astronomy, Santa Cruz, 1987.
  4. A. Baranne, “Sur l’emploi des réseaux par transmission en optique astronomique,” C. R. Acad. Sci. Paris B 291, 205 (1980).
  5. A. Maréchal, G. W. Stroke, “Sur l’origine des effets de polarisation et de diffraction dans les réseaux optiques,” C. R. Acad. Sci. B 249, 2042–2044 (1959).
  6. A. Hessel, J. Schmoys, D. Y. Tseng, “Bragg-angle blazing of diffraction gratings,” J. Opt. Soc. Am. 65, 380–384 (1975).
    [CrossRef]
  7. J. L. Roumiguieres, D. Maystre, R. Petit, “On the efficiencies of rectangular-groove gratings,” J. Opt. Soc. Am. 66, 772–775 (1976).
    [CrossRef]
  8. L. S. Cheo, J. Schmoys, A. Hessel, “On simultaneous blazing of triangular groove diffraction gratings,” J. Opt. Soc. Am. 67, 1686–1688 (1977).
    [CrossRef]
  9. M. Breidne, D. Maystre, “Perfect blaze in non-Littrow mountings. A systematic study,” Opt. Acta 28, 1321–1327 (1981).
    [CrossRef]
  10. D. Maystre, M. Cadilhac, J. Chandezon, “Gratings: a phenomenological approach and its applications, perfect blazing in a nonzero deviation mounting,” Opt. Acta 28, 457–470 (1981).
    [CrossRef]
  11. D. Maystre, M. Cadilhac, “A phenomenological theory for gratings: perfect blazing for polarized light in nonzero deviation mounting,” Radio Sci. 16, 1003–1008 (1981).
    [CrossRef]
  12. J. P. Laude, “Improved diffraction gratings and methods of making,” European Patent0332790, March18, 1988.

1981 (3)

M. Breidne, D. Maystre, “Perfect blaze in non-Littrow mountings. A systematic study,” Opt. Acta 28, 1321–1327 (1981).
[CrossRef]

D. Maystre, M. Cadilhac, J. Chandezon, “Gratings: a phenomenological approach and its applications, perfect blazing in a nonzero deviation mounting,” Opt. Acta 28, 457–470 (1981).
[CrossRef]

D. Maystre, M. Cadilhac, “A phenomenological theory for gratings: perfect blazing for polarized light in nonzero deviation mounting,” Radio Sci. 16, 1003–1008 (1981).
[CrossRef]

1980 (1)

A. Baranne, “Sur l’emploi des réseaux par transmission en optique astronomique,” C. R. Acad. Sci. Paris B 291, 205 (1980).

1977 (1)

L. S. Cheo, J. Schmoys, A. Hessel, “On simultaneous blazing of triangular groove diffraction gratings,” J. Opt. Soc. Am. 67, 1686–1688 (1977).
[CrossRef]

1976 (1)

J. L. Roumiguieres, D. Maystre, R. Petit, “On the efficiencies of rectangular-groove gratings,” J. Opt. Soc. Am. 66, 772–775 (1976).
[CrossRef]

1975 (1)

1959 (1)

A. Maréchal, G. W. Stroke, “Sur l’origine des effets de polarisation et de diffraction dans les réseaux optiques,” C. R. Acad. Sci. B 249, 2042–2044 (1959).

Baranne, A.

A. Baranne, “Sur l’emploi des réseaux par transmission en optique astronomique,” C. R. Acad. Sci. Paris B 291, 205 (1980).

A. Baranne, “The large pupil case: the Essefem multislit spectrograph,” presented at Summer Workshop on Instrumentation for Ground Based Optical Astronomy, Santa Cruz, 1987.

Breidne, M.

M. Breidne, D. Maystre, “Perfect blaze in non-Littrow mountings. A systematic study,” Opt. Acta 28, 1321–1327 (1981).
[CrossRef]

Cadilhac, M.

D. Maystre, M. Cadilhac, J. Chandezon, “Gratings: a phenomenological approach and its applications, perfect blazing in a nonzero deviation mounting,” Opt. Acta 28, 457–470 (1981).
[CrossRef]

D. Maystre, M. Cadilhac, “A phenomenological theory for gratings: perfect blazing for polarized light in nonzero deviation mounting,” Radio Sci. 16, 1003–1008 (1981).
[CrossRef]

Chandezon, J.

D. Maystre, M. Cadilhac, J. Chandezon, “Gratings: a phenomenological approach and its applications, perfect blazing in a nonzero deviation mounting,” Opt. Acta 28, 457–470 (1981).
[CrossRef]

Cheo, L. S.

L. S. Cheo, J. Schmoys, A. Hessel, “On simultaneous blazing of triangular groove diffraction gratings,” J. Opt. Soc. Am. 67, 1686–1688 (1977).
[CrossRef]

Hessel, A.

L. S. Cheo, J. Schmoys, A. Hessel, “On simultaneous blazing of triangular groove diffraction gratings,” J. Opt. Soc. Am. 67, 1686–1688 (1977).
[CrossRef]

A. Hessel, J. Schmoys, D. Y. Tseng, “Bragg-angle blazing of diffraction gratings,” J. Opt. Soc. Am. 65, 380–384 (1975).
[CrossRef]

Hutley, M. C.

M. C. Hutley, Diffraction Gratings, N. H. March, H. N. Daglish, eds. (Academic, New York, 1982).

Laude, J. P.

J. P. Laude, “Improved diffraction gratings and methods of making,” European Patent0332790, March18, 1988.

Maréchal, A.

A. Maréchal, G. W. Stroke, “Sur l’origine des effets de polarisation et de diffraction dans les réseaux optiques,” C. R. Acad. Sci. B 249, 2042–2044 (1959).

Maystre, D.

D. Maystre, M. Cadilhac, “A phenomenological theory for gratings: perfect blazing for polarized light in nonzero deviation mounting,” Radio Sci. 16, 1003–1008 (1981).
[CrossRef]

M. Breidne, D. Maystre, “Perfect blaze in non-Littrow mountings. A systematic study,” Opt. Acta 28, 1321–1327 (1981).
[CrossRef]

D. Maystre, M. Cadilhac, J. Chandezon, “Gratings: a phenomenological approach and its applications, perfect blazing in a nonzero deviation mounting,” Opt. Acta 28, 457–470 (1981).
[CrossRef]

J. L. Roumiguieres, D. Maystre, R. Petit, “On the efficiencies of rectangular-groove gratings,” J. Opt. Soc. Am. 66, 772–775 (1976).
[CrossRef]

Petit, R.

J. L. Roumiguieres, D. Maystre, R. Petit, “On the efficiencies of rectangular-groove gratings,” J. Opt. Soc. Am. 66, 772–775 (1976).
[CrossRef]

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
[CrossRef]

Roumiguieres, J. L.

J. L. Roumiguieres, D. Maystre, R. Petit, “On the efficiencies of rectangular-groove gratings,” J. Opt. Soc. Am. 66, 772–775 (1976).
[CrossRef]

Schmoys, J.

L. S. Cheo, J. Schmoys, A. Hessel, “On simultaneous blazing of triangular groove diffraction gratings,” J. Opt. Soc. Am. 67, 1686–1688 (1977).
[CrossRef]

A. Hessel, J. Schmoys, D. Y. Tseng, “Bragg-angle blazing of diffraction gratings,” J. Opt. Soc. Am. 65, 380–384 (1975).
[CrossRef]

Stroke, G. W.

A. Maréchal, G. W. Stroke, “Sur l’origine des effets de polarisation et de diffraction dans les réseaux optiques,” C. R. Acad. Sci. B 249, 2042–2044 (1959).

Tseng, D. Y.

C. R. Acad. Sci. B (1)

A. Maréchal, G. W. Stroke, “Sur l’origine des effets de polarisation et de diffraction dans les réseaux optiques,” C. R. Acad. Sci. B 249, 2042–2044 (1959).

C. R. Acad. Sci. Paris B (1)

A. Baranne, “Sur l’emploi des réseaux par transmission en optique astronomique,” C. R. Acad. Sci. Paris B 291, 205 (1980).

J. Opt. Soc. Am. (2)

J. L. Roumiguieres, D. Maystre, R. Petit, “On the efficiencies of rectangular-groove gratings,” J. Opt. Soc. Am. 66, 772–775 (1976).
[CrossRef]

L. S. Cheo, J. Schmoys, A. Hessel, “On simultaneous blazing of triangular groove diffraction gratings,” J. Opt. Soc. Am. 67, 1686–1688 (1977).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Acta (2)

M. Breidne, D. Maystre, “Perfect blaze in non-Littrow mountings. A systematic study,” Opt. Acta 28, 1321–1327 (1981).
[CrossRef]

D. Maystre, M. Cadilhac, J. Chandezon, “Gratings: a phenomenological approach and its applications, perfect blazing in a nonzero deviation mounting,” Opt. Acta 28, 457–470 (1981).
[CrossRef]

Radio Sci. (1)

D. Maystre, M. Cadilhac, “A phenomenological theory for gratings: perfect blazing for polarized light in nonzero deviation mounting,” Radio Sci. 16, 1003–1008 (1981).
[CrossRef]

Other (4)

J. P. Laude, “Improved diffraction gratings and methods of making,” European Patent0332790, March18, 1988.

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
[CrossRef]

M. C. Hutley, Diffraction Gratings, N. H. March, H. N. Daglish, eds. (Academic, New York, 1982).

A. Baranne, “The large pupil case: the Essefem multislit spectrograph,” presented at Summer Workshop on Instrumentation for Ground Based Optical Astronomy, Santa Cruz, 1987.

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Figures (4)

Fig. 1
Fig. 1

Reflection–refraction of a TM plane wave under normal incidence.

Fig. 2
Fig. 2

Reflection–refraction of a step.

Fig. 3
Fig. 3

Optimized transmission grating.

Fig. 4
Fig. 4

Magnetic-field formulas in a step with an antireflection coating. Hi = exp(−iky)ez; Ht = t exp(−ikny)ez; Hl = [f exp (−ikny) + g exp(ikny)]ez; Hr = [f exp(−ikny) + g exp(ikny)]ez.

Equations (25)

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

H i = exp ( i k y ) e z ,
H r = r exp ( + i k y ) e z ,
H t = t exp ( i k n y ) e z .
r = n 1 n + 1 ,
t = 2 n n + 1 .
exp ( i k a ) + r exp ( i k a ) = t exp ( i k n a ) ,
i k exp ( i k a ) + i k r exp ( i k a ) = i k t n exp ( i k a n ) .
a = p λ 2 ,
a = q λ n 1 ,
n = p + 2 q p .
a = λ n 1 .
1 = f + g ,
k = k n f + k n g
f exp ( i k n e ) + g exp ( i k n e ) = t exp ( i k n e ) ,
k n f exp ( i k n e ) + k n g exp ( i k n e ) = k n t exp ( i k n e )
exp ( i k a ) = f exp ( i k n a ) + g exp ( i k n a ) ,
k exp ( i k a ) = k n f exp ( i k n a ) + k n g exp ( i k n a )
f exp [ i k n ( a + e ) ] + g exp [ i k n ( a + e ) ] = t exp [ i k n ( a + e ) ] ,
k n f exp [ i k n ( a + e ) ] + k n g exp [ i k n ( a + e ) ] = k n t exp [ i k n ( a + e ) ] .
1 = f exp [ i k ( n 1 ) a ] + g exp [ i k ( n + 1 ) a ] ,
k = k n f exp [ i k ( n 1 ) a ] + k n g exp [ i k ( n + 1 ) a ] ,
f exp ( i k n e ) exp [ i k ( n n ) a ] + g exp ( i k n e ) × exp [ i k ( n + n ) a ] = t exp ( i k n e ) ,
k n f exp ( i k n e ) exp [ i k ( n n ) a ] + k n g exp ( i k n e ) × exp [ i k ( n + n ) a ] = k n t exp ( i k n e ) ;
f exp ( i k n e ) exp [ i k ( 1 n ) a ] + g exp ( i k n e ) × exp [ i k ( 1 + n ) g ] = t exp ( i k n e ) , k n f exp ( i k n e ) exp [ i k ( 1 n ) a ] + k n g exp ( i k n e ) × exp [ i k ( 1 + n ) a ] = k n t exp ( i k n e ) .
a = q λ n 1 ,

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