Abstract

The general equations for parameters of concave grating mounts that provide stationary and superstationary astigmatism at the wavelength of correction are derived for the first time, to the best of our knowledge. These can be used to design grating multi/demultiplexers for wavelength-division multiplexed optical communication systems and high-resolution, narrow-band spectrographs. Important special cases of stationary anastigmatic mounts and their performance are presented.

© 1997 Optical Society of America

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References

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  1. H. Noda, T. Namioka, M. Seya, “Geometric theory of the grating,” J. Opt. Soc. Am. 64, 1031–1048 (1974).
    [CrossRef]
  2. M. P. Chrisp, “Aberration-corrected holographic gratings and their mountings,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, London, 1987), Vol. 10, pp. 391–454.
  3. J. Cordelle, J. Flamand, G. Pieuchard, A. Labeyrie, “Aberration-corrected concave gratings made holographically,” in Optical Instruments and Techniques, J. H. Dikson, ed. (Oriel, Newcastle upon Tyne, U.K., 1970), pp. 117–124.
  4. R. Grange, “Aberration-reduced holographic spherical gratings for Rowland circle spectrographs,” Appl. Opt. 31, 3744–3749 (1992).
    [CrossRef] [PubMed]
  5. T. Kita, T. Harada, “Use of aberration-corrected concave gratings in optical demultiplexers,” Appl. Opt. 22, 819–825 (1983).
    [CrossRef] [PubMed]
  6. E. Desurvire, Erbium-doped fiber amplifiers: principles and applications (Wiley-Interscience, New York, 1994).
  7. I. V. Peisakhson, Yu. V. Bazharov, “Concave spherical diffraction gratings with compensated astigmatism in Rowland mountings,” Sov. J. Opt. Technol. 44(5) , 273–276 (1977).
  8. H. Beutler, “The theory of the concave grating,” J. Opt. Soc. Am. 35, 311–350 (1945).
    [CrossRef]
  9. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).
  10. T. Harada, T. Kita, “Mechanically ruled aberration-corrected concave gratings,” Appl. Opt. 19, 3987–3993 (1980).
    [CrossRef] [PubMed]
  11. R. Grange, “Holographic spherical gratings: a new family of quasi-stigmatic designs for the Rowland circle mounting,” Appl. Opt. 32, 4875–4880 (1993).
    [CrossRef] [PubMed]
  12. B. Gale, “The theory of variable spacing gratings,” Opt. Acta 13, 41–54 (1966).
    [CrossRef]
  13. Y. Sakayanagi, “A stigmatic concave grating with varying spacing,” Sci. Light (Tokyo) 16, 129–137 (1967).
  14. D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).
    [CrossRef]
  15. F. N. Timofeev, J. E. Midwinter, P. Bayvel, E. G. Churin, A. Stavdas, M. N. Sokolskii, “Free-space aberration-corrected grating demultiplexer for application in densely-spaced, subnanometre wavelength-routed optical networks,” Electron. Lett. 31, 1368–1370 (1995).
    [CrossRef]
  16. F. N. Timofeev, P. Bayvel, J. E. Midwinter, M. N. Sokolskii, “High performance, free-space ruled concave grating demultiplexer,” Electron. Lett. 31, 1466–1467 (1995).
    [CrossRef]
  17. I. V. Peisakhson, “Holographic diffraction gratings, focusing parallel ray bundles,” Sov. J. Opt. Technol. 46(6) , 338–340 (1979).

1995 (2)

F. N. Timofeev, J. E. Midwinter, P. Bayvel, E. G. Churin, A. Stavdas, M. N. Sokolskii, “Free-space aberration-corrected grating demultiplexer for application in densely-spaced, subnanometre wavelength-routed optical networks,” Electron. Lett. 31, 1368–1370 (1995).
[CrossRef]

F. N. Timofeev, P. Bayvel, J. E. Midwinter, M. N. Sokolskii, “High performance, free-space ruled concave grating demultiplexer,” Electron. Lett. 31, 1466–1467 (1995).
[CrossRef]

1993 (1)

1992 (1)

1983 (1)

1980 (1)

1979 (1)

I. V. Peisakhson, “Holographic diffraction gratings, focusing parallel ray bundles,” Sov. J. Opt. Technol. 46(6) , 338–340 (1979).

1977 (2)

I. V. Peisakhson, Yu. V. Bazharov, “Concave spherical diffraction gratings with compensated astigmatism in Rowland mountings,” Sov. J. Opt. Technol. 44(5) , 273–276 (1977).

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).
[CrossRef]

1974 (1)

1967 (1)

Y. Sakayanagi, “A stigmatic concave grating with varying spacing,” Sci. Light (Tokyo) 16, 129–137 (1967).

1966 (1)

B. Gale, “The theory of variable spacing gratings,” Opt. Acta 13, 41–54 (1966).
[CrossRef]

1945 (1)

Bayvel, P.

F. N. Timofeev, J. E. Midwinter, P. Bayvel, E. G. Churin, A. Stavdas, M. N. Sokolskii, “Free-space aberration-corrected grating demultiplexer for application in densely-spaced, subnanometre wavelength-routed optical networks,” Electron. Lett. 31, 1368–1370 (1995).
[CrossRef]

F. N. Timofeev, P. Bayvel, J. E. Midwinter, M. N. Sokolskii, “High performance, free-space ruled concave grating demultiplexer,” Electron. Lett. 31, 1466–1467 (1995).
[CrossRef]

Bazharov, Yu. V.

I. V. Peisakhson, Yu. V. Bazharov, “Concave spherical diffraction gratings with compensated astigmatism in Rowland mountings,” Sov. J. Opt. Technol. 44(5) , 273–276 (1977).

Beutler, H.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).

Chrisp, M. P.

M. P. Chrisp, “Aberration-corrected holographic gratings and their mountings,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, London, 1987), Vol. 10, pp. 391–454.

Churin, E. G.

F. N. Timofeev, J. E. Midwinter, P. Bayvel, E. G. Churin, A. Stavdas, M. N. Sokolskii, “Free-space aberration-corrected grating demultiplexer for application in densely-spaced, subnanometre wavelength-routed optical networks,” Electron. Lett. 31, 1368–1370 (1995).
[CrossRef]

Cordelle, J.

J. Cordelle, J. Flamand, G. Pieuchard, A. Labeyrie, “Aberration-corrected concave gratings made holographically,” in Optical Instruments and Techniques, J. H. Dikson, ed. (Oriel, Newcastle upon Tyne, U.K., 1970), pp. 117–124.

Desurvire, E.

E. Desurvire, Erbium-doped fiber amplifiers: principles and applications (Wiley-Interscience, New York, 1994).

Flamand, J.

J. Cordelle, J. Flamand, G. Pieuchard, A. Labeyrie, “Aberration-corrected concave gratings made holographically,” in Optical Instruments and Techniques, J. H. Dikson, ed. (Oriel, Newcastle upon Tyne, U.K., 1970), pp. 117–124.

Gale, B.

B. Gale, “The theory of variable spacing gratings,” Opt. Acta 13, 41–54 (1966).
[CrossRef]

Grange, R.

Harada, T.

Kita, T.

Labeyrie, A.

J. Cordelle, J. Flamand, G. Pieuchard, A. Labeyrie, “Aberration-corrected concave gratings made holographically,” in Optical Instruments and Techniques, J. H. Dikson, ed. (Oriel, Newcastle upon Tyne, U.K., 1970), pp. 117–124.

Marcuse, D.

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).
[CrossRef]

Midwinter, J. E.

F. N. Timofeev, P. Bayvel, J. E. Midwinter, M. N. Sokolskii, “High performance, free-space ruled concave grating demultiplexer,” Electron. Lett. 31, 1466–1467 (1995).
[CrossRef]

F. N. Timofeev, J. E. Midwinter, P. Bayvel, E. G. Churin, A. Stavdas, M. N. Sokolskii, “Free-space aberration-corrected grating demultiplexer for application in densely-spaced, subnanometre wavelength-routed optical networks,” Electron. Lett. 31, 1368–1370 (1995).
[CrossRef]

Namioka, T.

Noda, H.

Peisakhson, I. V.

I. V. Peisakhson, “Holographic diffraction gratings, focusing parallel ray bundles,” Sov. J. Opt. Technol. 46(6) , 338–340 (1979).

I. V. Peisakhson, Yu. V. Bazharov, “Concave spherical diffraction gratings with compensated astigmatism in Rowland mountings,” Sov. J. Opt. Technol. 44(5) , 273–276 (1977).

Pieuchard, G.

J. Cordelle, J. Flamand, G. Pieuchard, A. Labeyrie, “Aberration-corrected concave gratings made holographically,” in Optical Instruments and Techniques, J. H. Dikson, ed. (Oriel, Newcastle upon Tyne, U.K., 1970), pp. 117–124.

Sakayanagi, Y.

Y. Sakayanagi, “A stigmatic concave grating with varying spacing,” Sci. Light (Tokyo) 16, 129–137 (1967).

Seya, M.

Sokolskii, M. N.

F. N. Timofeev, J. E. Midwinter, P. Bayvel, E. G. Churin, A. Stavdas, M. N. Sokolskii, “Free-space aberration-corrected grating demultiplexer for application in densely-spaced, subnanometre wavelength-routed optical networks,” Electron. Lett. 31, 1368–1370 (1995).
[CrossRef]

F. N. Timofeev, P. Bayvel, J. E. Midwinter, M. N. Sokolskii, “High performance, free-space ruled concave grating demultiplexer,” Electron. Lett. 31, 1466–1467 (1995).
[CrossRef]

Stavdas, A.

F. N. Timofeev, J. E. Midwinter, P. Bayvel, E. G. Churin, A. Stavdas, M. N. Sokolskii, “Free-space aberration-corrected grating demultiplexer for application in densely-spaced, subnanometre wavelength-routed optical networks,” Electron. Lett. 31, 1368–1370 (1995).
[CrossRef]

Timofeev, F. N.

F. N. Timofeev, J. E. Midwinter, P. Bayvel, E. G. Churin, A. Stavdas, M. N. Sokolskii, “Free-space aberration-corrected grating demultiplexer for application in densely-spaced, subnanometre wavelength-routed optical networks,” Electron. Lett. 31, 1368–1370 (1995).
[CrossRef]

F. N. Timofeev, P. Bayvel, J. E. Midwinter, M. N. Sokolskii, “High performance, free-space ruled concave grating demultiplexer,” Electron. Lett. 31, 1466–1467 (1995).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).

Appl. Opt. (4)

Bell Syst. Tech. J. (1)

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).
[CrossRef]

Electron. Lett. (2)

F. N. Timofeev, J. E. Midwinter, P. Bayvel, E. G. Churin, A. Stavdas, M. N. Sokolskii, “Free-space aberration-corrected grating demultiplexer for application in densely-spaced, subnanometre wavelength-routed optical networks,” Electron. Lett. 31, 1368–1370 (1995).
[CrossRef]

F. N. Timofeev, P. Bayvel, J. E. Midwinter, M. N. Sokolskii, “High performance, free-space ruled concave grating demultiplexer,” Electron. Lett. 31, 1466–1467 (1995).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Acta (1)

B. Gale, “The theory of variable spacing gratings,” Opt. Acta 13, 41–54 (1966).
[CrossRef]

Sci. Light (Tokyo) (1)

Y. Sakayanagi, “A stigmatic concave grating with varying spacing,” Sci. Light (Tokyo) 16, 129–137 (1967).

Sov. J. Opt. Technol. (2)

I. V. Peisakhson, “Holographic diffraction gratings, focusing parallel ray bundles,” Sov. J. Opt. Technol. 46(6) , 338–340 (1979).

I. V. Peisakhson, Yu. V. Bazharov, “Concave spherical diffraction gratings with compensated astigmatism in Rowland mountings,” Sov. J. Opt. Technol. 44(5) , 273–276 (1977).

Other (4)

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).

M. P. Chrisp, “Aberration-corrected holographic gratings and their mountings,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, London, 1987), Vol. 10, pp. 391–454.

J. Cordelle, J. Flamand, G. Pieuchard, A. Labeyrie, “Aberration-corrected concave gratings made holographically,” in Optical Instruments and Techniques, J. H. Dikson, ed. (Oriel, Newcastle upon Tyne, U.K., 1970), pp. 117–124.

E. Desurvire, Erbium-doped fiber amplifiers: principles and applications (Wiley-Interscience, New York, 1994).

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Figures (18)

Fig. 1
Fig. 1

Schematic diagram of the optical scheme.

Fig. 2
Fig. 2

Diagram of solutions β00) providing stationary astigmatism on the Rowland circle.

Fig. 3
Fig. 3

Diagram of solutions β00) providing stationary astigmatism on the sagittal straight line x = R.

Fig. 4
Fig. 4

(a) Superstationary anastigmatic mount on the sagittal straight line (α0 = -9.447°, β0 = 31.399°) and (b) its rms wave aberration as a function of wavelength.

Fig. 5
Fig. 5

(a) Mount on the sagittal straight line stationary anastigmatic in both directions (α0 = 46.77866°, β0 = 13.22135°) and (b) its rms wave aberration for through (solid curve) and inverse (dashed curve) optical schemes.

Fig. 6
Fig. 6

(a) Stationary anastigmatic mount with normal imaging (α0 = 20.70481°, β0 = 8.421058°, r α0 = r β0 = 1.000673R) and (b) its rms wave aberration.

Fig. 7
Fig. 7

(a) Stationary anastigmatic mount on the Rowland circle (α0 = 20.48454°, β0 = 8.62930°) and (b) its rms wave aberration.

Fig. 8
Fig. 8

(a) Stationary anastigmatic mount on the sagittal straight line (α0 = 20.95274°, β0 = 8.186875°) and (b) its rms wave aberration.

Fig. 9
Fig. 9

(a) Superstationary anastigmatic mount with normal imaging (α0 = -18.37351°, β0 = 49.55110°, r α0 = r β0 = 0.943098R) and (b) its rms wave aberration.

Fig. 10
Fig. 10

(a) Stationary anastigmatic Littrow mount (α0 = β0 = 30°) and (b) its rms wave aberration.

Fig. 11
Fig. 11

Same as Fig. 10 except α0 = β0 = 45°.

Fig. 12
Fig. 12

Same as Fig. 10 except α0 = β0 = 60°.

Fig. 13
Fig. 13

(a) Wadsworth mount (α0 = 60°, r β0 = R/2) and (b) its rms wave aberration.

Fig. 14
Fig. 14

Same as Fig. 13 except for normal imaging (α0 = 60°, r β0 = R/1.5).

Fig. 15
Fig. 15

Same as Fig. 13 except α0 = 60°, r β0 = R.

Fig. 16
Fig. 16

Stationary anastigmatic mount with normal imaging for a parallel incident beam (α0 = -20.70481°, β0 = 45°, r β0 = 0.50098R) and (b) its rms wave aberration.

Fig. 17
Fig. 17

(a) Superstationary anastigmatic mount for a parallel incident beam (α0= -11.75530°, β0 = 33.62344°, r β0 = 0.618326R) and (b) its rms wave aberration.

Fig. 18
Fig. 18

(a) Superstationary anastigmatic mount with a flat image surface (α0 = 30°, β0 = 12.77°, r α0 = 2.146733R, r β0 = 1.66327R) and (b) its rms wave aberration.

Equations (34)

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xy, z=R-R2-y2-z21/2.
Fy, z=AP+PB-kλ0my, z,
AP=rα0 cos α0-xy, z2+rα0 sin α0-y2+z21/2,PB=rβ0 cos β0-xy, z2+rβ0 sin β0-y2+z21/2,
my, z|λ0, α0, β0, rα0, rβ0=1kλ0AP+PB-rα0+rβ0,
my, z=M10y+M20y2+M02z2,
M10=-1kλ0sin α0+sin β0
M20=12kλ0cos2 α0rα0+cos2 β0rβ0-cos α0+cos β0R
M02=12kλ01rα0+1rβ0-cos α0+cos β0R
βλ=arcsinλλ0sin α0+sin β0-sin α0,
rβM=cos2 βλλλ0cos2 α0rα0+cos2 β0rβ0-cos α0+cos β0R-cos2 α0rα0+cos α0+cos βλR-1,
rβSλ=λλ01rα0+1rβ0-cos α0+cos β0R-1rα0+cos α0+cos βλR-1.
W¯2=1σSW2y, zdydz-1σSWy, zdydz2,
W=kλΔm.
Wy, z=kλmy, z|λ0, α0, β0, rα0, rβ0-my, z|λ, α0, βλ, rα0, rβMλ,
rβM-rβSλ=0.
1rβ0=sin α0-sin β02rα0 sin β0+sin β01+cosβ0-α02Rq0 cos β0,
q0=sin α0+sin β0.
2rβM-rβSλ2=0.
1rα0=sin β0q02+cos2 β0q02-sin2 β0-α0+q0 cos β0 sinβ0-α0Rq03 cos3 β0,
1rβ0=sin β04 sin2 α0 cos2 β01+cosβ0-α0+q02 sin β0sin α0-sin β02Rq03 cos3β0.
rα0=R cos α0,  rβ0=R cos β0.
sin α02-sin2 β0+sin β0cos3 β0-sin2 α0sin β0 cos α0=0.
sin α0=sin β0cos2 β0±1+cos2 β01+sin2 β0 cos2 β0,
rα0=R/cos α0,  rβ0=R/cos β0.
sin β01+cosβ0-α0q0 cos β0-q0 cos α0+sin2β0-sin2α0sin β0=0.
cos2 α0rα0=1+cosβ0-α0R cos β0-cos2 β0+2q0 sin β0rβ0.
1rα0=sin β0q0+sin α01+cosβ0-α0Rq02 cos β0,
1rβ0=sin2 α01+cosβ0-α0Rq02 cos β0.
rα0=rβ0,  α0=β0,
rα0=2R cosα0,
rβ0=R/1+cos α0.
1rβ0=sin β01+cosβ0-α02Rq0 cos β0.
sin β0=-2sin α0
1rβ0=1+cosβ0-α0R cos β0.

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