Abstract

A simple equation for the parameters of the Rowland circle grating mount is derived that ensures that the astigmatism and the meridional spherical aberration are stationary at the wavelength of correction. This is important in optimizing the design of grating multiplexers–demultiplexers and cross connects in wavelength-division multiplexed networks and high-resolution narrow-band spectrographs. An analysis of aberrations in three-dimensional and planar two-dimensional optical schemes is presented, and it is shown that in the wavelength range of 1530–1570 nm diffraction-limited performance can be achieved for 160 channels in a three-dimensional multiplexer–demultiplexer and for more than 800 channels for a planar free-space scheme.

© 1996 Optical Society of America

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References

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  1. I. Hawker, V. Tandon, D. Cotter, A. Hill, Brit. Telecommun. Eng. 13, 103 (1994).
  2. M. Sabry, J. E. Midwinter, Proc. Inst. Electr. Eng. Part J. 141, 327 (1994).
  3. T. Harada, T. Kita, Appl. Opt. 22, 819 (1983).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  6. K. R. Poguntke, J. B. D. Soole, H. P. LeBlanc, N. C. Andreadakis, P. Grabbe, R. Bhat, C. Caneau, M. A. Koza, Electron. Lett. 30, 512 (1994).
    [CrossRef]
  7. F. N. Timofeev, J. E. Midwinter, P. Bayvel, E. G. Churin, A. Stavdas, M. N. Sokolskii, Electron. Lett. 31, 1368 (1995).
    [CrossRef]
  8. E. Desurvire, Erbium-Doped Fiber Amplifiers: Principles and Applications (Wiley-Interscience, New York, 1994).
  9. M. P. Crisp, in Applied Optics and Optical Engineering,R. R. Shannon, J. C. Wyant, eds. (Academic, London, 1987), Vol. 10, pp. 391–454.
  10. T. Harada, T. Kita, Appl. Opt. 19, 3987 (1980).
    [CrossRef] [PubMed]
  11. R. Grange, Appl. Opt. 32, 4875 (1993).
    [CrossRef] [PubMed]
  12. A. Stavdas, J. E. Midwinter, P. Bayvel, C. Todd, J. Mod. Opt. 42, 1863 (1995).
    [CrossRef]
  13. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).
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    [CrossRef]

1995 (2)

F. N. Timofeev, J. E. Midwinter, P. Bayvel, E. G. Churin, A. Stavdas, M. N. Sokolskii, Electron. Lett. 31, 1368 (1995).
[CrossRef]

A. Stavdas, J. E. Midwinter, P. Bayvel, C. Todd, J. Mod. Opt. 42, 1863 (1995).
[CrossRef]

1994 (3)

I. Hawker, V. Tandon, D. Cotter, A. Hill, Brit. Telecommun. Eng. 13, 103 (1994).

M. Sabry, J. E. Midwinter, Proc. Inst. Electr. Eng. Part J. 141, 327 (1994).

K. R. Poguntke, J. B. D. Soole, H. P. LeBlanc, N. C. Andreadakis, P. Grabbe, R. Bhat, C. Caneau, M. A. Koza, Electron. Lett. 30, 512 (1994).
[CrossRef]

1993 (1)

1983 (1)

1981 (1)

B. J. Brown, I. J. Wilson, Opt. Acta 28, 1587 (1981).
[CrossRef]

1980 (1)

1974 (2)

Andreadakis, N. C.

K. R. Poguntke, J. B. D. Soole, H. P. LeBlanc, N. C. Andreadakis, P. Grabbe, R. Bhat, C. Caneau, M. A. Koza, Electron. Lett. 30, 512 (1994).
[CrossRef]

Bayvel, P.

A. Stavdas, J. E. Midwinter, P. Bayvel, C. Todd, J. Mod. Opt. 42, 1863 (1995).
[CrossRef]

F. N. Timofeev, J. E. Midwinter, P. Bayvel, E. G. Churin, A. Stavdas, M. N. Sokolskii, Electron. Lett. 31, 1368 (1995).
[CrossRef]

Bhat, R.

K. R. Poguntke, J. B. D. Soole, H. P. LeBlanc, N. C. Andreadakis, P. Grabbe, R. Bhat, C. Caneau, M. A. Koza, Electron. Lett. 30, 512 (1994).
[CrossRef]

Born, M.

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

Brown, B. J.

B. J. Brown, I. J. Wilson, Opt. Acta 28, 1587 (1981).
[CrossRef]

Caneau, C.

K. R. Poguntke, J. B. D. Soole, H. P. LeBlanc, N. C. Andreadakis, P. Grabbe, R. Bhat, C. Caneau, M. A. Koza, Electron. Lett. 30, 512 (1994).
[CrossRef]

Churin, E. G.

F. N. Timofeev, J. E. Midwinter, P. Bayvel, E. G. Churin, A. Stavdas, M. N. Sokolskii, Electron. Lett. 31, 1368 (1995).
[CrossRef]

Cotter, D.

I. Hawker, V. Tandon, D. Cotter, A. Hill, Brit. Telecommun. Eng. 13, 103 (1994).

Crisp, M. P.

M. P. Crisp, in Applied Optics and Optical Engineering,R. R. Shannon, J. C. Wyant, eds. (Academic, London, 1987), Vol. 10, pp. 391–454.

Desurvire, E.

E. Desurvire, Erbium-Doped Fiber Amplifiers: Principles and Applications (Wiley-Interscience, New York, 1994).

Grabbe, P.

K. R. Poguntke, J. B. D. Soole, H. P. LeBlanc, N. C. Andreadakis, P. Grabbe, R. Bhat, C. Caneau, M. A. Koza, Electron. Lett. 30, 512 (1994).
[CrossRef]

Grange, R.

Harada, T.

Hawker, I.

I. Hawker, V. Tandon, D. Cotter, A. Hill, Brit. Telecommun. Eng. 13, 103 (1994).

Hill, A.

I. Hawker, V. Tandon, D. Cotter, A. Hill, Brit. Telecommun. Eng. 13, 103 (1994).

Kita, T.

Koza, M. A.

K. R. Poguntke, J. B. D. Soole, H. P. LeBlanc, N. C. Andreadakis, P. Grabbe, R. Bhat, C. Caneau, M. A. Koza, Electron. Lett. 30, 512 (1994).
[CrossRef]

LeBlanc, H. P.

K. R. Poguntke, J. B. D. Soole, H. P. LeBlanc, N. C. Andreadakis, P. Grabbe, R. Bhat, C. Caneau, M. A. Koza, Electron. Lett. 30, 512 (1994).
[CrossRef]

Midwinter, J. E.

A. Stavdas, J. E. Midwinter, P. Bayvel, C. Todd, J. Mod. Opt. 42, 1863 (1995).
[CrossRef]

F. N. Timofeev, J. E. Midwinter, P. Bayvel, E. G. Churin, A. Stavdas, M. N. Sokolskii, Electron. Lett. 31, 1368 (1995).
[CrossRef]

M. Sabry, J. E. Midwinter, Proc. Inst. Electr. Eng. Part J. 141, 327 (1994).

Namioka, T.

Noda, H.

Poguntke, K. R.

K. R. Poguntke, J. B. D. Soole, H. P. LeBlanc, N. C. Andreadakis, P. Grabbe, R. Bhat, C. Caneau, M. A. Koza, Electron. Lett. 30, 512 (1994).
[CrossRef]

Sabry, M.

M. Sabry, J. E. Midwinter, Proc. Inst. Electr. Eng. Part J. 141, 327 (1994).

Seya, M.

Sokolskii, M. N.

F. N. Timofeev, J. E. Midwinter, P. Bayvel, E. G. Churin, A. Stavdas, M. N. Sokolskii, Electron. Lett. 31, 1368 (1995).
[CrossRef]

Soole, J. B. D.

K. R. Poguntke, J. B. D. Soole, H. P. LeBlanc, N. C. Andreadakis, P. Grabbe, R. Bhat, C. Caneau, M. A. Koza, Electron. Lett. 30, 512 (1994).
[CrossRef]

Stavdas, A.

A. Stavdas, J. E. Midwinter, P. Bayvel, C. Todd, J. Mod. Opt. 42, 1863 (1995).
[CrossRef]

F. N. Timofeev, J. E. Midwinter, P. Bayvel, E. G. Churin, A. Stavdas, M. N. Sokolskii, Electron. Lett. 31, 1368 (1995).
[CrossRef]

Tandon, V.

I. Hawker, V. Tandon, D. Cotter, A. Hill, Brit. Telecommun. Eng. 13, 103 (1994).

Timofeev, F. N.

F. N. Timofeev, J. E. Midwinter, P. Bayvel, E. G. Churin, A. Stavdas, M. N. Sokolskii, Electron. Lett. 31, 1368 (1995).
[CrossRef]

Todd, C.

A. Stavdas, J. E. Midwinter, P. Bayvel, C. Todd, J. Mod. Opt. 42, 1863 (1995).
[CrossRef]

Wilson, I. J.

B. J. Brown, I. J. Wilson, Opt. Acta 28, 1587 (1981).
[CrossRef]

Wolf, E.

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

Woodgate, B. E.

Appl. Opt. (3)

Brit. Telecommun. Eng. (1)

I. Hawker, V. Tandon, D. Cotter, A. Hill, Brit. Telecommun. Eng. 13, 103 (1994).

Electron. Lett. (2)

K. R. Poguntke, J. B. D. Soole, H. P. LeBlanc, N. C. Andreadakis, P. Grabbe, R. Bhat, C. Caneau, M. A. Koza, Electron. Lett. 30, 512 (1994).
[CrossRef]

F. N. Timofeev, J. E. Midwinter, P. Bayvel, E. G. Churin, A. Stavdas, M. N. Sokolskii, Electron. Lett. 31, 1368 (1995).
[CrossRef]

J. Mod. Opt. (1)

A. Stavdas, J. E. Midwinter, P. Bayvel, C. Todd, J. Mod. Opt. 42, 1863 (1995).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Acta (1)

B. J. Brown, I. J. Wilson, Opt. Acta 28, 1587 (1981).
[CrossRef]

Proc. Inst. Electr. Eng. Part J. (1)

M. Sabry, J. E. Midwinter, Proc. Inst. Electr. Eng. Part J. 141, 327 (1994).

Other (3)

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

E. Desurvire, Erbium-Doped Fiber Amplifiers: Principles and Applications (Wiley-Interscience, New York, 1994).

M. P. Crisp, in Applied Optics and Optical Engineering,R. R. Shannon, J. C. Wyant, eds. (Academic, London, 1987), Vol. 10, pp. 391–454.

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of a Rowland circle grating mount.

Fig. 2
Fig. 2

Root-mean-square wave aberration versus wavelength λ for a three-dimensional optical system in the direct (solid curve) and inverse (dashed curve) mounts.

Fig. 3
Fig. 3

Root-mean-square aberration versus wavelength l for a two-dimensional optical system in the direct (solid curve) and inverse (dashed curve) mounts.

Equations (11)

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x ( y , z ) = R ( R 2 y 2 z 2 ) 1 / 2 .
β 0 ( λ ) = arcsin [ ( λ / λ 0 ) ( sin α 0 + sin β 0 ) sin α 0 ] .
W ( y , z ) = AP + P B ( λ / λ 0 ) ( AP + PB ) ,
A P = { [ R cos 2 α 0 x ( y , z ) ] 2 + ( R cos α 0 sin α 0 y ) 2 + z 2 } 1 / 2 , P B = { [ R cos 2 β 0 x ( y , z ) ] 2 + ( R cos β 0 sin β 0 y ) 2 + z 2 } 1 / 2 , P B = { [ R cos 2 β ( λ ) x ( y , z ) ] 2 + [ R cos β ( λ ) sin β ( λ ) y ] 2 + z 2 } 1 / 2 ,
W ( y , z ) = W 02 z 2 + W 12 y z 2 + W 40 y 4 + W 22 y 2 z 2 + W 04 z 4 + ,
W 02 = 1 2 R [ sin 2 α 0 cos α 0 + sin 2 β ( λ ) cos β ( λ ) λ λ 0 ( sin 2 α 0 cos α 0 + sin 2 β ( λ ) cos β ( λ ) ) ] ,
W 40 = W 02 / 4 R 2 .
d W 0 d λ | λ = λ 0 = sin β 0 2 R λ 0 [ sin α 0 ( 2 sin 2 β 0 ) + sin β 0 cos 3 β 0 sin 2 α 0 sin β 0 cos α 0 ] = 0.
sin α 0 = sin β 0 cos 2 β 0 ± ( 1 + cos 2 β 0 ) 1 / 2 1 + sin 2 β 0 cos 2 β 0 ,
W ¯ 2 = 1 σ S W 2 ( y , z ) d y d z [ 1 σ s W ( y , z ) d y d z ] 2 ,
D λ = λ 0 R ( sin α 0 + sin β 0 ) .

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