Abstract

A method of designing aberration-corrected concave gratings and their mounting for optical demultiplexers is described. An aberration-corrected concave grating for a demultiplexer has been designed and fabricated for use in a six-channel multiplex system in the 800-nm wavelength region. A coupling efficiency of 55% and signal cross talk of less than ~3 × 10−4 have been achieved experimentally.

© 1983 Optical Society of America

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References

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  1. T. Miki, H. Ishio, IEEE Trans. Commun. COM-26, 1082 (1978).
    [CrossRef]
  2. W. J. Tomlinson, Appl. Opt. 16, 2180 (1977).
    [CrossRef] [PubMed]
  3. S. Sugimoto et al.Electron. Lett. 13, 680 (1977).
    [CrossRef]
  4. S. Sugimoto et al., Electron. Lett. 14, 15 (1978).
    [CrossRef]
  5. W. J. Tomlinson, C. Lin, Electron. Lett. 14, 345 (1978).
    [CrossRef]
  6. K. Aoyama, J. Minowa, Appl. Opt. 18, 1253 (1979).
    [CrossRef] [PubMed]
  7. M. Seki et al., Electron Lett. 18, 257 (1982).
    [CrossRef]
  8. B. D. Metcalf, J. F. Providakes, Appl. Opt. 21, 794 (1982).
    [CrossRef] [PubMed]
  9. T. Harada, S. Moriyama, T. Kita, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 175 (1975).
  10. T. Harada, T. Kita, Appl. Opt. 19, 3987 (1980).
    [CrossRef] [PubMed]
  11. T. Kita, T. Harada, in Abstracts, Spectroscopic Society of Japan, Fall Meeting, Kyoto (1978), p. 25 (in Japanese).
  12. R. Watanabe, K. Nosu, T. Harada, T. Kita, Electron. Lett. 16, 106 (1980).
    [CrossRef]
  13. M. Seya, K. Goto, Sci. Light Tokyo 5, 119 (1956).
  14. T. Kita, T. Harada, J. Spectrosc. Soc. Jpn 29, 31 (1980).
    [CrossRef]

1982 (2)

1980 (3)

T. Harada, T. Kita, Appl. Opt. 19, 3987 (1980).
[CrossRef] [PubMed]

R. Watanabe, K. Nosu, T. Harada, T. Kita, Electron. Lett. 16, 106 (1980).
[CrossRef]

T. Kita, T. Harada, J. Spectrosc. Soc. Jpn 29, 31 (1980).
[CrossRef]

1979 (1)

1978 (3)

T. Miki, H. Ishio, IEEE Trans. Commun. COM-26, 1082 (1978).
[CrossRef]

S. Sugimoto et al., Electron. Lett. 14, 15 (1978).
[CrossRef]

W. J. Tomlinson, C. Lin, Electron. Lett. 14, 345 (1978).
[CrossRef]

1977 (2)

W. J. Tomlinson, Appl. Opt. 16, 2180 (1977).
[CrossRef] [PubMed]

S. Sugimoto et al.Electron. Lett. 13, 680 (1977).
[CrossRef]

1975 (1)

T. Harada, S. Moriyama, T. Kita, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 175 (1975).

1956 (1)

M. Seya, K. Goto, Sci. Light Tokyo 5, 119 (1956).

Aoyama, K.

Goto, K.

M. Seya, K. Goto, Sci. Light Tokyo 5, 119 (1956).

Harada, T.

T. Kita, T. Harada, J. Spectrosc. Soc. Jpn 29, 31 (1980).
[CrossRef]

R. Watanabe, K. Nosu, T. Harada, T. Kita, Electron. Lett. 16, 106 (1980).
[CrossRef]

T. Harada, T. Kita, Appl. Opt. 19, 3987 (1980).
[CrossRef] [PubMed]

T. Harada, S. Moriyama, T. Kita, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 175 (1975).

T. Kita, T. Harada, in Abstracts, Spectroscopic Society of Japan, Fall Meeting, Kyoto (1978), p. 25 (in Japanese).

Ishio, H.

T. Miki, H. Ishio, IEEE Trans. Commun. COM-26, 1082 (1978).
[CrossRef]

Kita, T.

T. Harada, T. Kita, Appl. Opt. 19, 3987 (1980).
[CrossRef] [PubMed]

R. Watanabe, K. Nosu, T. Harada, T. Kita, Electron. Lett. 16, 106 (1980).
[CrossRef]

T. Kita, T. Harada, J. Spectrosc. Soc. Jpn 29, 31 (1980).
[CrossRef]

T. Harada, S. Moriyama, T. Kita, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 175 (1975).

T. Kita, T. Harada, in Abstracts, Spectroscopic Society of Japan, Fall Meeting, Kyoto (1978), p. 25 (in Japanese).

Lin, C.

W. J. Tomlinson, C. Lin, Electron. Lett. 14, 345 (1978).
[CrossRef]

Metcalf, B. D.

Miki, T.

T. Miki, H. Ishio, IEEE Trans. Commun. COM-26, 1082 (1978).
[CrossRef]

Minowa, J.

Moriyama, S.

T. Harada, S. Moriyama, T. Kita, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 175 (1975).

Nosu, K.

R. Watanabe, K. Nosu, T. Harada, T. Kita, Electron. Lett. 16, 106 (1980).
[CrossRef]

Providakes, J. F.

Seki, M.

M. Seki et al., Electron Lett. 18, 257 (1982).
[CrossRef]

Seya, M.

M. Seya, K. Goto, Sci. Light Tokyo 5, 119 (1956).

Sugimoto, S.

S. Sugimoto et al., Electron. Lett. 14, 15 (1978).
[CrossRef]

S. Sugimoto et al.Electron. Lett. 13, 680 (1977).
[CrossRef]

Tomlinson, W. J.

W. J. Tomlinson, C. Lin, Electron. Lett. 14, 345 (1978).
[CrossRef]

W. J. Tomlinson, Appl. Opt. 16, 2180 (1977).
[CrossRef] [PubMed]

Watanabe, R.

R. Watanabe, K. Nosu, T. Harada, T. Kita, Electron. Lett. 16, 106 (1980).
[CrossRef]

Appl. Opt. (4)

Electron Lett. (1)

M. Seki et al., Electron Lett. 18, 257 (1982).
[CrossRef]

Electron. Lett. (4)

S. Sugimoto et al.Electron. Lett. 13, 680 (1977).
[CrossRef]

S. Sugimoto et al., Electron. Lett. 14, 15 (1978).
[CrossRef]

W. J. Tomlinson, C. Lin, Electron. Lett. 14, 345 (1978).
[CrossRef]

R. Watanabe, K. Nosu, T. Harada, T. Kita, Electron. Lett. 16, 106 (1980).
[CrossRef]

IEEE Trans. Commun. (1)

T. Miki, H. Ishio, IEEE Trans. Commun. COM-26, 1082 (1978).
[CrossRef]

J. Spectrosc. Soc. Jpn (1)

T. Kita, T. Harada, J. Spectrosc. Soc. Jpn 29, 31 (1980).
[CrossRef]

Jpn. J. Appl. Phys. (1)

T. Harada, S. Moriyama, T. Kita, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 175 (1975).

Sci. Light Tokyo (1)

M. Seya, K. Goto, Sci. Light Tokyo 5, 119 (1956).

Other (1)

T. Kita, T. Harada, in Abstracts, Spectroscopic Society of Japan, Fall Meeting, Kyoto (1978), p. 25 (in Japanese).

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Figures (14)

Fig. 1
Fig. 1

Schematic diagram of the optical system.

Fig. 2
Fig. 2

Horizontal and vertical focal conditions for normal incidence mounting of an aberration-corrected concave grating.

Fig. 3
Fig. 3

Optical layout of a demultiplexer using an aberration-corrected concave grating with a 50-mm radius and a 300-groove/mm groove number.

Fig. 4
Fig. 4

Relation of Σ(rarh)2 and Σ(rarυ)2 and mounting parameter θ.

Fig. 5
Fig. 5

Calculated horizontal and vertical defocusing of a demultiplexer with a flat detection field.

Fig. 6
Fig. 6

Calculated efficiency map of a tripartite aberration-corrected concave grating at wavelength λ = 800 nm. Radius of curvature is 50 mm, the groove number is 300 grooves/mm, and the ruled area is 15 × 15 mm2.

Fig. 7
Fig. 7

Comparison of ray-traced spectral images obtained with an aberration-corrected concave grating and a conventional concave grating. Both gratings have 50-mm radii of curvature, 300 grooves/mm, and 15 × 15-mm2 ruled areas.

Fig. 8
Fig. 8

Calculated values of coupling efficiencies obtained with a demultiplexer using the concave gratings of Fig. 7. All input and output fibers have 60-μm core diameters and are arranged along a straight line.

Fig. 9
Fig. 9

Aberration-corrected concave grating for demultiplexers. The grating has 50-mm radius of curvature, 300 grooves/mm, 15 × 15-mm2 ruled area and is coated with gold.

Fig. 10
Fig. 10

Schematic diagram of the experimental setup.

Fig. 11
Fig. 11

Measured changes in coupling efficiency as a function of the horizontal position of the output fiber.

Fig. 12
Fig. 12

Measured changes in coupling efficiency as a function of the vertical position of the output fiber.

Fig. 13
Fig. 13

Dependence of coupling efficiency on defocusing

Fig. 14
Fig. 14

Amount of scattered light measured in a focal plane.

Tables (4)

Tables Icon

Table I Ruling and Mounting parameters for an Aberration-Corrected Concave Grating for a Demultipluxer

Tables Icon

Table II Coupling Efficiencies Obtained with Optimum Optical Mounting

Tables Icon

Table III Grating Efficiencies observed at a Wavelength of 821.5 nm

Tables Icon

Table IV Comparison of Calculated and Observed Values for Coupling and Grating Efficiencies and Insertion Factors

Equations (17)

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σ = σ 0 / ( 1 + 2 b 2 R w + 3 b 3 R 2 w 2 + 4 b 4 R 3 w 3 ) ,
cos 2 α r cos α R + cos 2 β r h cos β R + m λ σ 0 2 b 2 R = 0 ,
1 r cos α R + 1 r υ cos β R = 0 ,
m λ = σ 0 ( sin α + sin β ) .
r h R = 1 ( m λ / σ 0 ) 2 1 ( m λ / σ 0 ) 2 2 b 2 m λ / σ 0 = cos 2 β cos β 2 b 2 sin β ,
r υ R = 1 1 ( m λ / σ 0 ) 2 = 1 cos β .
sin α 2 r ( cos 2 α r cos α R ) + sin β 2 r h ( cos 2 β r h cos β R ) + m λ σ 0 b 3 R 2 = 0 ,
1 8 [ 4 sin 2 α r 2 ( cos 2 α r cos α R ) 1 r ( cos 2 α r cos α R ) 2 + 1 R 2 ( 1 r cos α R ) ] + 1 8 [ 4 sin 2 β r h 2 ( cos 2 β r h cos β R ) 1 r h ( cos 2 β r h cos β R ) 2 + 1 R 2 ( 1 r h cos β R ) ] + m λ σ 0 b 4 R 3 = 0.
d x d λ = f d θ d λ d 0 Δ λ = 7500 ,
d x d λ = R σ 0 .
R sin ( α β max ) d 0 ,
λ max = σ 0 ( sin α + sin β max ) .
r = L [ cos α + sin α tan ( α θ ) ] ,
r a = L [ cos β + sin β tan ( β θ ) ] .
λ = 2 σ 0 sin θ b ,
E C = ( E i T i ) / N ,
E c ( λ ) = E g ( λ , 1 ) E f ( λ ) ,

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