Abstract

The capacity of optical fiber transmission systems could be increased by multiplexing several signals at different wavelengths on each fiber. This paper considers various multiplex system designs that might be used with multimode fiber transmission systems. In each case, the required multiplexer size and material properties are calculated as functions of the basic parameters of the fiber system. For fiber systems of the type currently being tested, a compact (~2 mm in diameter × 1 cm long), rugged, three-channel multiplexer could be constructed using a blazed plane reflection grating and graded-refractive-index (GRIN) optics; and it appears that such devices could be produced using available materials and technology. Multiplexers using thick gratings or multilayer dielectric filters are larger, more complicated, and require materials at the very edge of available technology. Multiplexers using a multiple thick grating or hologram could be even smaller than the blazed-grating devices, but materials having the required characteristics have not been demonstrated.

© 1977 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. I. Jacobs, Bell Lab. Rec. 54, 290 (1976).
  2. R. D. Burnham, D. R. Scifres, W. Streifer, Appl. Phys. Lett. 29, 287 (1976); F. K. Reinhart, R. A. Logan, C. V. Shank, Appl. Phys. Lett. 27, 45 (1975).
    [Crossref]
  3. K. Aiki, M. Nakamura, J. Umeda, Appl. Phys. Lett. 29, 506 (1976).
    [Crossref]
  4. D. Gloge, Bell Syst. Tech. J. 55, 905 (1976); C. M. Miller, Bell Syst. Tech. J. 55, 917 (1976).
  5. F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), pp. 454–5.
  6. S. S. Ballard, J. S. Browder, J. F. Ebersole, in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1972), p. 6–14.
  7. Ref. 6, p. 6–54
  8. For prism multiplexers the optical pathlength W is approximately equal to the prism base B and using Eq. (6) with m = 3, n′ = 1, B/b = 1, we find that S = 0.05(dn/dλ). Thus for all the prism materials discussed S ≲ 10−2.
  9. G. R. Harrison, R. C. Lord, J. R. Loofbourow, Practical Spectroscopy (Blackie, London, 1948), pp. 71–2.
  10. H. G. Beutler, J. Opt. Soc. Am. 35, 311 (1945).
    [Crossref]
  11. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  12. W. W. Rigrod, J. Opt. Soc. Am. 64, 97, 895 (1974).
    [Crossref]
  13. W. J. Tomlinson, E. A. Chandross, H. P. Weber, G. D. Aumiller, Appl. Opt. 15, 534 (1976).
    [Crossref] [PubMed]
  14. W. J. Tomlinson, Appl. Opt. 14, 2456 (1975).
    [Crossref] [PubMed]
  15. S. E. Miller, Bell Syst. Tech. J. 44, 2017 (1965).
  16. E. T. Kornhauser, A. D. YaghjianRadio Sci. 2, 299 (1967).
  17. E. G. Rawson, D. R. Herriot, J. McKenna, Appl. Opt. 9, 753 (1970).
    [Crossref] [PubMed]
  18. D. Kermisch, J. Opt. Soc. Am. 59, 1409 (1969).
    [Crossref]
  19. A. D. Pearson, W. G. French, E. G. Rawson, Appl. Phys. Lett. 15, 76 (1969).
    [Crossref]
  20. Y. Ohtsuka, Appl. Phys. Lett. 23, 247 (1973); K. Iga, K. Yokomori, T. Sakayori, Appl. Phys. Lett. 26, 578 (1975).
    [Crossref]
  21. E. G. Rawson, R. G. Murray, IEEE J. Quantum Electron. QE-9, 1114 (1973).
    [Crossref]
  22. W. G. French, J. B. MacChesney, A. D. Pearson, “Glass Fibers for Optical Communications,” in Annual Review of Materials Science (Annual Reviews, Palo Alto, 1975), (Vol. 5,) pp. 373–94.
    [Crossref]
  23. T. A. Litovitz, P. B. Macedo, C. T. Moynihan, C. J. Montrose, R. D. Mohr, J. H. Simmons, “Fiber Optic Waveguides by Molecular Stuffing,” ADA022272 (1975).
  24. W. J. Tomlinson, G. D. Aumiller (to be published in Appl. Phys. Lett.31, Aug.1977).
    [Crossref]

1976 (5)

I. Jacobs, Bell Lab. Rec. 54, 290 (1976).

R. D. Burnham, D. R. Scifres, W. Streifer, Appl. Phys. Lett. 29, 287 (1976); F. K. Reinhart, R. A. Logan, C. V. Shank, Appl. Phys. Lett. 27, 45 (1975).
[Crossref]

K. Aiki, M. Nakamura, J. Umeda, Appl. Phys. Lett. 29, 506 (1976).
[Crossref]

D. Gloge, Bell Syst. Tech. J. 55, 905 (1976); C. M. Miller, Bell Syst. Tech. J. 55, 917 (1976).

W. J. Tomlinson, E. A. Chandross, H. P. Weber, G. D. Aumiller, Appl. Opt. 15, 534 (1976).
[Crossref] [PubMed]

1975 (2)

W. J. Tomlinson, Appl. Opt. 14, 2456 (1975).
[Crossref] [PubMed]

T. A. Litovitz, P. B. Macedo, C. T. Moynihan, C. J. Montrose, R. D. Mohr, J. H. Simmons, “Fiber Optic Waveguides by Molecular Stuffing,” ADA022272 (1975).

1974 (1)

W. W. Rigrod, J. Opt. Soc. Am. 64, 97, 895 (1974).
[Crossref]

1973 (2)

Y. Ohtsuka, Appl. Phys. Lett. 23, 247 (1973); K. Iga, K. Yokomori, T. Sakayori, Appl. Phys. Lett. 26, 578 (1975).
[Crossref]

E. G. Rawson, R. G. Murray, IEEE J. Quantum Electron. QE-9, 1114 (1973).
[Crossref]

1970 (1)

1969 (3)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

D. Kermisch, J. Opt. Soc. Am. 59, 1409 (1969).
[Crossref]

A. D. Pearson, W. G. French, E. G. Rawson, Appl. Phys. Lett. 15, 76 (1969).
[Crossref]

1967 (1)

E. T. Kornhauser, A. D. YaghjianRadio Sci. 2, 299 (1967).

1965 (1)

S. E. Miller, Bell Syst. Tech. J. 44, 2017 (1965).

1945 (1)

Aiki, K.

K. Aiki, M. Nakamura, J. Umeda, Appl. Phys. Lett. 29, 506 (1976).
[Crossref]

Aumiller, G. D.

W. J. Tomlinson, E. A. Chandross, H. P. Weber, G. D. Aumiller, Appl. Opt. 15, 534 (1976).
[Crossref] [PubMed]

W. J. Tomlinson, G. D. Aumiller (to be published in Appl. Phys. Lett.31, Aug.1977).
[Crossref]

Ballard, S. S.

S. S. Ballard, J. S. Browder, J. F. Ebersole, in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1972), p. 6–14.

Beutler, H. G.

Browder, J. S.

S. S. Ballard, J. S. Browder, J. F. Ebersole, in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1972), p. 6–14.

Burnham, R. D.

R. D. Burnham, D. R. Scifres, W. Streifer, Appl. Phys. Lett. 29, 287 (1976); F. K. Reinhart, R. A. Logan, C. V. Shank, Appl. Phys. Lett. 27, 45 (1975).
[Crossref]

Chandross, E. A.

Ebersole, J. F.

S. S. Ballard, J. S. Browder, J. F. Ebersole, in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1972), p. 6–14.

French, W. G.

A. D. Pearson, W. G. French, E. G. Rawson, Appl. Phys. Lett. 15, 76 (1969).
[Crossref]

W. G. French, J. B. MacChesney, A. D. Pearson, “Glass Fibers for Optical Communications,” in Annual Review of Materials Science (Annual Reviews, Palo Alto, 1975), (Vol. 5,) pp. 373–94.
[Crossref]

Gloge, D.

D. Gloge, Bell Syst. Tech. J. 55, 905 (1976); C. M. Miller, Bell Syst. Tech. J. 55, 917 (1976).

Harrison, G. R.

G. R. Harrison, R. C. Lord, J. R. Loofbourow, Practical Spectroscopy (Blackie, London, 1948), pp. 71–2.

Herriot, D. R.

Jacobs, I.

I. Jacobs, Bell Lab. Rec. 54, 290 (1976).

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), pp. 454–5.

Kermisch, D.

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Kornhauser, E. T.

E. T. Kornhauser, A. D. YaghjianRadio Sci. 2, 299 (1967).

Litovitz, T. A.

T. A. Litovitz, P. B. Macedo, C. T. Moynihan, C. J. Montrose, R. D. Mohr, J. H. Simmons, “Fiber Optic Waveguides by Molecular Stuffing,” ADA022272 (1975).

Loofbourow, J. R.

G. R. Harrison, R. C. Lord, J. R. Loofbourow, Practical Spectroscopy (Blackie, London, 1948), pp. 71–2.

Lord, R. C.

G. R. Harrison, R. C. Lord, J. R. Loofbourow, Practical Spectroscopy (Blackie, London, 1948), pp. 71–2.

MacChesney, J. B.

W. G. French, J. B. MacChesney, A. D. Pearson, “Glass Fibers for Optical Communications,” in Annual Review of Materials Science (Annual Reviews, Palo Alto, 1975), (Vol. 5,) pp. 373–94.
[Crossref]

Macedo, P. B.

T. A. Litovitz, P. B. Macedo, C. T. Moynihan, C. J. Montrose, R. D. Mohr, J. H. Simmons, “Fiber Optic Waveguides by Molecular Stuffing,” ADA022272 (1975).

McKenna, J.

Miller, S. E.

S. E. Miller, Bell Syst. Tech. J. 44, 2017 (1965).

Mohr, R. D.

T. A. Litovitz, P. B. Macedo, C. T. Moynihan, C. J. Montrose, R. D. Mohr, J. H. Simmons, “Fiber Optic Waveguides by Molecular Stuffing,” ADA022272 (1975).

Montrose, C. J.

T. A. Litovitz, P. B. Macedo, C. T. Moynihan, C. J. Montrose, R. D. Mohr, J. H. Simmons, “Fiber Optic Waveguides by Molecular Stuffing,” ADA022272 (1975).

Moynihan, C. T.

T. A. Litovitz, P. B. Macedo, C. T. Moynihan, C. J. Montrose, R. D. Mohr, J. H. Simmons, “Fiber Optic Waveguides by Molecular Stuffing,” ADA022272 (1975).

Murray, R. G.

E. G. Rawson, R. G. Murray, IEEE J. Quantum Electron. QE-9, 1114 (1973).
[Crossref]

Nakamura, M.

K. Aiki, M. Nakamura, J. Umeda, Appl. Phys. Lett. 29, 506 (1976).
[Crossref]

Ohtsuka, Y.

Y. Ohtsuka, Appl. Phys. Lett. 23, 247 (1973); K. Iga, K. Yokomori, T. Sakayori, Appl. Phys. Lett. 26, 578 (1975).
[Crossref]

Pearson, A. D.

A. D. Pearson, W. G. French, E. G. Rawson, Appl. Phys. Lett. 15, 76 (1969).
[Crossref]

W. G. French, J. B. MacChesney, A. D. Pearson, “Glass Fibers for Optical Communications,” in Annual Review of Materials Science (Annual Reviews, Palo Alto, 1975), (Vol. 5,) pp. 373–94.
[Crossref]

Rawson, E. G.

E. G. Rawson, R. G. Murray, IEEE J. Quantum Electron. QE-9, 1114 (1973).
[Crossref]

E. G. Rawson, D. R. Herriot, J. McKenna, Appl. Opt. 9, 753 (1970).
[Crossref] [PubMed]

A. D. Pearson, W. G. French, E. G. Rawson, Appl. Phys. Lett. 15, 76 (1969).
[Crossref]

Rigrod, W. W.

W. W. Rigrod, J. Opt. Soc. Am. 64, 97, 895 (1974).
[Crossref]

Scifres, D. R.

R. D. Burnham, D. R. Scifres, W. Streifer, Appl. Phys. Lett. 29, 287 (1976); F. K. Reinhart, R. A. Logan, C. V. Shank, Appl. Phys. Lett. 27, 45 (1975).
[Crossref]

Simmons, J. H.

T. A. Litovitz, P. B. Macedo, C. T. Moynihan, C. J. Montrose, R. D. Mohr, J. H. Simmons, “Fiber Optic Waveguides by Molecular Stuffing,” ADA022272 (1975).

Streifer, W.

R. D. Burnham, D. R. Scifres, W. Streifer, Appl. Phys. Lett. 29, 287 (1976); F. K. Reinhart, R. A. Logan, C. V. Shank, Appl. Phys. Lett. 27, 45 (1975).
[Crossref]

Tomlinson, W. J.

Umeda, J.

K. Aiki, M. Nakamura, J. Umeda, Appl. Phys. Lett. 29, 506 (1976).
[Crossref]

Weber, H. P.

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), pp. 454–5.

Yaghjian, A. D.

E. T. Kornhauser, A. D. YaghjianRadio Sci. 2, 299 (1967).

ADA022272 (1)

T. A. Litovitz, P. B. Macedo, C. T. Moynihan, C. J. Montrose, R. D. Mohr, J. H. Simmons, “Fiber Optic Waveguides by Molecular Stuffing,” ADA022272 (1975).

Appl. Opt. (3)

Appl. Phys. Lett. (4)

R. D. Burnham, D. R. Scifres, W. Streifer, Appl. Phys. Lett. 29, 287 (1976); F. K. Reinhart, R. A. Logan, C. V. Shank, Appl. Phys. Lett. 27, 45 (1975).
[Crossref]

K. Aiki, M. Nakamura, J. Umeda, Appl. Phys. Lett. 29, 506 (1976).
[Crossref]

A. D. Pearson, W. G. French, E. G. Rawson, Appl. Phys. Lett. 15, 76 (1969).
[Crossref]

Y. Ohtsuka, Appl. Phys. Lett. 23, 247 (1973); K. Iga, K. Yokomori, T. Sakayori, Appl. Phys. Lett. 26, 578 (1975).
[Crossref]

Bell Lab. Rec. (1)

I. Jacobs, Bell Lab. Rec. 54, 290 (1976).

Bell Syst. Tech. J. (3)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

S. E. Miller, Bell Syst. Tech. J. 44, 2017 (1965).

D. Gloge, Bell Syst. Tech. J. 55, 905 (1976); C. M. Miller, Bell Syst. Tech. J. 55, 917 (1976).

IEEE J. Quantum Electron. (1)

E. G. Rawson, R. G. Murray, IEEE J. Quantum Electron. QE-9, 1114 (1973).
[Crossref]

J. Opt. Soc. Am. (3)

Radio Sci. (1)

E. T. Kornhauser, A. D. YaghjianRadio Sci. 2, 299 (1967).

Other (7)

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), pp. 454–5.

S. S. Ballard, J. S. Browder, J. F. Ebersole, in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1972), p. 6–14.

Ref. 6, p. 6–54

For prism multiplexers the optical pathlength W is approximately equal to the prism base B and using Eq. (6) with m = 3, n′ = 1, B/b = 1, we find that S = 0.05(dn/dλ). Thus for all the prism materials discussed S ≲ 10−2.

G. R. Harrison, R. C. Lord, J. R. Loofbourow, Practical Spectroscopy (Blackie, London, 1948), pp. 71–2.

W. J. Tomlinson, G. D. Aumiller (to be published in Appl. Phys. Lett.31, Aug.1977).
[Crossref]

W. G. French, J. B. MacChesney, A. D. Pearson, “Glass Fibers for Optical Communications,” in Annual Review of Materials Science (Annual Reviews, Palo Alto, 1975), (Vol. 5,) pp. 373–94.
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Schematic diagram of a multiplexed transmission system using beam splitters whose characteristics are not strongly wavelength-dependent.

Fig. 2
Fig. 2

Schematic drawing of a multiplexer using an angularly dispersive element.

Fig. 3
Fig. 3

Schematic drawings of multiplexers using prisms.

Fig. 4
Fig. 4

Schematic drawing of a multiplexer using a blazed plane reflection grating.

Fig. 5
Fig. 5

Cross section of a thick phase grating.

Fig. 6
Fig. 6

Schematic drawings of multiplexers using simple thick gratings: (a) reflection filter (ϕ = 0); (b) transmission filter (ϕ = π/2).

Fig. 7
Fig. 7

Efficiency of a simple thick reflection filter as a function of detuning from the Bragg condition for a grating with ν = π/2.

Fig. 8
Fig. 8

Schematic drawings of multiplexers using multiple-grating thick reflection filters.

Fig. 9
Fig. 9

Efficiency of a simple thick transmission filter as a function of detuning from the Bragg condition for a grating with ν = π/2.

Tables (3)

Tables Icon

Table I Insertion Loss and Crosstalk Resulting from Wavelength Errors for Angularly Dispersive Devices

Tables Icon

Table II Parameters of the Collimators Required for Multiplexers Using Various Wavelength-Sensitive Devices

Tables Icon

Table III Summary of Results for Multiplexers Using Various Types of Wavelength-Sensitive Elements a

Equations (56)

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

D λ ( N A ) d / Δ λ ,
d x / d λ = f [ d θ / d λ ] ,
[ d x / d λ ] Δ λ d ,
overlap = { 1 - 2 π | ( 1 - 2 ) 1 / 2 + sin - 1 ( ) | 0 1 0             > 1 ,
i = ( d x d λ Δ λ d ) ( δ λ Δ λ ) ,
c = ( d x d λ Δ λ d ) ( 1 - δ λ Δ λ ) .
b 2 f ( N A / n ) ,
b 2 ( N A / n ) d Δ λ ( d θ / d λ ) = 2 D λ ( d θ / d λ ) n .
S b - b b ( 1 + m ) W d ( N A ) b 2 n ,
d θ d λ = d θ d n d n d λ ,
d θ / d n = B / ( n b ) ,
b 2 d ( N A / n ) n Δ λ ( d n / d λ ) ( B / b ) ,
B 2 d ( N A / n ) n Δ λ ( d n / d λ ) = 2 D λ ( d n / d λ ) .
sin i + sin θ = ( k λ ) / ( n Λ ) ,
d θ / d i = - [ ( cos i ) / ( cos θ ) ] ,
d θ / d λ = ( 2 t a n θ ) / λ ,
b λ ( N A / n ) d Δ λ tan θ = D n tan θ .
S = 2 ( 1 + m ) tan 2 θ Δ λ / λ .
b D n [ 2 ( 1 + m ) Δ λ S λ ] 1 / 2 .
k λ / [ ( m - 1 ) Δ λ ] .
n ( x , y , z ) = n + n 1 cos [ 2 π Λ ( x sin ϕ + z cos ϕ ) ] .
sin θ = sin i - [ λ / ( n Λ ) ] sin ϕ ,
d θ / d i = ( cos i ) / ( cos θ ) ,
cos ( ϕ - i ) = λ / ( 2 n Λ ) ,
d θ / d λ = - [ ( 2 tan θ ) / λ ] sin ϕ ,
S = 2 ( m - 1 ) Δ θ = 2 ( m - 1 ) ( N A / n ) d / b ,
b = 2 ( m - 1 ) ( N A / n ) d S = D n [ 2 ( m - 1 ) Δ λ S λ ] .
η = { 1 1 + [ 1 - ( ζ / ν ) 2 / sinh 2 ( ν 2 - ζ 2 ) 1 / 2 ν 2 > ζ 2 ν 2 1 + ν 2 ν 2 = ζ 2 1 1 + [ ( ζ / ν ) 2 - 1 ] / sin 2 ( ζ 2 - ν 2 ) 1 / 2 ζ 2 > ν 2 ,
ν = ( π n 1 t ) / ( λ cos θ ) ,
ζ = ζ Δ λ + ζ Δ θ
ζ Δ θ = - [ ( 2 π n sin θ t ) / λ ] Δ θ ,
ζ Δ λ = - [ ( 2 π n cos θ t ) / λ ] [ ( Δ λ ) / λ ]
t = ( ζ Δ λ / π ) λ 2 n cos θ ( Δ λ / λ )
2 t Λ = 2 ( ζ Δ λ π ) ( λ Δ λ ) ,
ζ Δ θ π = tan θ S ( ζ Δ λ / π ) 2 ( m - 1 ) ( Δ λ / λ ) .
ζ δ λ / π = ( ζ Δ λ / π ) ( δ λ / Δ λ ) ,
n 1 n = cos 2 θ ( Δ λ / λ ) ( ζ Δ λ / π ) ,
ζ Δ θ = 2 π n t λ [ sin ( ϕ - θ ) Δ θ - cos ( ϕ - θ ) ( Δ θ ) 2 / 2 ] .
- 3 ( Δ θ ) 2 2 ζ Δ θ λ 2 π n t ( Δ θ ) 2 2 .
ζ Δ θ = ± [ ( 2 π n t ) / λ ] ( Δ θ ) 2 .
b = [ 8 t ( N A ) d S n ] 1 / 2 ,
ζ Δ θ / π = ± S ( N A ) d / ( 4 λ ) .
n 1 / n = ( Δ λ / λ ) / ( ζ Δ λ / π ) ,
t = [ ( ζ Δ λ / π ) λ ] / [ 2 n ( Δ λ / λ ) ] .
b = 1 n [ 4 D λ ( ζ Δ λ / π ) S ] 1 / 2 ,
η = sin 2 ( ν 2 + ζ 2 ) 1 / 2 1 + ( ζ / ν ) 2 ,
ν = ( π n 1 t ) / ( λ cos θ ) ,
ζ = ζ Δ λ + ζ Δ θ ,
ζ Δ θ = [ ( 2 π n sin θ t ) / λ ] Δ θ ,
ζ Δ λ = 2 π n sin 2 θ t λ cos θ Δ λ λ ,
t = ( ζ Δ λ / π ) λ cos θ 2 n sin 2 θ ( Δ λ / λ ) ,
ζ Δ θ π = S ( ζ Δ λ / π ) 2 ( m - 1 ) tan θ ( Δ λ / λ ) .
d x d λ Δ λ d = 2 ( m - 1 ) Δ λ S λ ,
n ( r ) = n A [ 1 - ( 1 / 2 ) α 2 r 2 ] ,
n ( r ) = n A sech ( α r ) ,
n ( r ) = n A ( 1 + α 2 r 2 ) - 1 / 2 .

Metrics