Abstract

The problem of signal degradation due to spatial filtration in graded-index fibers excited by single-mode lasers is considered. In particular, a computer simulation of the interfering pattern is used to predict the signal-to-noise ratios which would be measured given some degree of vignetting at the detector end of the fiber. An experiment is made and comparison with the simulation results shows acceptable agreement.

© 1983 Optical Society of America

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References

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  1. R. E. Epworth, “The Phenomena of Modal Noise in Analogue and Digital Optical Fibre Systems,” in Technical Digest, Fourth European Conference on Optical Communication, Genoa (1978), pp. 492–501.
  2. B. Crosignani, B. Daino, P. Di Porto, J. Opt. Soc. Am. 66, 1312 (1976).
    [CrossRef]
  3. H. Takahara, Appl.Opt. 15, 609 (1976).
    [CrossRef] [PubMed]
  4. B. Crosignani, P. Di Porto, Fiber Integr. Opt. 77, 49 (1976).
    [CrossRef]
  5. B. Crosignani, B. Daino, P. Di Porto, Appl. Phys. Lett. 27, 237 (1975).
    [CrossRef]
  6. D. Marcuse, J. Opt. Soc. Am. 67, 997 (1977).
    [CrossRef]
  7. B. Daino, G. DeMarchis, S. Piazzolla, Electron. Lett. 15, 755 (1979).
    [CrossRef]
  8. B. Daino, G. DeMarchis, S. Piazzolla, Opt. Acta 27, 1151 (1980).
    [CrossRef]
  9. G. DeMarchis, S. Piazzolla, B. Daino, “Modal Noise in Optical Fibres,” in Technical Digest, Sixth European Conference on Optical Communication, U. York (1980), pp. 76–79.
  10. B. Daino, G. DeMarchis, S. Piazzolla, Opt. Commun. 38, 340 (1981).
    [CrossRef]
  11. K. O. Hill, Y. Tremblay, B. S. Kawasaki, Opt. Lett. 5, 270 (1980).
    [CrossRef] [PubMed]
  12. Y. Tremblay, B. S. Kawasaki, K. O. Hill, Appl. Opt. 20, 1652 (1981).
    [CrossRef] [PubMed]
  13. E. G. Rawson, J. W. Goodman, R. E. Norton, Opt. Lett. 5, 357 (1980).
    [CrossRef] [PubMed]
  14. E. G. Rawson, J. W. Goodman, R. E. Norton, J. Opt. Soc. Am. 70, 968 (1980).
    [CrossRef]
  15. E. G. Rawson, J. W. Goodman, R. E. Norton, “Experimental and Analytical Study of Modal Noise in Optical Fibers,” in Technical Digest, Sixth European Conference on Optical Communications, U. York, (1980), pp. 72–75.
  16. J. W. Goodman, E. G. Rawson, Opt. Lett. 6, 324 (1981).
    [CrossRef] [PubMed]
  17. K-I. Kitayama, S. Seikai, Y. Kato, N. Uchida, O. Fukuda, K. Inada, IEEE J. Quantum Electron. QE-15, 638 (1979).
    [CrossRef]
  18. M. Eriksrud, A. Hordvik, N. Ryen, G. Nakken, Opt. Quantum Electron. 11, 517 (1979).
    [CrossRef]
  19. P. Facq, P. Fournet, J. Arnaud, Electron. Lett. 16, 648 (1980).
    [CrossRef]
  20. S. Berdagué, P. Facq, Appl. Opt. 21, 1950 (1982).
    [CrossRef] [PubMed]
  21. D. Marcuse, The Theory of Dielectric Optical Waveguides (Academic, New York, 1974), pp. 153–157.
  22. G. Le Noame, “Optical Cable Design,” in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), pp. 12.1-1–12.1-8.
  23. Most authors acknowledge the first work on this topic as having beenE. Snitzer, J. Opt. Soc. Am. 51, 491 (1961).The first work to find the exact equations of the modal fields is that ofC. N. Kurtz, W. Streifer, IEEE Trans. Microwave Theory Tech. MTT-17, 11 (1969).The first paper to discuss the use of solutions of scalar equations as generators of the exact vector fields in fibers wasC. N. Kurtz, J. Opt. Soc. Am. 65, 1235 (1975).An especially lucid exposition of the relation between LP modes and actual vector modes is given in:A. W. Synder, W. R. Young, J. Opt. Soc. Am. 68, 297 (1978).
    [CrossRef]
  24. G. B. Hocker, Appl. Opt. 18, 1445 (1979).
    [CrossRef] [PubMed]
  25. A. W. Snyder, W. R. Young, J. Opt. Soc. Am. 68, 297 (1978).
    [CrossRef]
  26. This is explained in a very pleasant way by Marcuse immediately after his presentation of the LP modes, in an attempt to explain the problems associated with LP modes. See Ref. 21, p. 69.
  27. The characteristic beat lengths of single-mode fibers vary from millimeters to hundreds of meters depending on the design. The order of magnitude of centimeters for beat lengths in fibers which are not specially designed could be surmised from any of various works on the topic.See, for example I. P. Kaminow, IEEE J. Quantum Electron. QE-17, 15 (1981).
    [CrossRef]
  28. This fact follows from the law of large numbers.This point, as it relates to conventional speckle theory, is discussed inJ. W. Goodman, “Statistical Properties of Laser Speckle,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, New York, 1975), pp. 14 and 15.
  29. K. Petermann, IEEE J. Quantum Electron. QE-16, 761 (1980).
    [CrossRef]
  30. K. Petermann, “Nonlinear Distortions Due to Fibre Connectors,” in Technical Digest, Sixth European Conference on Optical Communication, U. York (1980), pp. 80–83.
  31. K. Sato, K. Asatani, Electron. Lett. 16, 538 (1980).
    [CrossRef]
  32. Y. C. Chen, Appl. Phys. Lett. 37, 587 (1980).
    [CrossRef]
  33. A. Dandridge, R. O. Miles, Electron. Lett. 17, 273 (1981).
    [CrossRef]
  34. A. B. Sharma, E. J. R. Hubach, M. Lähteenoja, S. J. Halme, Electron. Lett. 18, 56 (1982).
    [CrossRef]
  35. The Gaussian-Laguerre solution was first derived for optical waveguides inW. Streifer, C. N. Kurtz, J. Opt. Soc. Am. 57, 779 (1967).The appellation LP modes was first used inD. Gloge, Appl. Opt. 10, 2252 (1971).
    [CrossRef] [PubMed]
  36. See, for example, A. R. Mickelson, M. Eriksrud, Opt. Lett. 7, 572 (1982).
    [CrossRef] [PubMed]
  37. J. C. Danity, Ed., Laser Speckle and Related Phenomena (Springer, New York, 1975).

1982 (3)

1981 (5)

A. Dandridge, R. O. Miles, Electron. Lett. 17, 273 (1981).
[CrossRef]

The characteristic beat lengths of single-mode fibers vary from millimeters to hundreds of meters depending on the design. The order of magnitude of centimeters for beat lengths in fibers which are not specially designed could be surmised from any of various works on the topic.See, for example I. P. Kaminow, IEEE J. Quantum Electron. QE-17, 15 (1981).
[CrossRef]

Y. Tremblay, B. S. Kawasaki, K. O. Hill, Appl. Opt. 20, 1652 (1981).
[CrossRef] [PubMed]

J. W. Goodman, E. G. Rawson, Opt. Lett. 6, 324 (1981).
[CrossRef] [PubMed]

B. Daino, G. DeMarchis, S. Piazzolla, Opt. Commun. 38, 340 (1981).
[CrossRef]

1980 (8)

K. O. Hill, Y. Tremblay, B. S. Kawasaki, Opt. Lett. 5, 270 (1980).
[CrossRef] [PubMed]

E. G. Rawson, J. W. Goodman, R. E. Norton, Opt. Lett. 5, 357 (1980).
[CrossRef] [PubMed]

E. G. Rawson, J. W. Goodman, R. E. Norton, J. Opt. Soc. Am. 70, 968 (1980).
[CrossRef]

B. Daino, G. DeMarchis, S. Piazzolla, Opt. Acta 27, 1151 (1980).
[CrossRef]

P. Facq, P. Fournet, J. Arnaud, Electron. Lett. 16, 648 (1980).
[CrossRef]

K. Petermann, IEEE J. Quantum Electron. QE-16, 761 (1980).
[CrossRef]

K. Sato, K. Asatani, Electron. Lett. 16, 538 (1980).
[CrossRef]

Y. C. Chen, Appl. Phys. Lett. 37, 587 (1980).
[CrossRef]

1979 (4)

G. B. Hocker, Appl. Opt. 18, 1445 (1979).
[CrossRef] [PubMed]

K-I. Kitayama, S. Seikai, Y. Kato, N. Uchida, O. Fukuda, K. Inada, IEEE J. Quantum Electron. QE-15, 638 (1979).
[CrossRef]

M. Eriksrud, A. Hordvik, N. Ryen, G. Nakken, Opt. Quantum Electron. 11, 517 (1979).
[CrossRef]

B. Daino, G. DeMarchis, S. Piazzolla, Electron. Lett. 15, 755 (1979).
[CrossRef]

1978 (1)

1977 (1)

1976 (3)

B. Crosignani, B. Daino, P. Di Porto, J. Opt. Soc. Am. 66, 1312 (1976).
[CrossRef]

H. Takahara, Appl.Opt. 15, 609 (1976).
[CrossRef] [PubMed]

B. Crosignani, P. Di Porto, Fiber Integr. Opt. 77, 49 (1976).
[CrossRef]

1975 (1)

B. Crosignani, B. Daino, P. Di Porto, Appl. Phys. Lett. 27, 237 (1975).
[CrossRef]

1967 (1)

1961 (1)

Arnaud, J.

P. Facq, P. Fournet, J. Arnaud, Electron. Lett. 16, 648 (1980).
[CrossRef]

Asatani, K.

K. Sato, K. Asatani, Electron. Lett. 16, 538 (1980).
[CrossRef]

Berdagué, S.

Chen, Y. C.

Y. C. Chen, Appl. Phys. Lett. 37, 587 (1980).
[CrossRef]

Crosignani, B.

B. Crosignani, B. Daino, P. Di Porto, J. Opt. Soc. Am. 66, 1312 (1976).
[CrossRef]

B. Crosignani, P. Di Porto, Fiber Integr. Opt. 77, 49 (1976).
[CrossRef]

B. Crosignani, B. Daino, P. Di Porto, Appl. Phys. Lett. 27, 237 (1975).
[CrossRef]

Daino, B.

B. Daino, G. DeMarchis, S. Piazzolla, Opt. Commun. 38, 340 (1981).
[CrossRef]

B. Daino, G. DeMarchis, S. Piazzolla, Opt. Acta 27, 1151 (1980).
[CrossRef]

B. Daino, G. DeMarchis, S. Piazzolla, Electron. Lett. 15, 755 (1979).
[CrossRef]

B. Crosignani, B. Daino, P. Di Porto, J. Opt. Soc. Am. 66, 1312 (1976).
[CrossRef]

B. Crosignani, B. Daino, P. Di Porto, Appl. Phys. Lett. 27, 237 (1975).
[CrossRef]

G. DeMarchis, S. Piazzolla, B. Daino, “Modal Noise in Optical Fibres,” in Technical Digest, Sixth European Conference on Optical Communication, U. York (1980), pp. 76–79.

Dandridge, A.

A. Dandridge, R. O. Miles, Electron. Lett. 17, 273 (1981).
[CrossRef]

DeMarchis, G.

B. Daino, G. DeMarchis, S. Piazzolla, Opt. Commun. 38, 340 (1981).
[CrossRef]

B. Daino, G. DeMarchis, S. Piazzolla, Opt. Acta 27, 1151 (1980).
[CrossRef]

B. Daino, G. DeMarchis, S. Piazzolla, Electron. Lett. 15, 755 (1979).
[CrossRef]

G. DeMarchis, S. Piazzolla, B. Daino, “Modal Noise in Optical Fibres,” in Technical Digest, Sixth European Conference on Optical Communication, U. York (1980), pp. 76–79.

Di Porto, P.

B. Crosignani, P. Di Porto, Fiber Integr. Opt. 77, 49 (1976).
[CrossRef]

B. Crosignani, B. Daino, P. Di Porto, J. Opt. Soc. Am. 66, 1312 (1976).
[CrossRef]

B. Crosignani, B. Daino, P. Di Porto, Appl. Phys. Lett. 27, 237 (1975).
[CrossRef]

Epworth, R. E.

R. E. Epworth, “The Phenomena of Modal Noise in Analogue and Digital Optical Fibre Systems,” in Technical Digest, Fourth European Conference on Optical Communication, Genoa (1978), pp. 492–501.

Eriksrud, M.

See, for example, A. R. Mickelson, M. Eriksrud, Opt. Lett. 7, 572 (1982).
[CrossRef] [PubMed]

M. Eriksrud, A. Hordvik, N. Ryen, G. Nakken, Opt. Quantum Electron. 11, 517 (1979).
[CrossRef]

Facq, P.

S. Berdagué, P. Facq, Appl. Opt. 21, 1950 (1982).
[CrossRef] [PubMed]

P. Facq, P. Fournet, J. Arnaud, Electron. Lett. 16, 648 (1980).
[CrossRef]

Fournet, P.

P. Facq, P. Fournet, J. Arnaud, Electron. Lett. 16, 648 (1980).
[CrossRef]

Fukuda, O.

K-I. Kitayama, S. Seikai, Y. Kato, N. Uchida, O. Fukuda, K. Inada, IEEE J. Quantum Electron. QE-15, 638 (1979).
[CrossRef]

Goodman, J. W.

J. W. Goodman, E. G. Rawson, Opt. Lett. 6, 324 (1981).
[CrossRef] [PubMed]

E. G. Rawson, J. W. Goodman, R. E. Norton, Opt. Lett. 5, 357 (1980).
[CrossRef] [PubMed]

E. G. Rawson, J. W. Goodman, R. E. Norton, J. Opt. Soc. Am. 70, 968 (1980).
[CrossRef]

E. G. Rawson, J. W. Goodman, R. E. Norton, “Experimental and Analytical Study of Modal Noise in Optical Fibers,” in Technical Digest, Sixth European Conference on Optical Communications, U. York, (1980), pp. 72–75.

This fact follows from the law of large numbers.This point, as it relates to conventional speckle theory, is discussed inJ. W. Goodman, “Statistical Properties of Laser Speckle,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, New York, 1975), pp. 14 and 15.

Halme, S. J.

A. B. Sharma, E. J. R. Hubach, M. Lähteenoja, S. J. Halme, Electron. Lett. 18, 56 (1982).
[CrossRef]

Hill, K. O.

Hocker, G. B.

Hordvik, A.

M. Eriksrud, A. Hordvik, N. Ryen, G. Nakken, Opt. Quantum Electron. 11, 517 (1979).
[CrossRef]

Hubach, E. J. R.

A. B. Sharma, E. J. R. Hubach, M. Lähteenoja, S. J. Halme, Electron. Lett. 18, 56 (1982).
[CrossRef]

Inada, K.

K-I. Kitayama, S. Seikai, Y. Kato, N. Uchida, O. Fukuda, K. Inada, IEEE J. Quantum Electron. QE-15, 638 (1979).
[CrossRef]

Kaminow, I. P.

The characteristic beat lengths of single-mode fibers vary from millimeters to hundreds of meters depending on the design. The order of magnitude of centimeters for beat lengths in fibers which are not specially designed could be surmised from any of various works on the topic.See, for example I. P. Kaminow, IEEE J. Quantum Electron. QE-17, 15 (1981).
[CrossRef]

Kato, Y.

K-I. Kitayama, S. Seikai, Y. Kato, N. Uchida, O. Fukuda, K. Inada, IEEE J. Quantum Electron. QE-15, 638 (1979).
[CrossRef]

Kawasaki, B. S.

Kitayama, K-I.

K-I. Kitayama, S. Seikai, Y. Kato, N. Uchida, O. Fukuda, K. Inada, IEEE J. Quantum Electron. QE-15, 638 (1979).
[CrossRef]

Kurtz, C. N.

Lähteenoja, M.

A. B. Sharma, E. J. R. Hubach, M. Lähteenoja, S. J. Halme, Electron. Lett. 18, 56 (1982).
[CrossRef]

Le Noame, G.

G. Le Noame, “Optical Cable Design,” in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), pp. 12.1-1–12.1-8.

Marcuse, D.

D. Marcuse, J. Opt. Soc. Am. 67, 997 (1977).
[CrossRef]

D. Marcuse, The Theory of Dielectric Optical Waveguides (Academic, New York, 1974), pp. 153–157.

Mickelson, A. R.

Miles, R. O.

A. Dandridge, R. O. Miles, Electron. Lett. 17, 273 (1981).
[CrossRef]

Nakken, G.

M. Eriksrud, A. Hordvik, N. Ryen, G. Nakken, Opt. Quantum Electron. 11, 517 (1979).
[CrossRef]

Norton, R. E.

E. G. Rawson, J. W. Goodman, R. E. Norton, Opt. Lett. 5, 357 (1980).
[CrossRef] [PubMed]

E. G. Rawson, J. W. Goodman, R. E. Norton, J. Opt. Soc. Am. 70, 968 (1980).
[CrossRef]

E. G. Rawson, J. W. Goodman, R. E. Norton, “Experimental and Analytical Study of Modal Noise in Optical Fibers,” in Technical Digest, Sixth European Conference on Optical Communications, U. York, (1980), pp. 72–75.

Petermann, K.

K. Petermann, IEEE J. Quantum Electron. QE-16, 761 (1980).
[CrossRef]

K. Petermann, “Nonlinear Distortions Due to Fibre Connectors,” in Technical Digest, Sixth European Conference on Optical Communication, U. York (1980), pp. 80–83.

Piazzolla, S.

B. Daino, G. DeMarchis, S. Piazzolla, Opt. Commun. 38, 340 (1981).
[CrossRef]

B. Daino, G. DeMarchis, S. Piazzolla, Opt. Acta 27, 1151 (1980).
[CrossRef]

B. Daino, G. DeMarchis, S. Piazzolla, Electron. Lett. 15, 755 (1979).
[CrossRef]

G. DeMarchis, S. Piazzolla, B. Daino, “Modal Noise in Optical Fibres,” in Technical Digest, Sixth European Conference on Optical Communication, U. York (1980), pp. 76–79.

Rawson, E. G.

J. W. Goodman, E. G. Rawson, Opt. Lett. 6, 324 (1981).
[CrossRef] [PubMed]

E. G. Rawson, J. W. Goodman, R. E. Norton, J. Opt. Soc. Am. 70, 968 (1980).
[CrossRef]

E. G. Rawson, J. W. Goodman, R. E. Norton, Opt. Lett. 5, 357 (1980).
[CrossRef] [PubMed]

E. G. Rawson, J. W. Goodman, R. E. Norton, “Experimental and Analytical Study of Modal Noise in Optical Fibers,” in Technical Digest, Sixth European Conference on Optical Communications, U. York, (1980), pp. 72–75.

Ryen, N.

M. Eriksrud, A. Hordvik, N. Ryen, G. Nakken, Opt. Quantum Electron. 11, 517 (1979).
[CrossRef]

Sato, K.

K. Sato, K. Asatani, Electron. Lett. 16, 538 (1980).
[CrossRef]

Seikai, S.

K-I. Kitayama, S. Seikai, Y. Kato, N. Uchida, O. Fukuda, K. Inada, IEEE J. Quantum Electron. QE-15, 638 (1979).
[CrossRef]

Sharma, A. B.

A. B. Sharma, E. J. R. Hubach, M. Lähteenoja, S. J. Halme, Electron. Lett. 18, 56 (1982).
[CrossRef]

Snitzer, E.

Snyder, A. W.

Streifer, W.

Takahara, H.

H. Takahara, Appl.Opt. 15, 609 (1976).
[CrossRef] [PubMed]

Tremblay, Y.

Uchida, N.

K-I. Kitayama, S. Seikai, Y. Kato, N. Uchida, O. Fukuda, K. Inada, IEEE J. Quantum Electron. QE-15, 638 (1979).
[CrossRef]

Young, W. R.

Appl. Opt. (3)

Appl. Phys. Lett. (2)

Y. C. Chen, Appl. Phys. Lett. 37, 587 (1980).
[CrossRef]

B. Crosignani, B. Daino, P. Di Porto, Appl. Phys. Lett. 27, 237 (1975).
[CrossRef]

Appl.Opt. (1)

H. Takahara, Appl.Opt. 15, 609 (1976).
[CrossRef] [PubMed]

Electron. Lett. (5)

B. Daino, G. DeMarchis, S. Piazzolla, Electron. Lett. 15, 755 (1979).
[CrossRef]

A. Dandridge, R. O. Miles, Electron. Lett. 17, 273 (1981).
[CrossRef]

A. B. Sharma, E. J. R. Hubach, M. Lähteenoja, S. J. Halme, Electron. Lett. 18, 56 (1982).
[CrossRef]

K. Sato, K. Asatani, Electron. Lett. 16, 538 (1980).
[CrossRef]

P. Facq, P. Fournet, J. Arnaud, Electron. Lett. 16, 648 (1980).
[CrossRef]

Fiber Integr. Opt. (1)

B. Crosignani, P. Di Porto, Fiber Integr. Opt. 77, 49 (1976).
[CrossRef]

IEEE J. Quantum Electron. (3)

K-I. Kitayama, S. Seikai, Y. Kato, N. Uchida, O. Fukuda, K. Inada, IEEE J. Quantum Electron. QE-15, 638 (1979).
[CrossRef]

The characteristic beat lengths of single-mode fibers vary from millimeters to hundreds of meters depending on the design. The order of magnitude of centimeters for beat lengths in fibers which are not specially designed could be surmised from any of various works on the topic.See, for example I. P. Kaminow, IEEE J. Quantum Electron. QE-17, 15 (1981).
[CrossRef]

K. Petermann, IEEE J. Quantum Electron. QE-16, 761 (1980).
[CrossRef]

J. Opt. Soc. Am. (6)

Opt. Acta (1)

B. Daino, G. DeMarchis, S. Piazzolla, Opt. Acta 27, 1151 (1980).
[CrossRef]

Opt. Commun. (1)

B. Daino, G. DeMarchis, S. Piazzolla, Opt. Commun. 38, 340 (1981).
[CrossRef]

Opt. Lett. (4)

Opt. Quantum Electron. (1)

M. Eriksrud, A. Hordvik, N. Ryen, G. Nakken, Opt. Quantum Electron. 11, 517 (1979).
[CrossRef]

Other (9)

E. G. Rawson, J. W. Goodman, R. E. Norton, “Experimental and Analytical Study of Modal Noise in Optical Fibers,” in Technical Digest, Sixth European Conference on Optical Communications, U. York, (1980), pp. 72–75.

G. DeMarchis, S. Piazzolla, B. Daino, “Modal Noise in Optical Fibres,” in Technical Digest, Sixth European Conference on Optical Communication, U. York (1980), pp. 76–79.

R. E. Epworth, “The Phenomena of Modal Noise in Analogue and Digital Optical Fibre Systems,” in Technical Digest, Fourth European Conference on Optical Communication, Genoa (1978), pp. 492–501.

J. C. Danity, Ed., Laser Speckle and Related Phenomena (Springer, New York, 1975).

K. Petermann, “Nonlinear Distortions Due to Fibre Connectors,” in Technical Digest, Sixth European Conference on Optical Communication, U. York (1980), pp. 80–83.

D. Marcuse, The Theory of Dielectric Optical Waveguides (Academic, New York, 1974), pp. 153–157.

G. Le Noame, “Optical Cable Design,” in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), pp. 12.1-1–12.1-8.

This is explained in a very pleasant way by Marcuse immediately after his presentation of the LP modes, in an attempt to explain the problems associated with LP modes. See Ref. 21, p. 69.

This fact follows from the law of large numbers.This point, as it relates to conventional speckle theory, is discussed inJ. W. Goodman, “Statistical Properties of Laser Speckle,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, New York, 1975), pp. 14 and 15.

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Figures (8)

Fig. 1
Fig. 1

Illustration of an ideal fiber link.

Fig. 2
Fig. 2

(a) Illustration of the drainpipe model of a fiber detector; (b) an illustration of the field sensitive coupling of two fibers.

Fig. 3
Fig. 3

Microscope pictures of polished fiber sections containing splices between graded-index fibers of 50-μm diam and 0.2 N.A. The splice losses are (a) 0.04 dB and (b) 0.1 dB, for 0.85-μm source excitation.

Fig. 4
Fig. 4

Sketch of the archetypal experimental setup used in measurements of modal noise-limited signal-to-noise ratios.

Fig. 5
Fig. 5

Sketch of the speedup unit employed in the measurements of modal noise-limited signal-to-noise ratios carried out in Trondheim.

Fig. 6
Fig. 6

Results of the computer simulation of the modal noise-limited integrated statistics as a function of the normalized radius (upper limit of integration).

Fig. 7
Fig. 7

Comparison of theoretical modal noise-limited integrated statistics curves for theories from different laboratories. Only theories concerning parabolic index fibers are included.

Fig. 8
Fig. 8

Comparison of theoretical and measured modal noise-limited signal-to-noise ratios. The simulation model for equal excitation of all mode groups and the theory of Ref. 11 are included for comparison.

Equations (10)

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

E t ( r ) = lm { E lm 1 ( r ) · ( A 1 lm c · cos l θ + A 1 lm s · sin l θ ) · exp ( i β 1 lm · z ) + E lm 2 ( r ) · ( A 2 lm c · cos l θ + A 2 lm s · sin l θ ) · exp ( i β 2 lm · z ) } ,
Δ L opt L opt = ( 1 L L T + 1 n n T ) Δ T .
E t ( r ) = μ ν E μ ν LP ( r ) · [ ê x · ( A x μ ν c · cos ν θ + A x μ ν s · sin ν θ ) + ê y · ( A y μ ν c · cos ν θ + A y μ ν s · sin ν θ ) ] · exp ( i β μ ν · z ) ,
P ( r ) = 0 r π μ , ν , μ Re [ ( A x μ ν c · A x μ ν * c + A x μ ν s · A x μ ν * s ) + ( A y μ ν c · A y μ ν * c + A y μ ν s · A y μ ν * s ) ] · E μ ν LP ( r ) · E μ ν LP ( r ) cos [ ( β μ ν β μ ν ) · z ] r d r .
P ( r ) = 0 r 2 π μ , ν , μ ( A x μ ν · A x μ ν + A y μ ν · A y μ ν ) · E μ ν LP ( r ) · E μ ν LP ( r ) * cos φ μ ν μ r d r ,
A x μ ν 2 + A y μ ν 2 = 1 1 [ N μ ν + 1 2 ] P equal excitation of all mode groups ,
t = 0 1 p ( R ) [ m ( R , o ) m ( R , s ) ] d R ,
m ( R , s ) = { V 2 R [ R 2 S 2 ] s R , 0 s > R ,
P ( R ) = { 1 equal exciation of all modes , 1 R 2 equal excitation of all mode groups .
η ( dB ) = 10 log { 1 ( 1 s 2 ) 2 equal excitation of all modes , s 2 2 s 2 lns equal excitation of all mode groups .

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