Abstract

The effect of microbending loss on SNRs received from multimode graded-index fibers excited by single-mode laser sources is considered. Analytical expressions are derived which describe the combined effects of microbending loss and detector misalignment loss on the integrated intensity statistics in the fiber. The theoretical predictions for the SNR are experimentally checked and found to be in good agreement with the experimental data.

© 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.This was the first paper to point out that speckle in fibers could be a noise generation mechanism, and in this paper the term modal noise was coined.
  2. See, for example, B. S. Kawasaki, K. O. Hill, Y. Tremblay, Opt. Lett. 6, 499 (1981).
    [CrossRef] [PubMed]
  3. G. E. Miller, in Technical Digest, Topical Meeting on Optical Fiber Communication, (Optical Society of America, Washington, D.C., 1983), paper TUG14.
  4. E. G. Rawson, R. V. Schmidt, R. E. Norton, M. D. Bailey, L. C. Stewart, H. G. Murray, in Technical Digest, Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1982), paper TUFF1.
  5. Y. Tremblay, B. S. Kawasaki, K. O. Hill, Appl. Opt. 20, 1652 (1981).This is a recent reference with a discussion of various previous results.
    [CrossRef] [PubMed]
  6. A. R. Mickelson, A. Weierholt, Appl. Opt. 22, 3084 (1983).
    [CrossRef]
  7. K. O. Hill, Y. Tremblay, B. S. Kawasaki, Opt. Lett. 5, 270 (1980).
    [CrossRef] [PubMed]
  8. J. W. Goodman, E. G. Rawson, Opt. Lett. 6, 324 (1981).
    [CrossRef] [PubMed]
  9. J. W. Goodman, “Statistical Properties of Laser Speckle Patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, New York, 1975).
    [CrossRef]
  10. B. Daino, G. DeMarchis, S. Piazzola, Electron. Lett. 15, 755 (1979).This work was the first one to apply conventional speckle statistics to an optical fiber. The theoretical prediction in this work was that the fiber speckle pattern should be open, that is, that its statistics should formally match those of a conventional speckle pattern, which is a small sample of a larger pattern. This result was indeed what was measured in this work probably due to a large microbending loss in the speedup unit employed here. One would expect a cable under the effect of strong microbending to exhibit an open speckle pattern.
    [CrossRef]
  11. M. Abramowtiz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).
  12. A. R. Mickelson, M. Eriksrud, Opt. Lett. 7, 572 (1982).
    [CrossRef] [PubMed]
  13. C. Pask, J. Opt. Soc. Am. 68, 572 (1978).
    [CrossRef]

1983 (1)

1982 (1)

1981 (3)

1980 (1)

1979 (1)

B. Daino, G. DeMarchis, S. Piazzola, Electron. Lett. 15, 755 (1979).This work was the first one to apply conventional speckle statistics to an optical fiber. The theoretical prediction in this work was that the fiber speckle pattern should be open, that is, that its statistics should formally match those of a conventional speckle pattern, which is a small sample of a larger pattern. This result was indeed what was measured in this work probably due to a large microbending loss in the speedup unit employed here. One would expect a cable under the effect of strong microbending to exhibit an open speckle pattern.
[CrossRef]

1978 (1)

Abramowtiz, M.

M. Abramowtiz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).

Bailey, M. D.

E. G. Rawson, R. V. Schmidt, R. E. Norton, M. D. Bailey, L. C. Stewart, H. G. Murray, in Technical Digest, Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1982), paper TUFF1.

Daino, B.

B. Daino, G. DeMarchis, S. Piazzola, Electron. Lett. 15, 755 (1979).This work was the first one to apply conventional speckle statistics to an optical fiber. The theoretical prediction in this work was that the fiber speckle pattern should be open, that is, that its statistics should formally match those of a conventional speckle pattern, which is a small sample of a larger pattern. This result was indeed what was measured in this work probably due to a large microbending loss in the speedup unit employed here. One would expect a cable under the effect of strong microbending to exhibit an open speckle pattern.
[CrossRef]

DeMarchis, G.

B. Daino, G. DeMarchis, S. Piazzola, Electron. Lett. 15, 755 (1979).This work was the first one to apply conventional speckle statistics to an optical fiber. The theoretical prediction in this work was that the fiber speckle pattern should be open, that is, that its statistics should formally match those of a conventional speckle pattern, which is a small sample of a larger pattern. This result was indeed what was measured in this work probably due to a large microbending loss in the speedup unit employed here. One would expect a cable under the effect of strong microbending to exhibit an open speckle pattern.
[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.This was the first paper to point out that speckle in fibers could be a noise generation mechanism, and in this paper the term modal noise was coined.

Eriksrud, M.

Goodman, J. W.

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

J. W. Goodman, “Statistical Properties of Laser Speckle Patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, New York, 1975).
[CrossRef]

Hill, K. O.

Kawasaki, B. S.

Mickelson, A. R.

Miller, G. E.

G. E. Miller, in Technical Digest, Topical Meeting on Optical Fiber Communication, (Optical Society of America, Washington, D.C., 1983), paper TUG14.

Murray, H. G.

E. G. Rawson, R. V. Schmidt, R. E. Norton, M. D. Bailey, L. C. Stewart, H. G. Murray, in Technical Digest, Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1982), paper TUFF1.

Norton, R. E.

E. G. Rawson, R. V. Schmidt, R. E. Norton, M. D. Bailey, L. C. Stewart, H. G. Murray, in Technical Digest, Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1982), paper TUFF1.

Pask, C.

Piazzola, S.

B. Daino, G. DeMarchis, S. Piazzola, Electron. Lett. 15, 755 (1979).This work was the first one to apply conventional speckle statistics to an optical fiber. The theoretical prediction in this work was that the fiber speckle pattern should be open, that is, that its statistics should formally match those of a conventional speckle pattern, which is a small sample of a larger pattern. This result was indeed what was measured in this work probably due to a large microbending loss in the speedup unit employed here. One would expect a cable under the effect of strong microbending to exhibit an open speckle pattern.
[CrossRef]

Rawson, E. G.

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

E. G. Rawson, R. V. Schmidt, R. E. Norton, M. D. Bailey, L. C. Stewart, H. G. Murray, in Technical Digest, Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1982), paper TUFF1.

Schmidt, R. V.

E. G. Rawson, R. V. Schmidt, R. E. Norton, M. D. Bailey, L. C. Stewart, H. G. Murray, in Technical Digest, Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1982), paper TUFF1.

Stegun, I.

M. Abramowtiz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).

Stewart, L. C.

E. G. Rawson, R. V. Schmidt, R. E. Norton, M. D. Bailey, L. C. Stewart, H. G. Murray, in Technical Digest, Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1982), paper TUFF1.

Tremblay, Y.

Weierholt, A.

Appl. Opt. (2)

Electron. Lett. (1)

B. Daino, G. DeMarchis, S. Piazzola, Electron. Lett. 15, 755 (1979).This work was the first one to apply conventional speckle statistics to an optical fiber. The theoretical prediction in this work was that the fiber speckle pattern should be open, that is, that its statistics should formally match those of a conventional speckle pattern, which is a small sample of a larger pattern. This result was indeed what was measured in this work probably due to a large microbending loss in the speedup unit employed here. One would expect a cable under the effect of strong microbending to exhibit an open speckle pattern.
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (4)

Other (5)

G. E. Miller, in Technical Digest, Topical Meeting on Optical Fiber Communication, (Optical Society of America, Washington, D.C., 1983), paper TUG14.

E. G. Rawson, R. V. Schmidt, R. E. Norton, M. D. Bailey, L. C. Stewart, H. G. Murray, in Technical Digest, Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1982), paper TUFF1.

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.This was the first paper to point out that speckle in fibers could be a noise generation mechanism, and in this paper the term modal noise was coined.

J. W. Goodman, “Statistical Properties of Laser Speckle Patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, New York, 1975).
[CrossRef]

M. Abramowtiz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).

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Figures (9)

Fig. 1
Fig. 1

Schematic of the experimental setup used in measuring SNRs which could be limited by both microbending loss and detector misalignment loss.

Fig. 2
Fig. 2

Schematic of the experimental setup used to measure the mean near-field intensity distribution propagating in the test fiber used in the experimental setup of Fig. 1.

Fig. 3
Fig. 3

Illustration of the problems associated with achieving uniform excitation of a multimode fiber with a highly coherent source, near-field intensity patterns measured with the same setup on consecutive days: □, measured points; lines, fits to curves of the form (a) P(R) = (1 − R2)1/2 and (b) P(R) = 1/R2 (equal excitation of all mode groups).

Fig. 4
Fig. 4

Comparison of the data measured in a step-index fiber with two of the theories (for equal excitation of all modes) in the literature. Note that the theory in Ref. 6 uses a computer simulation which employs Gaussian-Laguerre fields and, therefore, should only apply to the parabolic case but still gives a reasonably good fit here.

Fig. 5
Fig. 5

As in Fig. 4 but for parabolic-index fiber and using both types of measured near-field intensity distribution from Fig. 3. Note that although Ref. 7 discusses the parabolic-index fiber and Ref. 8 only the step-index fiber, the SNR derived in these two references agree to within an imperceptible limit.

Fig. 6
Fig. 6

Comparison of the theoretical (solid line) and measured (points) SNR as a function of microbending loss for a step-index fiber. Two types of bending plate were employed, a stochastic one and a purely periodic one.

Fig. 7
Fig. 7

As in Fig. 6 but measured in a parabolic-index fiber. Note that although the theory is only strictly applicable to the step-index case the agreement exhibited here is still quite reasonable.

Fig. 8
Fig. 8

Comparison of the theoretical (solid lines) and measured (points) SNR as a function of detector mismatch loss parametrized by microbending loss. Note that the 0-dB microbending loss corresponds to a closed speckle pattern, and the >3-dB microbending loss corresponds to an open speckle pattern.5

Fig. 9
Fig. 9

Similar to Fig. 8 but measured in a parabolic-index fiber. Note that although the theory strictly applied only to the step-index case, the agreement with the parabolic-index data is quite good.

Equations (20)

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f I ( I ) = 4 I Ī 2 exp ( 2 I Ī ) ,
f f ( P P T ) = f s ( P ) f s ( P T ) f s ( P T P ) ,
f c ( P ) = f f ( P P T ) f m ( P T ) d P T ,
f m ( P T ) = { f f ( P T P l ) P ¯ T P l > ½ , f s ( P T ) P ¯ T P l ½ ,
f s ( P ) = 1 Γ ( M ) ( M P ¯ ) M P M 1 exp ( M P P ¯ ) ,
f f ( P P T ) = Γ ( M T ) Γ ( M ) Γ ( M T M ) 1 P T ( P P T ) M 1 ( 1 P P T ) M T M 1 .
f c ( P ) = Γ ( M l ) 2 Γ ( M T ) Γ ( M ) Γ ( 2 M l M T M ) 1 P l ( P P l ) M + M T M l 1 × ( 1 P P l ) 2 M l M M T 1 F [ M l M T , M l M , 2 M l M M T ; ( P l P P ) ] for P ¯ T > P l / 2 ,
f c ( P ) = 1 Γ ( M ) ( M P ¯ ) M P M 1 exp ( M P P ¯ ) for P ¯ T P l / 2 ,
SNR = ( P ¯ 2 P 2 ¯ P ¯ 2 ) 1 / 2
P 2 ¯ P ¯ 2 = [ Γ ( M l ) Γ ( M l + 2 ) M l 2 M T M ] 2 Γ ( M + 2 ) Γ ( M T + 2 ) Γ ( M ) Γ ( M T ) for P ¯ T > P l / 2 ,
P 2 ¯ P ¯ 2 = Γ ( M + 2 ) Γ ( M ) 1 M 2 for P ¯ T P l / 2 ,
SNR = [ ( M l M l + 1 ) 2 M T + 1 M T M + 1 M 1 ] 1 / 2 for P ¯ T > P l / 2 ,
SNR = M l P ¯ / P ¯ T for P ¯ T P l / 2 .
η m = P ¯ T P l = M T M l ,
η d = P ¯ P ¯ T = M M l ,
SNR 1 M l + 1 = [ η m η d η m ( 1 η d ) + η d ( 1 η m ) ] 1 / 2 for η m > ½ ,
SNR 1 M l = η d for η m ½ .
SNR 1 M l + 1 = η d 1 η d η m 1 ,
I ( r / a ) ~ r / a 1 p ( R ) R d R . 12
( SNR ) Ref . 7 / ( SNR ) Ref . 8 = M T M T + 1 .

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