Abstract

A computer program has been developed to study the total pulse response of optical fibers with profile ripple and central index depressions in the presence of arbitrary mode coupling. We have found that the magnitude of the compression of the total pulse response generated by mode coupling depends significantly on the details of the refractive-index profile of the test fiber.

© 1983 Optical Society of America

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References

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  1. D. Gloge, Bell Syst. Tech. J. 52, 801 (1973).
  2. H.-G. Unger, Planar Optical Waveguides and Fibers (Oxford U.P., London, 1977).
  3. R. Olshansky, Appl. Opt. 14, 935 (1975).
    [PubMed]
  4. B. Stoltz, D. Yevick, Appl. Opt. 21, 4235 (1982).
    [CrossRef] [PubMed]
  5. B. Stoltz, D. Yevick, “Correcting Multimode Fibers with Differential Mode Delay,” submitted to Appl. Opt.
  6. R. Olshansky, Appl. Opt. 14, 20 (1975).
    [PubMed]
  7. K. Nagano, S. Kawakami, Appl. Opt. 19, 2426 (1980).
    [CrossRef] [PubMed]

1982 (1)

1980 (1)

1975 (2)

1973 (1)

D. Gloge, Bell Syst. Tech. J. 52, 801 (1973).

Gloge, D.

D. Gloge, Bell Syst. Tech. J. 52, 801 (1973).

Kawakami, S.

Nagano, K.

Olshansky, R.

Stoltz, B.

B. Stoltz, D. Yevick, Appl. Opt. 21, 4235 (1982).
[CrossRef] [PubMed]

B. Stoltz, D. Yevick, “Correcting Multimode Fibers with Differential Mode Delay,” submitted to Appl. Opt.

Unger, H.-G.

H.-G. Unger, Planar Optical Waveguides and Fibers (Oxford U.P., London, 1977).

Yevick, D.

B. Stoltz, D. Yevick, Appl. Opt. 21, 4235 (1982).
[CrossRef] [PubMed]

B. Stoltz, D. Yevick, “Correcting Multimode Fibers with Differential Mode Delay,” submitted to Appl. Opt.

Appl. Opt. (4)

Bell Syst. Tech. J. (1)

D. Gloge, Bell Syst. Tech. J. 52, 801 (1973).

Other (2)

H.-G. Unger, Planar Optical Waveguides and Fibers (Oxford U.P., London, 1977).

B. Stoltz, D. Yevick, “Correcting Multimode Fibers with Differential Mode Delay,” submitted to Appl. Opt.

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Figures (12)

Fig. 1
Fig. 1

Evolution of the total pulse response with fiber length in an optimal fiber profile, in the sense described in the text, perturbed by the ripple perturbation of Eq. (6). The incoming light wavelength in this and the other figures is 0.85 μm.

Fig. 2
Fig. 2

Same as Fig. 1 but in the presence of moderate ellipticity- and microbending-induced coupling (ɛ = 5 × E + 2 m−1, A = 2 × E12 m−5).

Fig. 3
Fig. 3

Propagation constants of all fiber modes associated with the profile of Eq. (6) displayed as a function of the azimuthal quantum number.

Fig. 4
Fig. 4

Total pulse response of a 700-m length of the fiber of Fig. 1 or Eq. (6) in the absence of microbending-induced coupling for ellipticity-induced coupling strengths ranging from 0 (bottom curve) to ɛ = 1.25 × E3 m−1.

Fig. 5
Fig. 5

Total pulse response of a 700-m length of the fiber of Fig. 1 or Eq. (6) in the absence of ellipticity-induced coupling for microbending-induced coupling strengths ranging from 0 (bottom curve) to A = 4 × E12 m−5.

Fig. 6
Fig. 6

Same as Fig. 5 but in the presence of ellipticity-induced coupling given by ɛ = 5 × E2 m−1.

Fig. 7
Fig. 7

Same as Fig. 3 but for a profile with a central index dip given Eq. (7).

Fig. 8
Fig. 8

Same as Fig. 4 but for a profile containing a central index dip and coupling strengths ranging from 0 to 4 × E3 m−1. The fiber length in this and the remaining figures is 1 km.

Fig. 9
Fig. 9

Same as Fig. 5 but for a profile containing a central index dip and for coupling strengths ranging from 0 to 5 × E12 m−5.

Fig. 10
Fig. 10

Total pulse response of a 1-km length of the fiber of Eq. (7) or Fig. 7 in the presence of ellipticity-induced coupling equal to ɛ = 1 × E3 for microbending-induced coupling strengths between 0 (bottom curve) and A = 2.5 × E12 m−5.

Fig. 11
Fig. 11

Same as Fig. 9 but at an incoming light wavelength equal to 1.3 μm.

Fig. 12
Fig. 12

Continuation of Fig. 11 to microbending-induced coupling strengths of A = 0.5 × E13 (bottom curve), A = 1 × E13, 2 × E13, 4 × E13, and A = 8 × E13 m−5, respectively.

Equations (9)

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d P n d z = P n z + τ n P n t = 2 α n P n + k d n k ( P k P n ) ,
m ( P ¯ m z + τ m P ¯ m t ) = 2 α m P ¯ m + m d m ( P ¯ m + 1 P ¯ m ) + ( m 1 ) d m 1 ( P ¯ m 1 P ¯ m ) m = 1 , , N ,
P n z + ( τ n τ g ) P n t 1 = 2 α n P n + k d n k ( P k P n ) .
P n , i + 1 , j = P n , i , j ( τ n τ g ) Δ z 2 Δ t ( P n , i , j + 1 P n , i , j 1 ) + Δ z k d n k ( P k , i , j P n , i , j ) .
| Δ z | < | 2 Δ t τ n τ g | ,
| Δ z | < 1 | d n k | .
Δ n ( r ) = 0.000385 sin ( 12 π r / a ) ,
Δ n ( r ) = 0.01 exp ( r 2 / w 2 ) ,
d m n ~ A / ( β m β n ) 2 p ,

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