Abstract

The manner in which the differential mode delay (DMD) pulse response is affected by ellipticity- and microbending-induced mode coupling has been analyzed numerically. We have considered both a fiber profile containing a central index dip and fiber profiles with sinusoidal ripples. We find that slowly varying profile components can be correctly estimated from DMD results even in the presence of substantial mode coupling.

© 1983 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. Stoltz, D. Yevick, Opt. Quantum Electron. 13, 487 (1981).
    [CrossRef]
  2. B. Stoltz, D. Yevick, submitted to J. Opt. Comm.
  3. K. Petermann, Arch. Elektronik. Übertragungstech. 30, 337 (1976).
  4. H.-G. Unger, Planar Optical Waveguides and Fibers (Oxford U.P., London, 1977).
  5. D. Yevick, B. Stoltz, Appl. Opt. 22, 1010 (1983).
    [CrossRef] [PubMed]
  6. B. Stoltz, D. Yevick, Appl. Opt. 21, 4235 (1982).
    [CrossRef] [PubMed]
  7. K. Petermann, Electron. Lett. 14, 793 (1978).
    [CrossRef]

1983 (1)

1982 (1)

1981 (1)

B. Stoltz, D. Yevick, Opt. Quantum Electron. 13, 487 (1981).
[CrossRef]

1978 (1)

K. Petermann, Electron. Lett. 14, 793 (1978).
[CrossRef]

1976 (1)

K. Petermann, Arch. Elektronik. Übertragungstech. 30, 337 (1976).

Petermann, K.

K. Petermann, Electron. Lett. 14, 793 (1978).
[CrossRef]

K. Petermann, Arch. Elektronik. Übertragungstech. 30, 337 (1976).

Stoltz, B.

D. Yevick, B. Stoltz, Appl. Opt. 22, 1010 (1983).
[CrossRef] [PubMed]

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

B. Stoltz, D. Yevick, Opt. Quantum Electron. 13, 487 (1981).
[CrossRef]

B. Stoltz, D. Yevick, submitted to J. Opt. Comm.

Unger, H.-G.

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

Yevick, D.

D. Yevick, B. Stoltz, Appl. Opt. 22, 1010 (1983).
[CrossRef] [PubMed]

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

B. Stoltz, D. Yevick, Opt. Quantum Electron. 13, 487 (1981).
[CrossRef]

B. Stoltz, D. Yevick, submitted to J. Opt. Comm.

Appl. Opt. (2)

Arch. Elektronik. Übertragungstech. (1)

K. Petermann, Arch. Elektronik. Übertragungstech. 30, 337 (1976).

Electron. Lett. (1)

K. Petermann, Electron. Lett. 14, 793 (1978).
[CrossRef]

Opt. Quantum Electron. (1)

B. Stoltz, D. Yevick, Opt. Quantum Electron. 13, 487 (1981).
[CrossRef]

Other (2)

B. Stoltz, D. Yevick, submitted to J. Opt. Comm.

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

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 (13)

Fig. 1
Fig. 1

Theoretical DMD response in the absence of mode coupling of a 1-km length of fiber with a central index dip given by Eq. (6) with h = 0.01 and w = 1.0 μm. The six curves correspond to input excitations centered from 0 to 25 μm from the fiber axis. Here λ0 = 0.85 μm, a = 25 μm, N.A. = 0.237, L = 1 km, and the input pulse width = 300 psec.

Fig. 2
Fig. 2

Same as Fig. 1 but with a microbending-induced coupling with strength A = 1012 m−5.

Fig. 3
Fig. 3

Center of τ ¯ gravity of the DMD pulse response for a profile with a low frequency ripple given by Eq. (5) with Δn = 3.85 × 10−4 and N = 1. The ellipticity-induced coupling parameter ε = 103 m−1 for all curves while the microbending coupling constant is equal to (from bottom to top) 0, 1, 2, 4, 8, and 16 × 1012 m−5.

Fig. 4
Fig. 4

First moment σ of the DMD pulse response for the same fiber and coupling constants as in Fig. 3.

Fig. 5
Fig. 5

Estimated deviation of the fiber profile of Fig. 3 from an optimal profile calculated from τ ¯ for microbending coupling strengths A equal to (bottom to top) 0, 4, and 16 × 1012 m−5.

Fig. 6
Fig. 6

τ ¯ for a profile with a high frequency ripple given by Eq. (5) with N = 12 in the absence of elliptical coupling and for values of the microbending coupling parameter A equal to 0, 1, 2, 4, and 8 × 1012 m−5. The fiber length in this and the following three curves is 700 m.

Fig. 7
Fig. 7

Same as Fig. 6 but for an ellipticity-induced coupling limit ε = 103 m−1.

Fig. 8
Fig. 8

First moment σ of the DMD pulse responses corresponding to Fig. 6.

Fig. 9
Fig. 9

Same as Fig. 8 but for an ellipticity-induced coupling limit ε = 103 m−1.

Fig. 10
Fig. 10

τ ¯ for a profile with a central index dip given by Eq. (6) with h = 0.01 and w = 1.0 μm in the absence of ellipticity-induced coupling and for values of A equal to 0, 1, 2, 4, and 8 × 1012 m−5.

Fig. 11
Fig. 11

Same as Fig. 10 but for an ellipticity-induced coupling described by ε = 103 m−1.

Fig. 12
Fig. 12

σ for the DMD pulse response corresponding to Fig. 10.

Fig. 13
Fig. 13

σ for the DMD pulse response corresponding to Fig. 11 (ε = 103 m−1).

Equations (9)

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

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 ) .
d n k = A / ( β n β k ) 2 p
d 2 E d r 2 + 1 r d E d r + [ n 2 ( r ) k 0 2 β 2 ] E l 2 E r 2 = 0 .
E ( r ) r l as r 0 , E ( a ) E ( a ) = V B K l ( V B ) K l ( V B ) ,
V = k 0 a n 0 2 n c l 2 , B = ( β 2 / k 0 2 n c l 2 ) / ( n 0 2 n c l 2 ) , k 0 = 2 π / λ 0 .
τ = k 0 c β n ( r ) N ( r ) E 2 ( r ) rdrd φ E 2 ( r ) rdrd φ ,
N ( r ) = n ( r ) λ 0 d n ( r ) d λ 0
Δ n ( r ) = Δ n sin ( N π r / a ) .
Δ n ( r ) = h exp ( r 2 / ω 2 ) .

Metrics