Abstract

In real single-mode optical fibers, imperfections cause the two possible polarizations to propagate at different phase velocities. This birefringence leads to different group velocities. We have measured the resulting mode dispersion in short fiber lengths (0.5–2.5 m) from the depolarization of broad-bandwidth light. In a typical fiber we found 30 psec/km at 0.69-μm wavelength, in good agreement with the observed birefringence. The effect of mode dispersion can be compensated by a ±68° double twist midway along the fiber, interchanging the fast and slow modes.

© 1978 Optical Society of America

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References

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  1. H.-G. Unger, Planar Optical Waveguides and Fibers (Oxford U.P., Oxford, England1977).
  2. V. Ramaswamy, W. G. French, Electron Lett. 14, 143 (1978).
    [Crossref]
  3. A. Simon, R. Ulrich, Appl. Phys. Lett. 31, 517 (1977).
    [Crossref]
  4. A. M. Smith, Appl. Opt. 17, 52 (1978).
    [Crossref] [PubMed]
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 491.
  6. D. C. Gloge, “Delay equalizers for multimode optical fibers,” U.S. Patent3,832,030 (1974).
  7. F. Lanzl, D. Rathjen, Wave Electron. 1, 69 (1974).
  8. R. Ulrich, A. Simon, Appl. Opt., to be published.

1978 (2)

V. Ramaswamy, W. G. French, Electron Lett. 14, 143 (1978).
[Crossref]

A. M. Smith, Appl. Opt. 17, 52 (1978).
[Crossref] [PubMed]

1977 (1)

A. Simon, R. Ulrich, Appl. Phys. Lett. 31, 517 (1977).
[Crossref]

1974 (1)

F. Lanzl, D. Rathjen, Wave Electron. 1, 69 (1974).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 491.

French, W. G.

V. Ramaswamy, W. G. French, Electron Lett. 14, 143 (1978).
[Crossref]

Gloge, D. C.

D. C. Gloge, “Delay equalizers for multimode optical fibers,” U.S. Patent3,832,030 (1974).

Lanzl, F.

F. Lanzl, D. Rathjen, Wave Electron. 1, 69 (1974).

Ramaswamy, V.

V. Ramaswamy, W. G. French, Electron Lett. 14, 143 (1978).
[Crossref]

Rathjen, D.

F. Lanzl, D. Rathjen, Wave Electron. 1, 69 (1974).

Simon, A.

A. Simon, R. Ulrich, Appl. Phys. Lett. 31, 517 (1977).
[Crossref]

R. Ulrich, A. Simon, Appl. Opt., to be published.

Smith, A. M.

Ulrich, R.

A. Simon, R. Ulrich, Appl. Phys. Lett. 31, 517 (1977).
[Crossref]

R. Ulrich, A. Simon, Appl. Opt., to be published.

Unger, H.-G.

H.-G. Unger, Planar Optical Waveguides and Fibers (Oxford U.P., Oxford, England1977).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 491.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. Simon, R. Ulrich, Appl. Phys. Lett. 31, 517 (1977).
[Crossref]

Electron Lett. (1)

V. Ramaswamy, W. G. French, Electron Lett. 14, 143 (1978).
[Crossref]

Wave Electron. (1)

F. Lanzl, D. Rathjen, Wave Electron. 1, 69 (1974).

Other (4)

R. Ulrich, A. Simon, Appl. Opt., to be published.

H.-G. Unger, Planar Optical Waveguides and Fibers (Oxford U.P., Oxford, England1977).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 491.

D. C. Gloge, “Delay equalizers for multimode optical fibers,” U.S. Patent3,832,030 (1974).

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Figures (2)

Fig. 1
Fig. 1

Experimental arrangement for the measurement of mode dispersion in single-mode fibers.

Fig. 2
Fig. 2

Visibility of the interference of the two modes in the fiber as a function of the optical bandwidth. Experimental values: … ; theoretical curve [Eq. (4)]: —. Upper curve: visibility after interchanging the modes midway by a double twist.

Equations (13)

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t m = k β = N 1 = N 2 / c + ( ω / c ) N 1 - N 2 ,
t m k β / ω .
η = ( I max - I min ) / ( I max + I min ) .
η = sin t m Δ ω L / ( t m Δ ω L ) .
Δ t N = 2 Δ ω k β 2 Δ ω k β / ω = 2 ( Δ ω / c ) N 1 - N 2 .
V 0 ( t ) = 2 0 v ( ω ) exp ( - i ω t ) d ω ,
v ( ω ) = ( 2 π ) - 1 - + V 0 ( t ) exp ( i ω t ) d t ,
V j ( t ) = 2 exp ( i ϕ j ) × 0 v ( ω ) exp [ i k j ( ω ) L - ω t ] d ω .
I = 1 2 V 1 ( t ) V 1 * ( t ) + 1 2 V 2 ( t ) V 2 * ( t ) + Re [ V 1 ( t ) V 2 * ( t ) ] ,
I = 2 π 0 v ( ω ) 2 d ω + 2 π Re [ exp ( i ϕ 1 - i ϕ 2 ) × 0 v ( ω ) 2 exp ( i k β L ) d ω ] .
k β ( ω ) = k β 0 + ( ω - ω 0 ) k β 0 + 1 2 ( ω - ω 0 ) 2 k β 0 + ,
I ( γ ) = 2 π 0 v ( ω ) 2 d ω + 2 π cos γ 0 v ( ω ) 2 × exp [ i ( ω - ω 0 ) k β 0 L + i χ ] d ω .
η = | 0 v ( ω ) 2 exp [ i ( ω - ω 0 ) k β 0 L + i χ ] d ω | / 0 v ( ω ) 2 d ω .

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