Abstract

The propagation of light in a multimode optical fiber waveguide results in speckle, a complicated mapping of the input field onto the output field. The speckle pattern changes as the fiber undergoes twists and bends. We show theoretically and demonstrate experimentally that changes in the mapping caused by bends in one region of the fiber can be compensated with bends applied along a fixed region of the fiber. In this way the output speckle pattern of the fiber can be stabilized. In this method it is supposed that the modes evolve adiabatically without intermixing and that the analytical dependence of perturbed propagation eigenvalues of the modes follows R−2 behavior, where R is the local value of bend radius.

© 1996 Optical Society of America

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References

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  1. A. W. Snyder, J. D. LoveOptical Waveguide Theory (Chapman & Hall, London, 1983).
  2. D. MarcuseTheory of Dielectric Optical Waveguides (Academic, New York, 1974).
  3. M. Miyagi, K. Harada, S. KawakamiIEEE Trans. Microwave Theory Tech. MTT-32, 513 (1984).
    [CrossRef]
  4. S. J. GarthProc. Inst. Electr. Eng. Part J 134, 1889 (1989).
  5. S. J. Garth, W. M. Henry, J. D. LoveOpt. Quantum Electron. 27, 15 (1995).
    [CrossRef]
  6. A. YarivAppl. Phys. Lett. 28, 88 (1976).
    [CrossRef]
  7. B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. ShkunovPrinciples of Phase Conjugation (Springer-Verlag, Berlin, 1985).
  8. M. A. Bolshtyansky, B. Ya. Zel’dovichOpt. Commun. 123, 629 (1996).
    [CrossRef]

1996

M. A. Bolshtyansky, B. Ya. Zel’dovichOpt. Commun. 123, 629 (1996).
[CrossRef]

1995

S. J. Garth, W. M. Henry, J. D. LoveOpt. Quantum Electron. 27, 15 (1995).
[CrossRef]

1989

S. J. GarthProc. Inst. Electr. Eng. Part J 134, 1889 (1989).

1984

M. Miyagi, K. Harada, S. KawakamiIEEE Trans. Microwave Theory Tech. MTT-32, 513 (1984).
[CrossRef]

1976

A. YarivAppl. Phys. Lett. 28, 88 (1976).
[CrossRef]

Bolshtyansky, M. A.

M. A. Bolshtyansky, B. Ya. Zel’dovichOpt. Commun. 123, 629 (1996).
[CrossRef]

Garth, S. J.

S. J. Garth, W. M. Henry, J. D. LoveOpt. Quantum Electron. 27, 15 (1995).
[CrossRef]

S. J. GarthProc. Inst. Electr. Eng. Part J 134, 1889 (1989).

Harada, K.

M. Miyagi, K. Harada, S. KawakamiIEEE Trans. Microwave Theory Tech. MTT-32, 513 (1984).
[CrossRef]

Henry, W. M.

S. J. Garth, W. M. Henry, J. D. LoveOpt. Quantum Electron. 27, 15 (1995).
[CrossRef]

Kawakami, S.

M. Miyagi, K. Harada, S. KawakamiIEEE Trans. Microwave Theory Tech. MTT-32, 513 (1984).
[CrossRef]

Love, J. D.

S. J. Garth, W. M. Henry, J. D. LoveOpt. Quantum Electron. 27, 15 (1995).
[CrossRef]

A. W. Snyder, J. D. LoveOptical Waveguide Theory (Chapman & Hall, London, 1983).

Marcuse, D.

D. MarcuseTheory of Dielectric Optical Waveguides (Academic, New York, 1974).

Miyagi, M.

M. Miyagi, K. Harada, S. KawakamiIEEE Trans. Microwave Theory Tech. MTT-32, 513 (1984).
[CrossRef]

Pilipetsky, N. F.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. ShkunovPrinciples of Phase Conjugation (Springer-Verlag, Berlin, 1985).

Shkunov, V. V.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. ShkunovPrinciples of Phase Conjugation (Springer-Verlag, Berlin, 1985).

Snyder, A. W.

A. W. Snyder, J. D. LoveOptical Waveguide Theory (Chapman & Hall, London, 1983).

Yariv, A.

A. YarivAppl. Phys. Lett. 28, 88 (1976).
[CrossRef]

Zel’dovich, B. Ya.

M. A. Bolshtyansky, B. Ya. Zel’dovichOpt. Commun. 123, 629 (1996).
[CrossRef]

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. ShkunovPrinciples of Phase Conjugation (Springer-Verlag, Berlin, 1985).

Appl. Phys. Lett.

A. YarivAppl. Phys. Lett. 28, 88 (1976).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

M. Miyagi, K. Harada, S. KawakamiIEEE Trans. Microwave Theory Tech. MTT-32, 513 (1984).
[CrossRef]

Opt. Commun.

M. A. Bolshtyansky, B. Ya. Zel’dovichOpt. Commun. 123, 629 (1996).
[CrossRef]

Opt. Quantum Electron.

S. J. Garth, W. M. Henry, J. D. LoveOpt. Quantum Electron. 27, 15 (1995).
[CrossRef]

Proc. Inst. Electr. Eng. Part J

S. J. GarthProc. Inst. Electr. Eng. Part J 134, 1889 (1989).

Other

A. W. Snyder, J. D. LoveOptical Waveguide Theory (Chapman & Hall, London, 1983).

D. MarcuseTheory of Dielectric Optical Waveguides (Academic, New York, 1974).

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. ShkunovPrinciples of Phase Conjugation (Springer-Verlag, Berlin, 1985).

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Figures (4)

Fig. 1
Fig. 1

Schematic of compensation of the bend-induced distortions: a, strongly prebent auxiliary and the straight utility parts, which define the transmission mapping to be stabilized; b, influence of bending of the utility part, which may be compensated by the actuator-controlled (A) loosening of the auxiliary part of the fiber.

Fig. 2
Fig. 2

Experimental setup: 1, Ar+ laser; 2, photographic camera; 3, LiNbO3 crystal; 4, plane reference wave for recording the holograms in the crystal; 5, shutter; 6, aperture; 7, photodetector.

Fig. 3
Fig. 3

(a) Starting output speckle pattern in the far-field zone; (b) output pattern, strongly distorted by bending of the utility portion of the fiber (the left-hand part of Fig. 2 shifted into the dashed position); (c) loosening of the bend of the auxiliary portion (the right-hand part of the fiber on Fig. 2 is also shifted into the dashed position), permitting compensation for distortions.

Fig. 4
Fig. 4

Dependence of the intensity of the reconstructed plane wave on the position of the utility part of the fiber during distortion (squares) and on the position of the auxiliary part during the compensation process (circles). The maximum of the second curve corresponds to the best compensation.

Equations (4)

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E in ( x , y ) = δ ( x x 0 ) δ ( y y 0 ) , G ( x 0 , y 0 , x , y , z = L ) = E out ( x , y ) = m , n M m n * ( x 0 , y 0 ) M m n ( x , y ) × exp ( i β m n L ) .
ϕ m n = 0 L [ β m n ( 0 ) + δ β m n ( l ) ] d l .
δ β m n ( l ) = C m n ρ 0 R 2 ( l ) + D m n ρ 0 R 4 ( l ) + ... ,
0 L d l R 2 ( l ) , 0 L d l R 4 ( l ) , ....

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