Abstract

Soliton propagation in a multimode optical fiber in the presence of an intensity-dependent refractive index is investigated by means of a set of nonlinear coupled equations derived in the frame of coupled-mode theory. In particular, the conditions on modal amplitudes and modal dispersion necessary for soliton existence are derived.

© 1981 Optical Society of America

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References

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  1. A. Hasegawa, F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
    [CrossRef]
  2. See, for example, B. Bendow, P. D. Gianino, N. Tzoar, M. Jain, “Theory of nonlinear pulse propagation in optical waveguides,” J. Opt. Soc. Am. 70, 539–546 (1980).
    [CrossRef]
  3. B. Crosignani, P. Di Porto, C. H. Papas, “The role of intensity fluctuations in nonlinear pulse propagation,” Opt. Lett. 5, 467–468 (1980).
    [CrossRef] [PubMed]
  4. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
    [CrossRef]
  5. A. Hasegawa, “Self-confinement of multimode optical pulse in a glass fiber,” Opt. Lett. 5, 416–417 (1980).
    [CrossRef] [PubMed]
  6. B. Crosignani, P. Di Porto, C. H. Papas, “Coupled-mode theory approach to nonlinear pulse propagation in optical fibers,” Opt. Lett. 6, 61–63 (1981).
    [CrossRef] [PubMed]
  7. A. Owyoung, “The origins of the nonlinear refractive indices of liquids and glasses,” Ph.D. Thesis (California Institute of Technology, Pasadena, Calif., 1971) (unpublished).
  8. B. Crosignani, P. Di Porto, S. Solimeno, “Influence of guiding structures on spontaneous and stimulated emission. Raman scattering in optical fibers,” Phys. Rev. A 21, 594–598 (1980).
    [CrossRef]
  9. R. H. Stolen, R. E. Wagner, W. Pleibel, “Linear polarization in birefringent multimode fibers,” in Proceedings of the Third International Conference on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D.C., 1981).

1981 (1)

1980 (5)

B. Crosignani, P. Di Porto, S. Solimeno, “Influence of guiding structures on spontaneous and stimulated emission. Raman scattering in optical fibers,” Phys. Rev. A 21, 594–598 (1980).
[CrossRef]

See, for example, B. Bendow, P. D. Gianino, N. Tzoar, M. Jain, “Theory of nonlinear pulse propagation in optical waveguides,” J. Opt. Soc. Am. 70, 539–546 (1980).
[CrossRef]

B. Crosignani, P. Di Porto, C. H. Papas, “The role of intensity fluctuations in nonlinear pulse propagation,” Opt. Lett. 5, 467–468 (1980).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

A. Hasegawa, “Self-confinement of multimode optical pulse in a glass fiber,” Opt. Lett. 5, 416–417 (1980).
[CrossRef] [PubMed]

1973 (1)

A. Hasegawa, F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Bendow, B.

Crosignani, B.

Di Porto, P.

Gianino, P. D.

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Hasegawa, A.

A. Hasegawa, “Self-confinement of multimode optical pulse in a glass fiber,” Opt. Lett. 5, 416–417 (1980).
[CrossRef] [PubMed]

A. Hasegawa, F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Jain, M.

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Owyoung, A.

A. Owyoung, “The origins of the nonlinear refractive indices of liquids and glasses,” Ph.D. Thesis (California Institute of Technology, Pasadena, Calif., 1971) (unpublished).

Papas, C. H.

Pleibel, W.

R. H. Stolen, R. E. Wagner, W. Pleibel, “Linear polarization in birefringent multimode fibers,” in Proceedings of the Third International Conference on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D.C., 1981).

Solimeno, S.

B. Crosignani, P. Di Porto, S. Solimeno, “Influence of guiding structures on spontaneous and stimulated emission. Raman scattering in optical fibers,” Phys. Rev. A 21, 594–598 (1980).
[CrossRef]

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

R. H. Stolen, R. E. Wagner, W. Pleibel, “Linear polarization in birefringent multimode fibers,” in Proceedings of the Third International Conference on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D.C., 1981).

Tappert, F.

A. Hasegawa, F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Tzoar, N.

Wagner, R. E.

R. H. Stolen, R. E. Wagner, W. Pleibel, “Linear polarization in birefringent multimode fibers,” in Proceedings of the Third International Conference on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D.C., 1981).

Appl. Phys. Lett. (1)

A. Hasegawa, F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (3)

Phys. Rev. A (1)

B. Crosignani, P. Di Porto, S. Solimeno, “Influence of guiding structures on spontaneous and stimulated emission. Raman scattering in optical fibers,” Phys. Rev. A 21, 594–598 (1980).
[CrossRef]

Phys. Rev. Lett. (1)

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Other (2)

R. H. Stolen, R. E. Wagner, W. Pleibel, “Linear polarization in birefringent multimode fibers,” in Proceedings of the Third International Conference on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D.C., 1981).

A. Owyoung, “The origins of the nonlinear refractive indices of liquids and glasses,” Ph.D. Thesis (California Institute of Technology, Pasadena, Calif., 1971) (unpublished).

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Equations (16)

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P NL ( t ) = ( σ / 2 ) E ( t ) E ( t ) E ( t ) ,
2 | E ^ x ( t ) | 2 ,
E ^ x ( r , z , t ) = ν E ν ( r ) exp [ i ω ν t i β ν ( ω ν ) z ] Φ ^ ν ( z , t ) ,
( r , z , ω ) = 1 ( r , ω ) + 2 | E ^ x ( r , z , t ) | 2 ,
L ν Φ ^ ν ( z , t ) = 2 i [ μ ν R μν | Φ ^ μ | 2 + ( 1 / 2 ) R νν | Φ ^ ν | 2 ] Φ ^ ν , ν = 1 , 2 , ,
R μν = [ ω 0 ( 2 / 0 ) / 2 n 1 c ] + E μ 2 ( r ) E ν 2 ( r ) d x d y + E ν 2 ( r ) d x d y [ ω 0 ( 2 / 0 ) / 2 n 1 c ] α μν
L ν = [ / z + ( 1 / V ν ) / t ( i / 2 A ν ) 2 / t 2 ] ,
V ν 2 = ( d β ν / d ω ) ω = ω ν , A ν 2 = ( d 2 β ν / d ω 2 ) ω = ω ν ,
V 1 = ( d β 1 / d ω ) ω = ω 1 = ( d β 2 / d ω ) ω = ω 2 = ,
Φ ^ ν ( z , t ) = Φ ^ 0 ν exp ( iz / 2 A ν τ 2 ) sech [ ( t z / V ) / τ ] , ν = 1 , 2 , ,
1 / A ν τ 2 = 2 μ R μν | Φ ^ 0 μ | 2 R νν | Φ ^ 0 ν | 2 , ν = 1 , 2 , .
2 R | Φ ^ 0 | 2 = 1 / A τ 2 ,
R = [ ω 0 ( 2 / 0 ) / 2 n 1 c ] μ E μ 2 ( r = 0 ) .
μ E μ 2 ( r ) μ E μ 2 ( 0 ) = n 1 2 ( r ) n 1 2 ( a ) n 1 2 ( 0 ) n 1 2 ( a ) ,
μ E μ 2 ( 0 ) = ( ω 0 2 / 4 π c 2 ) ( n 1 2 n 2 2 ) ,
( V ν V ) 2 / V 2 ( V 2 / A ν ) [ ω 0 ( 2 / 0 ) / n 1 c ] × μ α μν | Φ ^ μ | 2 , ν = 1 , 2 , ,

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