Abstract

A set of equations describing pulse propagation in multimode optical fibers in the presence of an intensity-dependent refractive index is derived by taking advantage of the coupled-mode theory usually employed for describing the influence of fiber imperfections on linear propagation. This approach takes into account in a natural way the role of the waveguide structure in terms of the propagation constants and the spatial configurations of the propagating modes and can be applied to the most general refractive-index distribution. The conditions under which soliton propagation and longitudinal self-confinement can be achieved are examined.

© 1982 Optical Society of America

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  1. R. G. Smith, "Optical power handling capability of low loss optical fibers as determined by stimulated Raman and Brillouin scattering," Appl. Opt. 11, 2489–2494 (1972).
  2. R. H. Stolen and C. Lin, "Self-phase modulation in silica optical fibers," Phys. Rev. A 17, 1448–1453 (1978).
  3. See, for example, A. Owyoung, "The origins of the nonlinear refractive indices of liquids and glasses," Ph.D. Thesis (California Institute of Technology, Pasadena, Calif., 1971, unpublished).
  4. R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beams," Phys. Rev. Lett. 13, 479–482 (1964).
  5. See, for example, R. H. Stolen, "Nonlinear properties of optical fibers," in Optical Fiber Telecommunications, S. C. Miller and A. G. Chynoweth, eds. (Academic, New York, 1979).
  6. A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion," Appl. Phys. Lett. 23, 147–149 (1973).
  7. A. Hasegawa and Y. Kodama, "Signal transmission by optical solitons in monomode fibers," Proc. IEEE 69, 1145–1150 (1981).
  8. M. Jain and N. Tzoar, "Propagation of nonlinear optical pulses in inhomogeneus media," J. Appl. Phys. 49, 4649–4654 (1981).
  9. B. Bendow, P. D. Gianino, N. Tzoar, and M. Jain, "Theory of nonlinear pulse propagation in optical waveguides," J. Opt. Soc. Am. 70, 539–546 (1980).
  10. A. Hasegawa, "Self-confinement of multimode optical pulses in a glass fiber," Opt. Lett. 5, 416–417 (1980).
  11. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).
  12. B. Crosignani, P. Di Porto, and C. H. Papas, "Coupled-mode theory approach to nonlinear pulse propagation in optical fibers," Opt. Lett. 6, 61–63 (1981).
  13. B. Crosignani and P. Di Porto, "Soliton propagation in multimode optical fibers," Opt. Lett. 6, 329–330 (1981).
  14. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of picosecond pulse narrowing and solitons in optical fibers," Phys. Rev. Lett. 45, 1095–1098 (1980).
  15. H. Nakatsuka, D. Grischkowsky, and A. C. Balant, "Nonlinear picosecond pulse propagation through optical fibers with positive group velocity dispersion," Phys. Rev. Lett. 47, 910–913 (1981).
  16. B. Crosignani, P. Di Porto, and C. H. Papas, "Theory of timedependent propagation in multimode lightguides," J. Opt. Soc. Am. 67, 1300–1307 (1977).
  17. See, for example, T. Okoshi, "Single-polarization single-mode optical fibers," IEEE J. Quantum Electron. QE-14, 879–884 (1981).
  18. R. E. Wagner, R. H. Stolen, and W. Pleibel, "Polarisation preservation in multimode fibres," Electron. Lett. 17, 177–178 (1981).
  19. B. Crosignani, P. Di Porto, and C. H. Papas, "The role of intensity fluctuations in nonlinear pulse propagation," Opt. Lett. 5, 467–468 (1980).
  20. A. W. Snyder, "Understanding monomode optical fibers," Proc. IEEE 69, 6–13 (1981).
  21. See, for example, L. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1949), p. 45.

1981

M. Jain and N. Tzoar, "Propagation of nonlinear optical pulses in inhomogeneus media," J. Appl. Phys. 49, 4649–4654 (1981).

B. Crosignani, P. Di Porto, and C. H. Papas, "Coupled-mode theory approach to nonlinear pulse propagation in optical fibers," Opt. Lett. 6, 61–63 (1981).

B. Crosignani and P. Di Porto, "Soliton propagation in multimode optical fibers," Opt. Lett. 6, 329–330 (1981).

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, "Nonlinear picosecond pulse propagation through optical fibers with positive group velocity dispersion," Phys. Rev. Lett. 47, 910–913 (1981).

See, for example, T. Okoshi, "Single-polarization single-mode optical fibers," IEEE J. Quantum Electron. QE-14, 879–884 (1981).

R. E. Wagner, R. H. Stolen, and W. Pleibel, "Polarisation preservation in multimode fibres," Electron. Lett. 17, 177–178 (1981).

1980

1978

R. H. Stolen and C. Lin, "Self-phase modulation in silica optical fibers," Phys. Rev. A 17, 1448–1453 (1978).

1977

1973

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion," Appl. Phys. Lett. 23, 147–149 (1973).

1972

1964

R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beams," Phys. Rev. Lett. 13, 479–482 (1964).

Balant, A. C.

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, "Nonlinear picosecond pulse propagation through optical fibers with positive group velocity dispersion," Phys. Rev. Lett. 47, 910–913 (1981).

Bendow, B.

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beams," Phys. Rev. Lett. 13, 479–482 (1964).

Crosignani, B.

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beams," Phys. Rev. Lett. 13, 479–482 (1964).

Gianino, P. D.

Gordon, J. P.

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

Grischkowsky, D.

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, "Nonlinear picosecond pulse propagation through optical fibers with positive group velocity dispersion," Phys. Rev. Lett. 47, 910–913 (1981).

Hasegawa, A.

A. Hasegawa, "Self-confinement of multimode optical pulses in a glass fiber," Opt. Lett. 5, 416–417 (1980).

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion," Appl. Phys. Lett. 23, 147–149 (1973).

A. Hasegawa and Y. Kodama, "Signal transmission by optical solitons in monomode fibers," Proc. IEEE 69, 1145–1150 (1981).

Jain, M.

M. Jain and N. Tzoar, "Propagation of nonlinear optical pulses in inhomogeneus media," J. Appl. Phys. 49, 4649–4654 (1981).

B. Bendow, P. D. Gianino, N. Tzoar, and M. Jain, "Theory of nonlinear pulse propagation in optical waveguides," J. Opt. Soc. Am. 70, 539–546 (1980).

Kodama, Y.

A. Hasegawa and Y. Kodama, "Signal transmission by optical solitons in monomode fibers," Proc. IEEE 69, 1145–1150 (1981).

Lin, C.

R. H. Stolen and C. Lin, "Self-phase modulation in silica optical fibers," Phys. Rev. A 17, 1448–1453 (1978).

Marcuse, D.

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

Mollenauer, L. F.

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

Nakatsuka, H.

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, "Nonlinear picosecond pulse propagation through optical fibers with positive group velocity dispersion," Phys. Rev. Lett. 47, 910–913 (1981).

Okoshi, T.

See, for example, T. Okoshi, "Single-polarization single-mode optical fibers," IEEE J. Quantum Electron. QE-14, 879–884 (1981).

Owyoung, A.

See, for example, 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. E. Wagner, R. H. Stolen, and W. Pleibel, "Polarisation preservation in multimode fibres," Electron. Lett. 17, 177–178 (1981).

Porto, P. Di

Schiff, L.

See, for example, L. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1949), p. 45.

Smith, R. G.

Snyder, A. W.

A. W. Snyder, "Understanding monomode optical fibers," Proc. IEEE 69, 6–13 (1981).

Stolen, R. H.

R. E. Wagner, R. H. Stolen, and W. Pleibel, "Polarisation preservation in multimode fibres," Electron. Lett. 17, 177–178 (1981).

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

R. H. Stolen and C. Lin, "Self-phase modulation in silica optical fibers," Phys. Rev. A 17, 1448–1453 (1978).

See, for example, R. H. Stolen, "Nonlinear properties of optical fibers," in Optical Fiber Telecommunications, S. C. Miller and A. G. Chynoweth, eds. (Academic, New York, 1979).

Tappert, F.

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion," Appl. Phys. Lett. 23, 147–149 (1973).

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beams," Phys. Rev. Lett. 13, 479–482 (1964).

Tzoar, N.

M. Jain and N. Tzoar, "Propagation of nonlinear optical pulses in inhomogeneus media," J. Appl. Phys. 49, 4649–4654 (1981).

B. Bendow, P. D. Gianino, N. Tzoar, and M. Jain, "Theory of nonlinear pulse propagation in optical waveguides," J. Opt. Soc. Am. 70, 539–546 (1980).

Wagner, R. E.

R. E. Wagner, R. H. Stolen, and W. Pleibel, "Polarisation preservation in multimode fibres," Electron. Lett. 17, 177–178 (1981).

Appl. Opt.

Appl. Phys. Lett.

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion," Appl. Phys. Lett. 23, 147–149 (1973).

Electron. Lett.

R. E. Wagner, R. H. Stolen, and W. Pleibel, "Polarisation preservation in multimode fibres," Electron. Lett. 17, 177–178 (1981).

IEEE J. Quantum Electron.

See, for example, T. Okoshi, "Single-polarization single-mode optical fibers," IEEE J. Quantum Electron. QE-14, 879–884 (1981).

J. Appl. Phys.

M. Jain and N. Tzoar, "Propagation of nonlinear optical pulses in inhomogeneus media," J. Appl. Phys. 49, 4649–4654 (1981).

J. Opt. Soc. Am.

Opt. Lett.

Phys. Rev. A

R. H. Stolen and C. Lin, "Self-phase modulation in silica optical fibers," Phys. Rev. A 17, 1448–1453 (1978).

Phys. Rev. Lett.

R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beams," Phys. Rev. Lett. 13, 479–482 (1964).

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

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, "Nonlinear picosecond pulse propagation through optical fibers with positive group velocity dispersion," Phys. Rev. Lett. 47, 910–913 (1981).

Other

A. W. Snyder, "Understanding monomode optical fibers," Proc. IEEE 69, 6–13 (1981).

See, for example, L. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1949), p. 45.

See, for example, R. H. Stolen, "Nonlinear properties of optical fibers," in Optical Fiber Telecommunications, S. C. Miller and A. G. Chynoweth, eds. (Academic, New York, 1979).

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

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

A. Hasegawa and Y. Kodama, "Signal transmission by optical solitons in monomode fibers," Proc. IEEE 69, 1145–1150 (1981).

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