Abstract

A first-order spectral perturbation theory of resonant modes that evolve with periodically amplified optical fiber solitons is presented. In contrast with the modulational instability, these modes exhibit a linear growth in amplitude with respect to propagation and have a tuning characteristic that follows an inverse square-root dependence on the amplification period. Numerical results based on a complete solution of the nonlinear Schrödinger equation are also presented that confirm and quantify this behavior.

© 1993 Optical Society of America

Full Article  |  PDF Article

Errata

J. N. Elgin and S. M. J. Kelly, "Spectral modulation and the growth of resonant modes associated with periodically amplified solitons: erratum," Opt. Lett. 18, 1574-1574 (1993)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-18-18-1574

References

  • View by:
  • |
  • |
  • |

  1. A. Hasegawa, Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
    [CrossRef] [PubMed]
  2. L. F. Mollenauer, S. G. Evangelides, H. A. Haus, Lightwave Technol. 9, 194 (1991).
    [CrossRef]
  3. S. M. J. Kelly, K. Smith, K. J. Blow, N. J. Doran, Opt. Lett. 16, 1337 (1991).
    [CrossRef] [PubMed]
  4. J. P. Gordon, J. Opt. Soc. Am. B 9, 91 (1992).
    [CrossRef]
  5. S. M. J. Kelly, Electron. Lett. 28, 806 (1992).Note that the +1 in Eq. (5) of this Letter should read −1 [seeS. M. J. Kelly errata, Electron. Lett. 28, 1562 (1992)].
    [CrossRef]
  6. N. K. Smith, K. J. Blow, I. Andonovic, J. Lightwave Technol. 10, 1329 (1992).
    [CrossRef]
  7. V. J. Matsas, T. P. Newson, D. J. Richardson, D. N. Payne, Electron. Lett. 28, 1391 (1992).
    [CrossRef]
  8. M. Nakazawa, E. Yoshida, Y. Kimiura, Appl. Phys. Lett. 59, 2073 (1991).
    [CrossRef]
  9. N. Pandit, D. U. Noske, J. R. Taylor, Opt. Lett. 17, 1515 (1992).
    [CrossRef] [PubMed]
  10. A. Hasegawa, W. Brinkman, IEEE J. Quantum Electron. QE-16, 694 (1980).
    [CrossRef]
  11. M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1981).
    [CrossRef]
  12. D. J. Kaup, SIAM J. Appl. Math. 31, 121 (1976).
    [CrossRef]
  13. J. N. Elgin, Opt. Lett. 17, 1409 (1992).
    [CrossRef] [PubMed]
  14. A. Hasegawa, Appl. Opt. 23, 3302 (1984).
    [CrossRef] [PubMed]

1992 (6)

J. P. Gordon, J. Opt. Soc. Am. B 9, 91 (1992).
[CrossRef]

S. M. J. Kelly, Electron. Lett. 28, 806 (1992).Note that the +1 in Eq. (5) of this Letter should read −1 [seeS. M. J. Kelly errata, Electron. Lett. 28, 1562 (1992)].
[CrossRef]

N. K. Smith, K. J. Blow, I. Andonovic, J. Lightwave Technol. 10, 1329 (1992).
[CrossRef]

V. J. Matsas, T. P. Newson, D. J. Richardson, D. N. Payne, Electron. Lett. 28, 1391 (1992).
[CrossRef]

N. Pandit, D. U. Noske, J. R. Taylor, Opt. Lett. 17, 1515 (1992).
[CrossRef] [PubMed]

J. N. Elgin, Opt. Lett. 17, 1409 (1992).
[CrossRef] [PubMed]

1991 (4)

A. Hasegawa, Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
[CrossRef] [PubMed]

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, Lightwave Technol. 9, 194 (1991).
[CrossRef]

S. M. J. Kelly, K. Smith, K. J. Blow, N. J. Doran, Opt. Lett. 16, 1337 (1991).
[CrossRef] [PubMed]

M. Nakazawa, E. Yoshida, Y. Kimiura, Appl. Phys. Lett. 59, 2073 (1991).
[CrossRef]

1984 (1)

1980 (1)

A. Hasegawa, W. Brinkman, IEEE J. Quantum Electron. QE-16, 694 (1980).
[CrossRef]

1976 (1)

D. J. Kaup, SIAM J. Appl. Math. 31, 121 (1976).
[CrossRef]

Ablowitz, M. J.

M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1981).
[CrossRef]

Andonovic, I.

N. K. Smith, K. J. Blow, I. Andonovic, J. Lightwave Technol. 10, 1329 (1992).
[CrossRef]

Blow, K. J.

N. K. Smith, K. J. Blow, I. Andonovic, J. Lightwave Technol. 10, 1329 (1992).
[CrossRef]

S. M. J. Kelly, K. Smith, K. J. Blow, N. J. Doran, Opt. Lett. 16, 1337 (1991).
[CrossRef] [PubMed]

Brinkman, W.

A. Hasegawa, W. Brinkman, IEEE J. Quantum Electron. QE-16, 694 (1980).
[CrossRef]

Doran, N. J.

Elgin, J. N.

Evangelides, S. G.

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, Lightwave Technol. 9, 194 (1991).
[CrossRef]

Gordon, J. P.

Hasegawa, A.

A. Hasegawa, Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
[CrossRef] [PubMed]

A. Hasegawa, Appl. Opt. 23, 3302 (1984).
[CrossRef] [PubMed]

A. Hasegawa, W. Brinkman, IEEE J. Quantum Electron. QE-16, 694 (1980).
[CrossRef]

Haus, H. A.

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, Lightwave Technol. 9, 194 (1991).
[CrossRef]

Kaup, D. J.

D. J. Kaup, SIAM J. Appl. Math. 31, 121 (1976).
[CrossRef]

Kelly, S. M. J.

S. M. J. Kelly, Electron. Lett. 28, 806 (1992).Note that the +1 in Eq. (5) of this Letter should read −1 [seeS. M. J. Kelly errata, Electron. Lett. 28, 1562 (1992)].
[CrossRef]

S. M. J. Kelly, K. Smith, K. J. Blow, N. J. Doran, Opt. Lett. 16, 1337 (1991).
[CrossRef] [PubMed]

Kimiura, Y.

M. Nakazawa, E. Yoshida, Y. Kimiura, Appl. Phys. Lett. 59, 2073 (1991).
[CrossRef]

Kodama, Y.

A. Hasegawa, Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
[CrossRef] [PubMed]

Matsas, V. J.

V. J. Matsas, T. P. Newson, D. J. Richardson, D. N. Payne, Electron. Lett. 28, 1391 (1992).
[CrossRef]

Mollenauer, L. F.

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, Lightwave Technol. 9, 194 (1991).
[CrossRef]

Nakazawa, M.

M. Nakazawa, E. Yoshida, Y. Kimiura, Appl. Phys. Lett. 59, 2073 (1991).
[CrossRef]

Newson, T. P.

V. J. Matsas, T. P. Newson, D. J. Richardson, D. N. Payne, Electron. Lett. 28, 1391 (1992).
[CrossRef]

Noske, D. U.

Pandit, N.

Payne, D. N.

V. J. Matsas, T. P. Newson, D. J. Richardson, D. N. Payne, Electron. Lett. 28, 1391 (1992).
[CrossRef]

Richardson, D. J.

V. J. Matsas, T. P. Newson, D. J. Richardson, D. N. Payne, Electron. Lett. 28, 1391 (1992).
[CrossRef]

Segur, H.

M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1981).
[CrossRef]

Smith, K.

Smith, N. K.

N. K. Smith, K. J. Blow, I. Andonovic, J. Lightwave Technol. 10, 1329 (1992).
[CrossRef]

Taylor, J. R.

Yoshida, E.

M. Nakazawa, E. Yoshida, Y. Kimiura, Appl. Phys. Lett. 59, 2073 (1991).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. Nakazawa, E. Yoshida, Y. Kimiura, Appl. Phys. Lett. 59, 2073 (1991).
[CrossRef]

Electron. Lett. (2)

S. M. J. Kelly, Electron. Lett. 28, 806 (1992).Note that the +1 in Eq. (5) of this Letter should read −1 [seeS. M. J. Kelly errata, Electron. Lett. 28, 1562 (1992)].
[CrossRef]

V. J. Matsas, T. P. Newson, D. J. Richardson, D. N. Payne, Electron. Lett. 28, 1391 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Hasegawa, W. Brinkman, IEEE J. Quantum Electron. QE-16, 694 (1980).
[CrossRef]

J. Lightwave Technol. (1)

N. K. Smith, K. J. Blow, I. Andonovic, J. Lightwave Technol. 10, 1329 (1992).
[CrossRef]

J. Opt. Soc. Am. B (1)

Lightwave Technol. (1)

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, Lightwave Technol. 9, 194 (1991).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

A. Hasegawa, Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
[CrossRef] [PubMed]

SIAM J. Appl. Math. (1)

D. J. Kaup, SIAM J. Appl. Math. 31, 121 (1976).
[CrossRef]

Other (1)

M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1981).
[CrossRef]

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 (3)

Fig. 1
Fig. 1

Spectral evolution of the soliton profile over 50 amplification periods. Depicted are the resonant n = 1 mode, weak spectral modulations (point a), and the slow (8Z0) amplitude modulation.

Fig. 2
Fig. 2

Loge (intensity) plot of the profile at in 50za Fig. 1, showing the higher-order modes n = 2,3... ≈12 that accompany the n = 1 component. Positions of the normalized resonant frequencies (τδνn) according to Eq. (8) are indicated by the filled circles.

Fig. 3
Fig. 3

Evolution of the normalized mode intensity δÎ(δνn, Z)/|s(δνn)|2 for n = 1 over 50 amplification periods for gains of ≈14 dB (filled diamonds)and ≈2 dB (filled circles). The filled diamonds correspond to the resonant frequency n = 1 displayed in Fig. 1.

Equations (10)

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

i q z - 2 q t 2 - 2 q 2 q = i Γ q - i L n = 1 δ ( z - n z a ) q .
q ( z , t ) q s = 2 η 0 sech ( 2 η 0 t ) exp ( - i 4 η 0 2 z ) ,
c 0 = - + q 2 d t = 4 η 0 - 1 π - + log e [ 1 - b ( ξ , z ) 2 ] d ξ ,
b z = - i 4 ξ 2 b ( ξ , z ) - A ( z ) p ^ s * ( ξ , z ) ,
B z = - π 1 + 4 Γ z { Γ exp [ + i 4 ( ξ 2 + η 0 2 ) z ] - L n = - exp [ + i ( n k a + 4 ξ 2 + 4 η 0 2 ) z ] } × sech ( π ξ / 2 η 0 ) ,
B ( ξ , z ) - π { Γ exp [ + i 4 ( ξ 2 + η 0 2 ) z ] - 1 i 4 ( ξ 2 + η 0 2 ) - L n = - + exp ( + i D n z ) - 1 i D n } × sech ( π ξ / 2 η 0 ) ,
δ ν m = ± 1 2 π τ p [ ( 8 m π Z 0 / Z ) - 1 ] 1 / 2 ,
δ ν 1 = ± 1 2 π τ p [ ( 8 l π Z 0 / Z ) + 8 n Z 0 / Z a - 1 ] 1 / 2 ,
δ ν n = ± 1 2 π τ p [ ( 8 n Z 0 / Z a ) - 1 ] 1 / 2 ,
δ I ^ ( δ ν n , Z ) = π / 2 [ exp ( + Γ z a ) - 1 ] Z 0 p ^ s ( δ ν n , Z ) 2 Z .

Metrics