Abstract

We examine collisions between soliton trains in the case in which initially all pulses in a train are copolarized. We demonstrate that an optical kink arises, which is destroyed when the effects of weak birefringence are included. We also investigate collisions between trains that consist of orthogonal pulse pairs and find that, when considered pairwise, collisions do not affect the polarization states of pulses in either train. The consequences of this for optical transmission systems that use both wavelength-division multiplexing and polarization-division multiplexing are examined.

© 1999 Optical Society of America

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  1. L. F. Mollenauer, J. P. Gordon, and F. Heismann, “Polarization scattering by soliton–soliton collisions,” Opt. Lett. 20, 2060–2062 (1995).
    [CrossRef] [PubMed]
  2. J. P. Silmon-Clyde and J. N. Elgin, “Incompatibility of polarization-division multiplexing with wavelength-division multiplexing in soliton transmission systems,” Opt. Lett. 23, 180–182 (1998).
    [CrossRef]
  3. S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Zh. Eksp. Teor. Fiz. 65, 505 (1973) [Sov. Phys. JETP 38, 248–253 (1974)].
  4. P. K. Wai, C. R. Menyuk, and M. H. Chen, “Stability of solitons in randomly varying birefringent fibers,” Opt. Lett. 16, 1231–1233 (1991).
    [CrossRef] [PubMed]
  5. P. K. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
    [CrossRef]
  6. S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).
    [CrossRef]
  7. M. Midrio, P. Franco, M. Crivellari, M. Romagnoli, and F. Matera, “Polarization shift keying for high-bit-rate multilevel soliton transmissions,” J. Opt. Soc. Am. B 13, 1526–1535 (1996).
    [CrossRef]
  8. M. Suzuki, I. Morita, K. Tanaka, N. Edagawa, S. Yamamoto, and S. Akiba, “160 Gbit/s (8×20 Gbit/s) soliton WDM transmission experiments using dispersion flattened fiber and periodic dispersion compensation,” Electron. Lett. 34, 475–476 (1998).
    [CrossRef]
  9. K. Tanaka, I. Morita, M. Suzuki, N. Edagawa, and S. Yamamoto, “400 Gbit/s (20×20 Gbit/s) dense WDM soliton-based RZ signal transmission using dispersion flattened fiber,” Electron. Lett. 34, 2257–2258 (1998).
    [CrossRef]
  10. D. LeGuen, A. O’Hare, S. Del Burgo, D. Grot, F. Favre, and T. Georges, “Narrowband 640 Gbit/s soliton DWDM transmission over 1200 km of standard fiber with 100 km–21 dB amplifier spans,” Electron. Lett. 34, 2345–2346 (1998).
    [CrossRef]

1998 (4)

J. P. Silmon-Clyde and J. N. Elgin, “Incompatibility of polarization-division multiplexing with wavelength-division multiplexing in soliton transmission systems,” Opt. Lett. 23, 180–182 (1998).
[CrossRef]

M. Suzuki, I. Morita, K. Tanaka, N. Edagawa, S. Yamamoto, and S. Akiba, “160 Gbit/s (8×20 Gbit/s) soliton WDM transmission experiments using dispersion flattened fiber and periodic dispersion compensation,” Electron. Lett. 34, 475–476 (1998).
[CrossRef]

K. Tanaka, I. Morita, M. Suzuki, N. Edagawa, and S. Yamamoto, “400 Gbit/s (20×20 Gbit/s) dense WDM soliton-based RZ signal transmission using dispersion flattened fiber,” Electron. Lett. 34, 2257–2258 (1998).
[CrossRef]

D. LeGuen, A. O’Hare, S. Del Burgo, D. Grot, F. Favre, and T. Georges, “Narrowband 640 Gbit/s soliton DWDM transmission over 1200 km of standard fiber with 100 km–21 dB amplifier spans,” Electron. Lett. 34, 2345–2346 (1998).
[CrossRef]

1996 (2)

P. K. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
[CrossRef]

M. Midrio, P. Franco, M. Crivellari, M. Romagnoli, and F. Matera, “Polarization shift keying for high-bit-rate multilevel soliton transmissions,” J. Opt. Soc. Am. B 13, 1526–1535 (1996).
[CrossRef]

1995 (1)

1992 (1)

S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).
[CrossRef]

1991 (1)

1974 (1)

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Zh. Eksp. Teor. Fiz. 65, 505 (1973) [Sov. Phys. JETP 38, 248–253 (1974)].

Akiba, S.

M. Suzuki, I. Morita, K. Tanaka, N. Edagawa, S. Yamamoto, and S. Akiba, “160 Gbit/s (8×20 Gbit/s) soliton WDM transmission experiments using dispersion flattened fiber and periodic dispersion compensation,” Electron. Lett. 34, 475–476 (1998).
[CrossRef]

Bergano, N. S.

S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).
[CrossRef]

Chen, M. H.

Crivellari, M.

Del Burgo, S.

D. LeGuen, A. O’Hare, S. Del Burgo, D. Grot, F. Favre, and T. Georges, “Narrowband 640 Gbit/s soliton DWDM transmission over 1200 km of standard fiber with 100 km–21 dB amplifier spans,” Electron. Lett. 34, 2345–2346 (1998).
[CrossRef]

Edagawa, N.

K. Tanaka, I. Morita, M. Suzuki, N. Edagawa, and S. Yamamoto, “400 Gbit/s (20×20 Gbit/s) dense WDM soliton-based RZ signal transmission using dispersion flattened fiber,” Electron. Lett. 34, 2257–2258 (1998).
[CrossRef]

M. Suzuki, I. Morita, K. Tanaka, N. Edagawa, S. Yamamoto, and S. Akiba, “160 Gbit/s (8×20 Gbit/s) soliton WDM transmission experiments using dispersion flattened fiber and periodic dispersion compensation,” Electron. Lett. 34, 475–476 (1998).
[CrossRef]

Elgin, J. N.

Evangelides Jr., S. G.

S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).
[CrossRef]

Favre, F.

D. LeGuen, A. O’Hare, S. Del Burgo, D. Grot, F. Favre, and T. Georges, “Narrowband 640 Gbit/s soliton DWDM transmission over 1200 km of standard fiber with 100 km–21 dB amplifier spans,” Electron. Lett. 34, 2345–2346 (1998).
[CrossRef]

Franco, P.

Georges, T.

D. LeGuen, A. O’Hare, S. Del Burgo, D. Grot, F. Favre, and T. Georges, “Narrowband 640 Gbit/s soliton DWDM transmission over 1200 km of standard fiber with 100 km–21 dB amplifier spans,” Electron. Lett. 34, 2345–2346 (1998).
[CrossRef]

Gordon, J. P.

L. F. Mollenauer, J. P. Gordon, and F. Heismann, “Polarization scattering by soliton–soliton collisions,” Opt. Lett. 20, 2060–2062 (1995).
[CrossRef] [PubMed]

S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).
[CrossRef]

Grot, D.

D. LeGuen, A. O’Hare, S. Del Burgo, D. Grot, F. Favre, and T. Georges, “Narrowband 640 Gbit/s soliton DWDM transmission over 1200 km of standard fiber with 100 km–21 dB amplifier spans,” Electron. Lett. 34, 2345–2346 (1998).
[CrossRef]

Heismann, F.

LeGuen, D.

D. LeGuen, A. O’Hare, S. Del Burgo, D. Grot, F. Favre, and T. Georges, “Narrowband 640 Gbit/s soliton DWDM transmission over 1200 km of standard fiber with 100 km–21 dB amplifier spans,” Electron. Lett. 34, 2345–2346 (1998).
[CrossRef]

Manakov, S. V.

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Zh. Eksp. Teor. Fiz. 65, 505 (1973) [Sov. Phys. JETP 38, 248–253 (1974)].

Matera, F.

Menyuk, C. R.

P. K. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
[CrossRef]

P. K. Wai, C. R. Menyuk, and M. H. Chen, “Stability of solitons in randomly varying birefringent fibers,” Opt. Lett. 16, 1231–1233 (1991).
[CrossRef] [PubMed]

Midrio, M.

Mollenauer, L. F.

L. F. Mollenauer, J. P. Gordon, and F. Heismann, “Polarization scattering by soliton–soliton collisions,” Opt. Lett. 20, 2060–2062 (1995).
[CrossRef] [PubMed]

S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).
[CrossRef]

Morita, I.

M. Suzuki, I. Morita, K. Tanaka, N. Edagawa, S. Yamamoto, and S. Akiba, “160 Gbit/s (8×20 Gbit/s) soliton WDM transmission experiments using dispersion flattened fiber and periodic dispersion compensation,” Electron. Lett. 34, 475–476 (1998).
[CrossRef]

K. Tanaka, I. Morita, M. Suzuki, N. Edagawa, and S. Yamamoto, “400 Gbit/s (20×20 Gbit/s) dense WDM soliton-based RZ signal transmission using dispersion flattened fiber,” Electron. Lett. 34, 2257–2258 (1998).
[CrossRef]

O’Hare, A.

D. LeGuen, A. O’Hare, S. Del Burgo, D. Grot, F. Favre, and T. Georges, “Narrowband 640 Gbit/s soliton DWDM transmission over 1200 km of standard fiber with 100 km–21 dB amplifier spans,” Electron. Lett. 34, 2345–2346 (1998).
[CrossRef]

Romagnoli, M.

Silmon-Clyde, J. P.

Suzuki, M.

K. Tanaka, I. Morita, M. Suzuki, N. Edagawa, and S. Yamamoto, “400 Gbit/s (20×20 Gbit/s) dense WDM soliton-based RZ signal transmission using dispersion flattened fiber,” Electron. Lett. 34, 2257–2258 (1998).
[CrossRef]

M. Suzuki, I. Morita, K. Tanaka, N. Edagawa, S. Yamamoto, and S. Akiba, “160 Gbit/s (8×20 Gbit/s) soliton WDM transmission experiments using dispersion flattened fiber and periodic dispersion compensation,” Electron. Lett. 34, 475–476 (1998).
[CrossRef]

Tanaka, K.

M. Suzuki, I. Morita, K. Tanaka, N. Edagawa, S. Yamamoto, and S. Akiba, “160 Gbit/s (8×20 Gbit/s) soliton WDM transmission experiments using dispersion flattened fiber and periodic dispersion compensation,” Electron. Lett. 34, 475–476 (1998).
[CrossRef]

K. Tanaka, I. Morita, M. Suzuki, N. Edagawa, and S. Yamamoto, “400 Gbit/s (20×20 Gbit/s) dense WDM soliton-based RZ signal transmission using dispersion flattened fiber,” Electron. Lett. 34, 2257–2258 (1998).
[CrossRef]

Wai, P. K.

P. K. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
[CrossRef]

P. K. Wai, C. R. Menyuk, and M. H. Chen, “Stability of solitons in randomly varying birefringent fibers,” Opt. Lett. 16, 1231–1233 (1991).
[CrossRef] [PubMed]

Yamamoto, S.

M. Suzuki, I. Morita, K. Tanaka, N. Edagawa, S. Yamamoto, and S. Akiba, “160 Gbit/s (8×20 Gbit/s) soliton WDM transmission experiments using dispersion flattened fiber and periodic dispersion compensation,” Electron. Lett. 34, 475–476 (1998).
[CrossRef]

K. Tanaka, I. Morita, M. Suzuki, N. Edagawa, and S. Yamamoto, “400 Gbit/s (20×20 Gbit/s) dense WDM soliton-based RZ signal transmission using dispersion flattened fiber,” Electron. Lett. 34, 2257–2258 (1998).
[CrossRef]

Electron. Lett. (3)

M. Suzuki, I. Morita, K. Tanaka, N. Edagawa, S. Yamamoto, and S. Akiba, “160 Gbit/s (8×20 Gbit/s) soliton WDM transmission experiments using dispersion flattened fiber and periodic dispersion compensation,” Electron. Lett. 34, 475–476 (1998).
[CrossRef]

K. Tanaka, I. Morita, M. Suzuki, N. Edagawa, and S. Yamamoto, “400 Gbit/s (20×20 Gbit/s) dense WDM soliton-based RZ signal transmission using dispersion flattened fiber,” Electron. Lett. 34, 2257–2258 (1998).
[CrossRef]

D. LeGuen, A. O’Hare, S. Del Burgo, D. Grot, F. Favre, and T. Georges, “Narrowband 640 Gbit/s soliton DWDM transmission over 1200 km of standard fiber with 100 km–21 dB amplifier spans,” Electron. Lett. 34, 2345–2346 (1998).
[CrossRef]

J. Lightwave Technol. (2)

P. K. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
[CrossRef]

S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).
[CrossRef]

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

Opt. Lett. (3)

Sov. Phys. JETP (1)

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Zh. Eksp. Teor. Fiz. 65, 505 (1973) [Sov. Phys. JETP 38, 248–253 (1974)].

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Figures (8)

Fig. 1
Fig. 1

Geometric interpretation of a collision on the Poincaré sphere.

Fig. 2
Fig. 2

Iterated map for a pulse colliding with a train consisting of copolarized pulses.

Fig. 3
Fig. 3

Schematic diagram of the kink in the polarization states of the pulse train at constant z. Only the R-pulse polarizations are shown; the L train has a complementary form.

Fig. 4
Fig. 4

Kink in the polarization states of the R-pulse train. The angle that each R pulse makes with the unperturbed L0 pulse is plotted against distance down the fiber. For this plot, the collision parameter μ=0.5 and γ11=π/4.

Fig. 5
Fig. 5

Numerically generated plot dpol for the R train plotted against distance z down the fiber in collision units. Three initial conditions are shown: solid line, γ11=0; long-dashed curve, γ11=π/8; short-dashed curve, γ11=π/4. In all plots n=40, μ=0.5.

Fig. 6
Fig. 6

Numerically generated plot of dpol as a function of distance z in collision units. The effects of weak birefringence are incorporated, and the L train has a random bit pattern; results for three different random bit patterns are plotted. For all plots μ=0.5, N=40, Δα=0.08 rad.

Fig. 7
Fig. 7

Iterated map for a pulse colliding with a train consisting of orthogonally polarized pulse pairs.

Fig. 8
Fig. 8

Reduction of polarization scattering through use of orthogonal pulse pairs. Numerically generated plot of dˆpol as a function of distance z in collision units. The effects of weak birefringence are incorporated, and the L train has a random bit pattern: Results for the three random bit patterns used in Fig. 6 are plotted. For all plots μ=0.5, N=40, and Δα=0.08 rad.

Equations (28)

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iqz=qtt+2qqq.
q(z, t)=2ηc exp{-i[2ξt+4(η2-ξ2)z]}×sech 2η(t-4ξz),
c=cos θ exp(iα1)sin θ exp(iα2).
Si=cσic,
|c1c2|2=(1/2)(1+S1·S2).
S1+=aS1-+bS2-+cS1-×S2-,
S2+=aS2-+bS1-+cS2-×S1-,
a=1/(μ2 cos2 γ+1),
b=1-a,
c=aμ,
μ=2η/(ξ2-ξ1).
cos β=2a-1.
Lji=aijLj-1i+bijRi-1j+cijLj-1i×Ri-1j,
Rij=aijRi-1j+bijLj-1i+cijRi-1j×Lj-1i,
cos 2γij=Lj-1i·Ri-1j.
xi+1=1-f(xi),
f(x)=(1-x)/(1+μ2x).
tan2 γi1=tan2 γ11(1+μ2)i-1,i1.
i>n*=1+ln(tan2 γ11/tan2 δ)ln(1+μ2).
i>η*8/μ2.
dpol=1Ni=1NRMi(z)i,
U=1000cos Δαsin Δα0-sin Δαcos Δα.
xi+1=f(xi),
x¯=1μ2[-1+(1+μ2)1/2].
R21=R01,L12=-L11.
dˆpol=1Ni=1,iodd2NRMi(z)i,
Uˆ=1000cos Δα/2sin Δα/20-sin Δα/2cos Δα/2.
δθi(1+μ2)i/2δθ0.

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