Abstract

We suggest a method that permits generation of a train of solitons with an arbitrary phase difference between adjacent pulses in a single-mode optical fiber. Specifically, a sequence of solitons in quadrature (i.e., where successive pulses differ in phase by π/2) can permit high-bit-rate transmission. It is shown that this train of pulses has advantages for use in optical transmission lines as a premodulated sequence of pulses because neighboring solitons in the train neither attract nor repel. The case in which this train of pulses is generated in an optical fiber with gain is also considered.

© 1994 Optical Society of America

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References

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  1. P. V. Mamyshev, S. V. Chernikov, E. M. Dianov, IEEE J. Quantum Electron. 27, 1347 (1991).
    [CrossRef]
  2. N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, Zh. Eksp. Teor. Fiz. 89, 1542 (1985) [Sov. Phys. JETP 62, 894 (1985)].
  3. E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, S. V. Chernikov, Opt. Lett. 14, 1008 (1989).
    [CrossRef] [PubMed]
  4. K. Tai, A. Tomita, J. L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
    [CrossRef]
  5. C. Desem, P. L. Chu, Proc. Inst. Electr. Eng. Part J 134, 145 (1987); G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989), Sec. 5.4.3.
  6. A. P. Prudnikov, Yu. A. Brychkov, O. A. Marichev, Tables of Series, Integrals and Products (Gordon & Breach, New York, 1986), Vol. 1, pp. 723–724.

1991 (1)

P. V. Mamyshev, S. V. Chernikov, E. M. Dianov, IEEE J. Quantum Electron. 27, 1347 (1991).
[CrossRef]

1989 (1)

1987 (1)

C. Desem, P. L. Chu, Proc. Inst. Electr. Eng. Part J 134, 145 (1987); G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989), Sec. 5.4.3.

1986 (1)

K. Tai, A. Tomita, J. L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

1985 (1)

N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, Zh. Eksp. Teor. Fiz. 89, 1542 (1985) [Sov. Phys. JETP 62, 894 (1985)].

Akhmediev, N. N.

N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, Zh. Eksp. Teor. Fiz. 89, 1542 (1985) [Sov. Phys. JETP 62, 894 (1985)].

Brychkov, Yu. A.

A. P. Prudnikov, Yu. A. Brychkov, O. A. Marichev, Tables of Series, Integrals and Products (Gordon & Breach, New York, 1986), Vol. 1, pp. 723–724.

Chernikov, S. V.

P. V. Mamyshev, S. V. Chernikov, E. M. Dianov, IEEE J. Quantum Electron. 27, 1347 (1991).
[CrossRef]

E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, S. V. Chernikov, Opt. Lett. 14, 1008 (1989).
[CrossRef] [PubMed]

Chu, P. L.

C. Desem, P. L. Chu, Proc. Inst. Electr. Eng. Part J 134, 145 (1987); G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989), Sec. 5.4.3.

Desem, C.

C. Desem, P. L. Chu, Proc. Inst. Electr. Eng. Part J 134, 145 (1987); G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989), Sec. 5.4.3.

Dianov, E. M.

P. V. Mamyshev, S. V. Chernikov, E. M. Dianov, IEEE J. Quantum Electron. 27, 1347 (1991).
[CrossRef]

E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, S. V. Chernikov, Opt. Lett. 14, 1008 (1989).
[CrossRef] [PubMed]

Eleonskii, V. M.

N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, Zh. Eksp. Teor. Fiz. 89, 1542 (1985) [Sov. Phys. JETP 62, 894 (1985)].

Hasegawa, A.

K. Tai, A. Tomita, J. L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Jewell, J. L.

K. Tai, A. Tomita, J. L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Kulagin, N. E.

N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, Zh. Eksp. Teor. Fiz. 89, 1542 (1985) [Sov. Phys. JETP 62, 894 (1985)].

Mamyshev, P. V.

P. V. Mamyshev, S. V. Chernikov, E. M. Dianov, IEEE J. Quantum Electron. 27, 1347 (1991).
[CrossRef]

E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, S. V. Chernikov, Opt. Lett. 14, 1008 (1989).
[CrossRef] [PubMed]

Marichev, O. A.

A. P. Prudnikov, Yu. A. Brychkov, O. A. Marichev, Tables of Series, Integrals and Products (Gordon & Breach, New York, 1986), Vol. 1, pp. 723–724.

Prokhorov, A. M.

Prudnikov, A. P.

A. P. Prudnikov, Yu. A. Brychkov, O. A. Marichev, Tables of Series, Integrals and Products (Gordon & Breach, New York, 1986), Vol. 1, pp. 723–724.

Tai, K.

K. Tai, A. Tomita, J. L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Tomita, A.

K. Tai, A. Tomita, J. L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Appl. Phys. Lett. (1)

K. Tai, A. Tomita, J. L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. V. Mamyshev, S. V. Chernikov, E. M. Dianov, IEEE J. Quantum Electron. 27, 1347 (1991).
[CrossRef]

Opt. Lett. (1)

Proc. Inst. Electr. Eng. Part J (1)

C. Desem, P. L. Chu, Proc. Inst. Electr. Eng. Part J 134, 145 (1987); G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989), Sec. 5.4.3.

Zh. Eksp. Teor. Fiz. (1)

N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, Zh. Eksp. Teor. Fiz. 89, 1542 (1985) [Sov. Phys. JETP 62, 894 (1985)].

Other (1)

A. P. Prudnikov, Yu. A. Brychkov, O. A. Marichev, Tables of Series, Integrals and Products (Gordon & Breach, New York, 1986), Vol. 1, pp. 723–724.

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Figures (2)

Fig. 1
Fig. 1

Spectra of a train of solitons with various phase relations between neighboring solitons: (a) n = 0, so solitons are in phase; (b) n = 1, so φd = π (c) n = 3, so φd = π/2.

Fig. 2
Fig. 2

Generation of a train of solitons with a dual-frequency input.

Equations (9)

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E ( t ) = A [ cos ( ω 1 t ) + cos ( ω 2 t + φ ) ] ,
E ( t ) = A { cos [ ( ω 0 - Ω ) t ] + cos [ ( ω 0 + n Ω ) t + φ ] } = 2 A cos [ ( n + 1 ) 2 Ω t + φ 2 ] × cos [ ω 0 t + ( n - 1 ) 2 Ω t + φ 2 ] .
φ d = 2 π ( ω 0 - ω 1 ) / ( ω 2 - ω 1 ) = 2 π / ( n + 1 ) .
f ( t ) = α sech ( α t ) ,
α T n + 1 1.76.
F ˜ m π ( n + 1 ) T ( - 1 ) m exp ( - i π n + 1 ) × sech { π 2 α T [ ( n + 1 ) m - 1 ] } ,             m = 0 , ± 1 , ± 2 , .
m = - sech 2 { π 2 α T [ ( n + 1 ) m - 1 ] } = 2 α T π 2 ( n + 1 ) ,
F ˜ m = 4 π T ( - 1 ) m exp ( ± i π / 4 ) sech [ π 2 α T ( 4 m ± 1 ) ] ,             m = 0 , ± 1 , ± 2 , .
i ψ z + ψ t t - ψ + ψ 2 ψ = i γ ψ .

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