Abstract

We demonstrate that in stationary, spatially homogeneous nonlinear media, interconversion of different-type solitary waves can occur as a result of spectral inhomogeneity of the medium parameters. As compared with the classical mode conversion in propagation through a spatially nonuniform medium, this interconversion effect is accompanied by a drift of the wave spectra in the frequency domain and their subsequent conversion by reflection at spectral turning points. By analyzing the Schrödinger and dissipative optical solitons, we show that such interconversion may result in the periodic self-oscillations of soliton spectra in nonlinear media with a frequency-dependent gain.

© 1998 Optical Society of America

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References

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  1. J. Herrmann and B. Wilhelmi, Lasers for Ultrashort Light Pulses (Akademe-Verlag, Berlin, 1987).
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    [CrossRef]
  3. C.-J. Chen, P. K. A. Wai, and C. R. Menyuk, Opt. Lett. 19, 198 (1994).
    [CrossRef]
  4. A. M. Sergeev and E. V. Vanin, Proc. SPIE 2377, 32 (1995).
    [CrossRef]
  5. W. H. Knox, IEEE J. Quantum Electron. 24, 388 (1988).
    [CrossRef]
  6. G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, 1989).
  7. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
    [CrossRef]
  8. F. M. Mitschke and L. F. Molenauer, Opt. Lett. 11, 659 (1986).
    [CrossRef] [PubMed]
  9. S. V. Chernikov, E. M. Dianov, D. J. Richardson, and D. N. Payne, Opt. Lett. 18, 476 (1993).
    [CrossRef] [PubMed]
  10. V. S. Grigoryan, A. I. Maimistov, and Yu. M. Sklyarov, Zh. Eksp. Teor. Fiz. 94, 174 (1988) [Sov. Phys. JETP 67, 530 (1988)].
  11. E. V. Vanin, A. I. Korytin, A. M. Sergeev, D. Anderson, M. Lisak, and L. Vázquez, Phys. Rev. A 49, 2806 (1994).
    [CrossRef] [PubMed]
  12. D. Anderson, A. I. Korytin, M. Lisak, A. M. Sergeev, and E. V. Vanin, Phys Rev. A 52, 1570 (1995).
    [CrossRef] [PubMed]

1995 (2)

A. M. Sergeev and E. V. Vanin, Proc. SPIE 2377, 32 (1995).
[CrossRef]

D. Anderson, A. I. Korytin, M. Lisak, A. M. Sergeev, and E. V. Vanin, Phys Rev. A 52, 1570 (1995).
[CrossRef] [PubMed]

1994 (2)

C.-J. Chen, P. K. A. Wai, and C. R. Menyuk, Opt. Lett. 19, 198 (1994).
[CrossRef]

E. V. Vanin, A. I. Korytin, A. M. Sergeev, D. Anderson, M. Lisak, and L. Vázquez, Phys. Rev. A 49, 2806 (1994).
[CrossRef] [PubMed]

1993 (1)

1991 (1)

1988 (2)

W. H. Knox, IEEE J. Quantum Electron. 24, 388 (1988).
[CrossRef]

V. S. Grigoryan, A. I. Maimistov, and Yu. M. Sklyarov, Zh. Eksp. Teor. Fiz. 94, 174 (1988) [Sov. Phys. JETP 67, 530 (1988)].

1986 (1)

1980 (1)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

IEEE J. Quantum Electron. (1)

W. H. Knox, IEEE J. Quantum Electron. 24, 388 (1988).
[CrossRef]

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

Opt. Lett. (3)

Phys Rev. A (1)

D. Anderson, A. I. Korytin, M. Lisak, A. M. Sergeev, and E. V. Vanin, Phys Rev. A 52, 1570 (1995).
[CrossRef] [PubMed]

Phys. Rev. A (1)

E. V. Vanin, A. I. Korytin, A. M. Sergeev, D. Anderson, M. Lisak, and L. Vázquez, Phys. Rev. A 49, 2806 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Proc. SPIE (1)

A. M. Sergeev and E. V. Vanin, Proc. SPIE 2377, 32 (1995).
[CrossRef]

Sov. Phys. JETP (1)

V. S. Grigoryan, A. I. Maimistov, and Yu. M. Sklyarov, Zh. Eksp. Teor. Fiz. 94, 174 (1988) [Sov. Phys. JETP 67, 530 (1988)].

Other (2)

J. Herrmann and B. Wilhelmi, Lasers for Ultrashort Light Pulses (Akademe-Verlag, Berlin, 1987).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, 1989).

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Figures (5)

Fig. 1
Fig. 1

Schrödinger Eq. (3) (dashed curve) and dissipative Eq. (4) (solid curve) solitons for g = 0.01. g = 0.25, and g = 9.

Fig. 2
Fig. 2

Central-frequency ω¯(z) evolution obtained by numerical simulation of Eqs. (2) and (9) in the absence of Kerr nonlinearity (dots); sd=-1,gc=h=1, A(0,τ)=70[exp(-i224τ)]/ cosh(22.5τ), and analytical solution Eq. (15) (solid curve).

Fig. 3
Fig. 3

(a) Optical pulse intensity |A(z,τ)|2 and (b) the spectrum |A(z,ω)|2 demonstrating periodic soliton interconversion; numerical solution of Eqs. (2) and (9) at sd = -1, gc=1, and h=0.2. The boundary field distribution is A(0,τ) = 2 2I[exp(-i15τ)]/cosh(2τ). The time position of the optical pulse τc(z)=-+τ|A(z,τ)|2dτ/-+|A(z,τ)|2dτ is used in (a).

Fig. 4
Fig. 4

Central frequency versus the distance of pulse propagation through a nonlinear active medium; numerical simulation of Eqs. (2) and (9) for sd = -1, gc = 1, and different values of gain-inhomogeneity parameter h.

Fig. 5
Fig. 5

Domain of self-oscillations of the optical pulse spectrum.

Equations (21)

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-i Ez-12 k0 2Eτ2+ω0c n2|E|2E
=-i 12 (g0-α)E+i g02Ws E-τ|E(z, τ)|2dτ,
-i Az-sd 2Aτ2+A|A|2
=-igA+iA-τ|A(z, τ)|2dτ.
αsa=α0sa exp-c2k08πWsaω0 -τ|E(z, τ)|2dτ
AShr(z, τ)=g2 cosh-1g2 [τ+(2ω¯+2)z]×exp(iωτ¯+iω¯2z-ig2z/4),
A(z, τ)=g3/4D(ξ)expiω¯(z)τ+i-ξ[ω(ξ)-ω]dξ+i 23 a˜2z3g3
dω¯dz=g3/2a˜.
d2Ddξ2-Ω2D+a˜ξD+μD3=0,
ΩD2=U22-U,
dUdξ=D2,
gAgˆA=gcA+ih Aτ,
ω¯(z)12πW¯ -+ω|Aω|2dω=1W¯ -+|A(z, τ)|2  arg[A(z, τ)]τ dτ.
W¯ dω¯dz=2-+gc--τ|A(z, τ)|2dτ|A(z, τ)|2× arg[A(z, τ)]τ-ω¯dτ-2h-+|A(z, τ)|τ2+ arg[A(z, τ)]τ-ω¯2|A(z, τ)2dτ.
dω¯dz=-h6 (gc-hω¯)2.
ω¯(z)=1h gc-gc-hω¯(z0)1-h2(z-z0)[gc-hω¯(z0)]/6,
h Aτ=ih[ω¯(z)+Δω(z, τ)]A+h A|A| |A|τ,
Δω(z, τ)= arg[A(z, τ)]τ-ω¯(z)
h A|A| |A|τh(gc-hω¯)2,
dω¯dz=(gc-hω¯)3/2a˜(μ),μ=(gc-hω¯)1/2.
ω¯(z)=1h gc-gc-hω¯(z0)[1+12ha˜(z-z0)gc-hω¯(z0)]2.

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