Abstract

In dual-core fibers the variation of the coupling coefficient with frequency leads to intermodal dispersion that perturbs the switching of ultrashort pulses. Using a new version of the split-step Fourier method based on a model that includes intermodal dispersion, we show that this effect cannot be neglected when the switching of picosecond solitons at different wavelengths in half-beat twin-core fiber couplers is analyzed, although picosecond solitons at the central wavelength are not significantly affected. We also show that to study the switching of wavelength-division-multiplexed solitons one should always take into account the effect of intermodal dispersion.

© 1999 Optical Society of America

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References

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  1. M. Romagnoli, S. Trillo, and S. Wabnitz, “Soliton switching in nonlinear couplers,” Opt. Quantum Electron. 24, S1237–S1267 (1992).
    [CrossRef]
  2. S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Soliton switching in fiber nonlinear directional couplers,” Opt. Lett. 13, 672–674 (1988).
    [CrossRef] [PubMed]
  3. S. Trillo and S. Wabnitz, “Weak-pulse-activated coherent soliton switching in nonlinear couplers,” Opt. Lett. 16, 1–3 (1991).
    [CrossRef] [PubMed]
  4. S. L. Chuang, Physics of Optoelectronic Devices (Wiley, New York, 1995), Chap. 8.
  5. K. S. Chiang, “Intermodal dispersion in two-core optical fibers,” Opt. Lett. 20, 997–999 (1995).
    [CrossRef] [PubMed]
  6. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995), Chap. 7, pp. 295–301.
  7. P. M. Ramos and C. R. Paiva, “Influence of cross-phase modulation on self-routing pulse switching in nonlinear optical fibers,” Microwave Opt. Technol. Lett. 15, 91–95 (1997).
    [CrossRef]
  8. P. M. Ramos and C. R. Paiva, “Optimization and characterization of phase-controlled all-optical switching with fiber solitons,” IEEE J. Sel. Top. Quantum Electron. 3, 1224–1231 (1997).
    [CrossRef]
  9. K. S. Chiang, “Propagation of short optical pulses in directional couplers with Kerr nonlinearity,” J. Opt. Soc. Am. B 14, 1437–1443 (1997).
    [CrossRef]
  10. K. S. Chiang, “Coupled-mode equations for the pulse switching in parallel waveguides,” IEEE J. Quantum Electron. 33, 950–954 (1997).
    [CrossRef]
  11. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 18, p. 392.

1997 (4)

P. M. Ramos and C. R. Paiva, “Influence of cross-phase modulation on self-routing pulse switching in nonlinear optical fibers,” Microwave Opt. Technol. Lett. 15, 91–95 (1997).
[CrossRef]

P. M. Ramos and C. R. Paiva, “Optimization and characterization of phase-controlled all-optical switching with fiber solitons,” IEEE J. Sel. Top. Quantum Electron. 3, 1224–1231 (1997).
[CrossRef]

K. S. Chiang, “Propagation of short optical pulses in directional couplers with Kerr nonlinearity,” J. Opt. Soc. Am. B 14, 1437–1443 (1997).
[CrossRef]

K. S. Chiang, “Coupled-mode equations for the pulse switching in parallel waveguides,” IEEE J. Quantum Electron. 33, 950–954 (1997).
[CrossRef]

1995 (1)

1992 (1)

M. Romagnoli, S. Trillo, and S. Wabnitz, “Soliton switching in nonlinear couplers,” Opt. Quantum Electron. 24, S1237–S1267 (1992).
[CrossRef]

1991 (1)

1988 (1)

Chiang, K. S.

Paiva, C. R.

P. M. Ramos and C. R. Paiva, “Optimization and characterization of phase-controlled all-optical switching with fiber solitons,” IEEE J. Sel. Top. Quantum Electron. 3, 1224–1231 (1997).
[CrossRef]

P. M. Ramos and C. R. Paiva, “Influence of cross-phase modulation on self-routing pulse switching in nonlinear optical fibers,” Microwave Opt. Technol. Lett. 15, 91–95 (1997).
[CrossRef]

Ramos, P. M.

P. M. Ramos and C. R. Paiva, “Optimization and characterization of phase-controlled all-optical switching with fiber solitons,” IEEE J. Sel. Top. Quantum Electron. 3, 1224–1231 (1997).
[CrossRef]

P. M. Ramos and C. R. Paiva, “Influence of cross-phase modulation on self-routing pulse switching in nonlinear optical fibers,” Microwave Opt. Technol. Lett. 15, 91–95 (1997).
[CrossRef]

Romagnoli, M.

M. Romagnoli, S. Trillo, and S. Wabnitz, “Soliton switching in nonlinear couplers,” Opt. Quantum Electron. 24, S1237–S1267 (1992).
[CrossRef]

Stegeman, G. I.

Trillo, S.

Wabnitz, S.

Wright, E. M.

IEEE J. Quantum Electron. (1)

K. S. Chiang, “Coupled-mode equations for the pulse switching in parallel waveguides,” IEEE J. Quantum Electron. 33, 950–954 (1997).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

P. M. Ramos and C. R. Paiva, “Optimization and characterization of phase-controlled all-optical switching with fiber solitons,” IEEE J. Sel. Top. Quantum Electron. 3, 1224–1231 (1997).
[CrossRef]

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

Microwave Opt. Technol. Lett. (1)

P. M. Ramos and C. R. Paiva, “Influence of cross-phase modulation on self-routing pulse switching in nonlinear optical fibers,” Microwave Opt. Technol. Lett. 15, 91–95 (1997).
[CrossRef]

Opt. Lett. (3)

Opt. Quantum Electron. (1)

M. Romagnoli, S. Trillo, and S. Wabnitz, “Soliton switching in nonlinear couplers,” Opt. Quantum Electron. 24, S1237–S1267 (1992).
[CrossRef]

Other (3)

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995), Chap. 7, pp. 295–301.

S. L. Chuang, Physics of Optoelectronic Devices (Wiley, New York, 1995), Chap. 8.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 18, p. 392.

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Figures (6)

Fig. 1
Fig. 1

Transfer functions t(λ) and tx(λ) for the twin-core fiber coupler in the linear regime. We consider half-beat couplers (i.e., ζc=π/2 as κ=1) with central wavelength λ0=1.55 µm. The results obtained with Eqs. (20), the exact expressions, are compared with those obtained with relations (21), the approximate expressions.

Fig. 2
Fig. 2

Transmission coefficient T as a function of normalized input peak power p for λ=1.52 µm, λ=λ0, and λ=1.58 µm with intermodal dispersion. When δ=μ=0 all the curves are identical to T(p) for λ=λ0 with intermodal dispersion.

Fig. 3
Fig. 3

Transmission coefficient T as a function of normalized input peak power p for λ=1.52 µm and λ=1.58 µm obtained with the common model, Eqs. (7), and with the new model, Eqs. (13), which accounts for intermodal dispersion.

Fig. 4
Fig. 4

Transmission coefficient T as a function of wavelength λ for p=3 and p=9 with intermodal dispersion. When δ=μ=0 we obtain flat responses (not shown) with T(λ)=T(λ0).

Fig. 5
Fig. 5

Output signal |u1| for a four-channel WDM soliton system (λ1=1.52 µm, λ2=1.54 µm, λ3=1.56 µm, λ4=1.58 µm; p=9) with intermodal dispersion, i.e., with Eqs. (13).

Fig. 6
Fig. 6

Output signal |u1| for a four-channel WDM soliton system (λ1=1.52 µm, λ2=1.54 µm, λ3=1.56 µm, λ4=1.58µm; p=9) without intermodal dispersion, i.e., with Eqs. (7).

Equations (39)

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En(x, y, z, t)=F(x, y)Bn(z, t),
Bn(z, t)=An(z, t)exp[i(β0z-ω0t)],
β(ω0+Ω)=β0+β1Ω+½β2Ω2
iA1z+β1A1t-β222A1t2+γ|A1|2A1+C0A2=0,
iA2z+β1A2t-β222A2t2+γ|A2|2A2+C0A1=0.
Lc=π/2C0,
ζ=zLD,τ=t-β1zτ0,
iu1ζ+122u1τ2+|u1|2u1+κu2=0,
iu2ζ+122u2τ2+|u2|2u2+κu1=0,
un(ζ, τ)=NAn(ζ, τ)P0.
κ=C0LD.
β±(ω)=β(ω)±C(ω).
C(ω0+Ω)=C0+C1Ω+½C2Ω2,
iA1z+β1A1t+C1A2t-β222A1t2-C222A2t2
+γ|A1|2A1+C0A2=0,
iA2z+β1A2t+C1A1t-β222A2t2-C222A1t2
+γ|A2|2A2+C0A1=0
iu1ζ+δu2τ+122u1τ2-μ2u2τ2
+|u1|2u1+κu2=0,
iu2ζ+δu1τ+122u2τ2-μ2u1τ2
+|u2|2u2+κu1=0,
δ=C1LDτ0,μ=C2LDτ02.
C=2ΔaU2V3K0(sW)K12(W),
B˜n(z, ω)=-Bn(z, t)exp(iωt)dt,
zB˜1(z, ω)B˜2(z, ω)=iβ(ω)C(ω)C(ω)β(ω)B˜1(0, ω)B˜2(0, ω)
B˜1(z, ω)=B˜1(0, ω)exp[iβ(ω)z]cos[C(ω)z],
B˜2(z, ω)=iB˜1(0, ω)exp[iβ(ω)z]sin[C(ω)z].
t(ω)=B˜1(LC, ω)B˜1(0, ω)2,tx(ω)=B˜2(LC, ω)B˜1(0, ω)2,
t(ω)=cos2[C(ω)LC],tx(ω)=sin2[C(ω)LC].
t(ξ)sin2π2κδξ+12μξ2,
tx(ξ)cos2π2κδξ+12μξ2,
ξ=Ωτ0,
vn(ζ, τ)=un(ζ, τ)exp[ih|un(ζ, τ)|2].
u˜1(ζ+h, ξ)u˜2(ζ+h, ξ)=exp-ihξ22×cos[ϑ(ξ, h)]i sin[ϑ(ξ, h)]i sin[ϑ(ξ, h)]cos[ϑ(ξ, h)]×v˜1(ζ, ξ)v˜2(ζ, ξ),
ϑ(ξ, h)=(κ+ξδ+½ξ2μ)h.
T=1Q-|u1(ζC, τ)|2dτ,
Q=-(|u1(ζC, τ)|2+|u2(ζC, τ)|2)dτ
u1(0, τ)=p sech(pτ)exp(-iξτ),
u1(0, τ)=p sech(pτ)k=14 exp(-iξkτ),

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