Abstract

The switching dynamics of short optical pulses in a directional coupler made of two single-mode fibers (or waveguides), which is assumed to possess uniform Kerr nonlinearity, is investigated theoretically. When the nonlinearity is weak, the function of the coupler can be described by the beating between the symmetric and the antisymmetric modes of the composite waveguide structure. The group-delay difference between these two modes (intermodal dispersion) can give rise to pulse broadening or even pulse breakup. New normal-mode equations and coupled-mode equations that include the effect of intermodal dispersion are derived and discussed. The intermodal dispersion in the normal-mode formulation is found to be equivalent to the coupling-coefficient dispersion in the coupled-mode formulation. In many practical cases the intermodal dispersion is much more significant than the group-velocity dispersion, and soliton pulses are switched in the same way as any low-power linear pulses. Only in the special case that the intermodal dispersion is negligible, compared with the group-velocity dispersion, do the new coupled-mode equations reduce to the well-known linearly coupled nonlinear Schrödinger equations. A normalized parameter is proposed to determine the relative importance of the two dispersion effects.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. S. Chiang, “Intermodal dispersion in two-core optical fibers,” Opt. Lett. 20, 997 (1995).
    [CrossRef] [PubMed]
  2. K. S. Chiang, “Bandwidths of optical fibre directional couplers,” J. Electr. Electron. Eng. Australia 15, 261 (1995).
  3. S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 158 (1982).
  4. S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Soliton switching in fiber nonlinear directional couplers,” Opt. Lett. 13, 672 (1988).
    [CrossRef] [PubMed]
  5. C. Paré and M. Florjańczyk, “Approximate model of soliton dynamics in all-optical couplers,” Phys. Rev. A 41, 6287 (1990).
    [CrossRef] [PubMed]
  6. J. M. Soto-Crespo and E. M. Wright, “All-optical switching of solitons in two- and three-core nonlinear fiber couplers,” J. Appl. Phys. 70, 7240 (1991).
    [CrossRef]
  7. M. Romagnoli, S. Trillo, and S. Wabnitz, “Soliton switching in nonlinear couplers,” Opt. Quantum Electron. 24, S1237 (1992).
    [CrossRef]
  8. P. L. Chu, B. A. Malomed, and G. D. Peng, “Analytical solution to soliton switching in nonlinear twin-core fibers,” Opt. Lett. 18, 328 (1993).
    [CrossRef] [PubMed]
  9. Y. S. Kivshar, “Switching dynamics of solitons in fiber directional couplers,” Opt. Lett. 18, 7 (1993).
    [CrossRef] [PubMed]
  10. N. Akhmediev and A. Ankiewicz, “Novel soliton states and bifurcation phenomena in nonlinear fiber couplers,” Phys. Rev. Lett. 70, 2395 (1993).
    [CrossRef] [PubMed]
  11. P. L. Chu, B. A. Malomed, and G.-D. Peng, “Soliton switching and propagation in nonlinear fiber couplers: analytical results,” J. Opt. Soc. Am. B 10, 1379 (1993).
    [CrossRef]
  12. S. R. Friberg, Y. Silberberg, M. K. Oliver, M. J. Andrejco, M. A. Saifi, and P. W. Smith, “Ultrafast all-optical switching in a dual-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135 (1987).
    [CrossRef]
  13. S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. W. Smith, “Femtosecond switching in a dual-core-fiber nonlinear coupler,” Opt. Lett. 13, 904 (1988).
    [CrossRef] [PubMed]
  14. K. Kitayama and S. Wang, “Optical pulse compression by nonlinear coupling,” Appl. Phys. Lett. 43, 17 (1983).
    [CrossRef]
  15. A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, and P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25, 2648 (1989).
    [CrossRef]
  16. Y. Silberberg and G. I. Stegeman, “Nonlinear coupling of waveguide modes,” Appl. Phys. Lett. 50, 801 (1987).
    [CrossRef]
  17. A. Hasegawa, “Self-confinement of multimode optical pulse in a glass fiber,” Opt. Lett. 5, 416 (1980).
    [CrossRef] [PubMed]
  18. B. Crosignani and P. Di Porto, “Soliton propagation in multimode optical fibers,” Opt. Lett. 6, 329 (1981).
    [CrossRef] [PubMed]
  19. C. R. Menyuk, “Stability of solitons in birefringent optical fibers. I. Equal propagation amplitudes,” Opt. Lett. 12, 614 (1987).
    [CrossRef] [PubMed]
  20. C. R. Menyuk, “Stability of solitons in birefringent optical fibers. II. Arbitrary amplitudes,” J. Opt. Soc. Am. B 5, 392 (1988).
    [CrossRef]

1995

1993

1992

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

1991

J. M. Soto-Crespo and E. M. Wright, “All-optical switching of solitons in two- and three-core nonlinear fiber couplers,” J. Appl. Phys. 70, 7240 (1991).
[CrossRef]

1990

C. Paré and M. Florjańczyk, “Approximate model of soliton dynamics in all-optical couplers,” Phys. Rev. A 41, 6287 (1990).
[CrossRef] [PubMed]

1989

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, and P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25, 2648 (1989).
[CrossRef]

1988

1987

Y. Silberberg and G. I. Stegeman, “Nonlinear coupling of waveguide modes,” Appl. Phys. Lett. 50, 801 (1987).
[CrossRef]

S. R. Friberg, Y. Silberberg, M. K. Oliver, M. J. Andrejco, M. A. Saifi, and P. W. Smith, “Ultrafast all-optical switching in a dual-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135 (1987).
[CrossRef]

C. R. Menyuk, “Stability of solitons in birefringent optical fibers. I. Equal propagation amplitudes,” Opt. Lett. 12, 614 (1987).
[CrossRef] [PubMed]

1983

K. Kitayama and S. Wang, “Optical pulse compression by nonlinear coupling,” Appl. Phys. Lett. 43, 17 (1983).
[CrossRef]

1982

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 158 (1982).

1981

1980

Akhmediev, N.

N. Akhmediev and A. Ankiewicz, “Novel soliton states and bifurcation phenomena in nonlinear fiber couplers,” Phys. Rev. Lett. 70, 2395 (1993).
[CrossRef] [PubMed]

Andrejco, M. J.

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, and P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25, 2648 (1989).
[CrossRef]

S. R. Friberg, Y. Silberberg, M. K. Oliver, M. J. Andrejco, M. A. Saifi, and P. W. Smith, “Ultrafast all-optical switching in a dual-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135 (1987).
[CrossRef]

Ankiewicz, A.

N. Akhmediev and A. Ankiewicz, “Novel soliton states and bifurcation phenomena in nonlinear fiber couplers,” Phys. Rev. Lett. 70, 2395 (1993).
[CrossRef] [PubMed]

Chiang, K. S.

Chu, P. L.

Crosignani, B.

Di Porto, P.

Florjanczyk, M.

C. Paré and M. Florjańczyk, “Approximate model of soliton dynamics in all-optical couplers,” Phys. Rev. A 41, 6287 (1990).
[CrossRef] [PubMed]

Fouckhardt, H.

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, and P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25, 2648 (1989).
[CrossRef]

Friberg, S. R.

S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. W. Smith, “Femtosecond switching in a dual-core-fiber nonlinear coupler,” Opt. Lett. 13, 904 (1988).
[CrossRef] [PubMed]

S. R. Friberg, Y. Silberberg, M. K. Oliver, M. J. Andrejco, M. A. Saifi, and P. W. Smith, “Ultrafast all-optical switching in a dual-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135 (1987).
[CrossRef]

Hasegawa, A.

Jensen, S. M.

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 158 (1982).

Kitayama, K.

K. Kitayama and S. Wang, “Optical pulse compression by nonlinear coupling,” Appl. Phys. Lett. 43, 17 (1983).
[CrossRef]

Kivshar, Y. S.

Leaird, D. E.

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, and P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25, 2648 (1989).
[CrossRef]

Malomed, B. A.

Menyuk, C. R.

Oliver, M. K.

S. R. Friberg, Y. Silberberg, M. K. Oliver, M. J. Andrejco, M. A. Saifi, and P. W. Smith, “Ultrafast all-optical switching in a dual-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135 (1987).
[CrossRef]

Paré, C.

C. Paré and M. Florjańczyk, “Approximate model of soliton dynamics in all-optical couplers,” Phys. Rev. A 41, 6287 (1990).
[CrossRef] [PubMed]

Peng, G. D.

Peng, G.-D.

Romagnoli, M.

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

Saifi, M. A.

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, and P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25, 2648 (1989).
[CrossRef]

S. R. Friberg, Y. Silberberg, M. K. Oliver, M. J. Andrejco, M. A. Saifi, and P. W. Smith, “Ultrafast all-optical switching in a dual-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135 (1987).
[CrossRef]

Sfez, B. G.

Silberberg, Y.

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, and P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25, 2648 (1989).
[CrossRef]

S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. W. Smith, “Femtosecond switching in a dual-core-fiber nonlinear coupler,” Opt. Lett. 13, 904 (1988).
[CrossRef] [PubMed]

S. R. Friberg, Y. Silberberg, M. K. Oliver, M. J. Andrejco, M. A. Saifi, and P. W. Smith, “Ultrafast all-optical switching in a dual-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135 (1987).
[CrossRef]

Y. Silberberg and G. I. Stegeman, “Nonlinear coupling of waveguide modes,” Appl. Phys. Lett. 50, 801 (1987).
[CrossRef]

Smith, P. W.

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, and P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25, 2648 (1989).
[CrossRef]

S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. W. Smith, “Femtosecond switching in a dual-core-fiber nonlinear coupler,” Opt. Lett. 13, 904 (1988).
[CrossRef] [PubMed]

S. R. Friberg, Y. Silberberg, M. K. Oliver, M. J. Andrejco, M. A. Saifi, and P. W. Smith, “Ultrafast all-optical switching in a dual-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135 (1987).
[CrossRef]

Soto-Crespo, J. M.

J. M. Soto-Crespo and E. M. Wright, “All-optical switching of solitons in two- and three-core nonlinear fiber couplers,” J. Appl. Phys. 70, 7240 (1991).
[CrossRef]

Stegeman, G. I.

Trillo, S.

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

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Soliton switching in fiber nonlinear directional couplers,” Opt. Lett. 13, 672 (1988).
[CrossRef] [PubMed]

Wabnitz, S.

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

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Soliton switching in fiber nonlinear directional couplers,” Opt. Lett. 13, 672 (1988).
[CrossRef] [PubMed]

Wang, S.

K. Kitayama and S. Wang, “Optical pulse compression by nonlinear coupling,” Appl. Phys. Lett. 43, 17 (1983).
[CrossRef]

Weiner, A. M.

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, and P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25, 2648 (1989).
[CrossRef]

S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. W. Smith, “Femtosecond switching in a dual-core-fiber nonlinear coupler,” Opt. Lett. 13, 904 (1988).
[CrossRef] [PubMed]

Wright, E. M.

J. M. Soto-Crespo and E. M. Wright, “All-optical switching of solitons in two- and three-core nonlinear fiber couplers,” J. Appl. Phys. 70, 7240 (1991).
[CrossRef]

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Soliton switching in fiber nonlinear directional couplers,” Opt. Lett. 13, 672 (1988).
[CrossRef] [PubMed]

Appl. Phys. Lett.

Y. Silberberg and G. I. Stegeman, “Nonlinear coupling of waveguide modes,” Appl. Phys. Lett. 50, 801 (1987).
[CrossRef]

S. R. Friberg, Y. Silberberg, M. K. Oliver, M. J. Andrejco, M. A. Saifi, and P. W. Smith, “Ultrafast all-optical switching in a dual-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135 (1987).
[CrossRef]

K. Kitayama and S. Wang, “Optical pulse compression by nonlinear coupling,” Appl. Phys. Lett. 43, 17 (1983).
[CrossRef]

IEEE J. Quantum Electron.

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, and P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25, 2648 (1989).
[CrossRef]

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 158 (1982).

J. Appl. Phys.

J. M. Soto-Crespo and E. M. Wright, “All-optical switching of solitons in two- and three-core nonlinear fiber couplers,” J. Appl. Phys. 70, 7240 (1991).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Opt. Quantum Electron.

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

Phys. Rev. A

C. Paré and M. Florjańczyk, “Approximate model of soliton dynamics in all-optical couplers,” Phys. Rev. A 41, 6287 (1990).
[CrossRef] [PubMed]

Phys. Rev. Lett.

N. Akhmediev and A. Ankiewicz, “Novel soliton states and bifurcation phenomena in nonlinear fiber couplers,” Phys. Rev. Lett. 70, 2395 (1993).
[CrossRef] [PubMed]

Other

K. S. Chiang, “Bandwidths of optical fibre directional couplers,” J. Electr. Electron. Eng. Australia 15, 261 (1995).

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 (1)

Fig. 1
Fig. 1

Switching dynamics of a Gaussian pulse in an evanescent-field coupler in the presence of large intermodal dispersion (2t0=1 ps, δτ=1 ps m-1, and Lc=4 cm). The pulse is launched into Core 1 of the coupler at z=0.

Tables (1)

Tables Icon

Table 1 Typical Values of the Parameters R, |R|, and |R| for Various Pulse Widths t0 for a Step-index Two-Core Fiber

Equations (46)

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

E(x, y, z, t)=A+(z, t)ψ+(x, y)exp(iβ+z)+A-(z, t)ψ-(x, y)exp(iβ-z),
iA+z+τ+A+t-k+22A+t2=0,
iA-z+τ-A-t-k-22A-t2=0,
δτ=τ+-τ-=2 dCdω,
I(x, y, z, t)=|E(x, y, z, t)|22=12|A(t-τ+z)|2ψ+2(x, y)+12|A(t-τ-z)|2ψ-2(x, y)+A(t-τ+z)A(t-τ-z)×cosπzLcψ+(x, y)ψ-(x, y),
Lc=π2C
ψ+(x, y)=ψ1(x, y)+ψ2(x, y),
ψ-(x, y)=ψ1(x, y)-ψ2(x, y),
I(z, τ)=12Aτ-δτ2z2+Aτ+δτ2z2+2Aτ-δτ2zAτ+δτ2z×cosπzLc-+-+ψ12(x, y)dxdy+12Aτ-δτ2z2+Aτ+δτ2z2-2Aτ-δτ2zAτ+δτ2z×cosπzLc-+-+ψ22(x, y)dxdy.
I1(z, τ)=12Aτ-δτ2z2+Aτ+δτ2z2+2Aτ-δτ2zAτ+δτ2zcosπzLc,
I2(z, τ)=12Aτ-δτ2z2+Aτ+δτ2z2-2Aτ-δτ2zAτ+δτ2zcosπzLc.
L<0.2 t0|δτ|,
numberofcouplinglengths<0.2 t0|δτc|,
iA+z+τ+A+t-k+22A+t2+2πn2αλ[(|A+|2
+2|A-|2)A++A-2A+* exp(-i4Cz)]=0,
iA-z+τ-A-t-k-22A-t2+2πn2αλ[(|A-|2
+2|A+|2)A-+A+2A-* exp(i4Cz)]=0,
a+=2πn2αt02-λk1/2A+,
a-=2πn2αt02-λk1/2A-,
T=1t0t-τ++τ-2z,
Z=--kt02z,
R=Ct02-k,
R=t0-2kδτ,
R=k+-k--2k,
ia+Z+Ra+T+1-R22a+T2+(|a+|2+2|a-|2)a+
+a-2a+* exp(-i4RZ)=0,
ia-Z-Ra-T+1+R22a-T2+(|a-|2+2|a+|2)a-
+a+2a-* exp(i4RZ)=0.
a+(Z, T)=expi2[1+(R)2]Z-iRTsech T.
a+(Z, T)=13expi2[1+(R)2]Z-iRTsech T,
a-(Z, T)=13expi2[1+(R)2]Z+iRTsech T.
Icλ(δτ)224πn2|k|.
Isλ|k|πn2t02.
IcIs(δτ)2t0224|k|2.
E(x, y, z, t)=A1(z, t)ψ1(x, y)exp(iβ0z)+A2(z, t)ψ2(x, y)exp(iβ0z),
A+=12(A1+A2)exp(-iCz),
A-=12(A1-A2)exp(iCz).
iA1z+δτ2A2τ-k22A1τ2-R2A2τ2+CA2+2πn2αλ|A1|2A1=0,
iA2z+δτ2A1τ-k22A2τ2-R2A1τ2+CA1
+2πn2αλ|A2|2A2=0,
ia1Z+Ra2T+122a1T2+Ra2-R22a2T2
+|a1|2a1=0,
ia2Z+Ra1T+122a2T2+Ra1-R22a1T2
+|a2|2a2=0,
ia1Z+Ra2T+Ra2=0,
ia2Z+Ra1T+Ra1=0.

Metrics