Abstract

A unified framework to optimize power discrimination for self-routing switching of solitonlike pulses in multiple-core fiber arrays is presented. This framework, based on the variational approach, is applicable to all-optical switching in N-core nonlinear fiber arrays for any configuration of the cores. By defining a quality factor as the product of the maxima of all the transmission curves characterizing the switching process in the fiber array, we show that when linearly varying coupling coefficients are considered improved performance can be achieved. By use of the split-step Fourier method the accuracy of the reduced formulation is ensured.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Jensen, “The nonlinear coupler,” IEEE J. Quantum Electron. 18, 1580–1583 (1982).
    [CrossRef]
  2. A. W. Snyder, D. J. Mitchell, L. Poladian, D. R. Rowland, and Y. Chen, “Physics of nonlinear fiber couplers,” J. Opt. Soc. Am. B 8, 2102–2118 (1991).
    [CrossRef]
  3. C. Schmidt-Hattenberger, U. Trutschel, and F. Lederer, “Nonlinear switching in multiple-core couplers,” Opt. Lett. 16, 294–296 (1991).
    [CrossRef] [PubMed]
  4. 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]
  5. S. Trillo and S. Wabnitz, “Weak-pulse-activated coherent soliton switching in nonlinear couplers,” Opt. Lett. 16, 1–3 (1991).
    [CrossRef] [PubMed]
  6. M. Romagnoli, S. Trillo, and S. Wabnitz, “Soliton switching in nonlinear couplers,” Opt. Quantum Electron. 24, S1237–S1267 (1992).
    [CrossRef]
  7. 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, 7240–7243 (1991).
    [CrossRef]
  8. A. V. Buryak and N. N. Akhmediev, “Stationary pulse propagation in N-core nonlinear fiber directional couplers,” IEEE J. Quantum Electron. 31, 682–688 (1995).
    [CrossRef]
  9. D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135–3145 (1983).
    [CrossRef]
  10. 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]
  11. 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 (1998).
    [CrossRef]
  12. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, Boston, Mass., 1995).
  13. 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, 1379–1385 (1993).
    [CrossRef]
  14. I. Uzunov, R. Muschall, M. Gölles, Yu. Kivshar, B. Malomed, and F. Lederer, “Pulse switching in nonlinear fiber directional couplers,” Phys. Rev. E 51, 2527–2537 (1995).
    [CrossRef]
  15. N. Akhmediev and A. Ankiewicz, “Novel soliton states and bifurcation phenomena in nonlinear fiber couplers,” Phys. Rev. Lett. 70, 2395–2398 (1993).
    [CrossRef] [PubMed]
  16. W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in C, 3rd ed. (Cambridge Univ. Press, Cambridge, UK, 1994), pp. 710–722.
  17. P. L. Chu and B. Wu, “Optical switching in twin-core erbium-doped fibers,” Opt. Lett. 17, 255–257 (1992).
    [CrossRef] [PubMed]
  18. J. Wilson, G. I. Stegeman, and E. M. Wright, “All-optical switching of solitons in an active nonlinear directional coupler,” Opt. Quantum Electron. 24, S1325–S1336 (1992).
    [CrossRef]
  19. H. A. Haus and L. Molter-Orr, “Coupled multiple waveguide system,” IEEE J. Quantum Electron. 19, 840–844 (1983).
    [CrossRef]

1998 (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 (1998).
[CrossRef]

1997 (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]

1995 (2)

I. Uzunov, R. Muschall, M. Gölles, Yu. Kivshar, B. Malomed, and F. Lederer, “Pulse switching in nonlinear fiber directional couplers,” Phys. Rev. E 51, 2527–2537 (1995).
[CrossRef]

A. V. Buryak and N. N. Akhmediev, “Stationary pulse propagation in N-core nonlinear fiber directional couplers,” IEEE J. Quantum Electron. 31, 682–688 (1995).
[CrossRef]

1993 (2)

N. Akhmediev and A. Ankiewicz, “Novel soliton states and bifurcation phenomena in nonlinear fiber couplers,” Phys. Rev. Lett. 70, 2395–2398 (1993).
[CrossRef] [PubMed]

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, 1379–1385 (1993).
[CrossRef]

1992 (3)

P. L. Chu and B. Wu, “Optical switching in twin-core erbium-doped fibers,” Opt. Lett. 17, 255–257 (1992).
[CrossRef] [PubMed]

J. Wilson, G. I. Stegeman, and E. M. Wright, “All-optical switching of solitons in an active nonlinear directional coupler,” Opt. Quantum Electron. 24, S1325–S1336 (1992).
[CrossRef]

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

1991 (4)

1988 (1)

1983 (2)

D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135–3145 (1983).
[CrossRef]

H. A. Haus and L. Molter-Orr, “Coupled multiple waveguide system,” IEEE J. Quantum Electron. 19, 840–844 (1983).
[CrossRef]

1982 (1)

S. Jensen, “The nonlinear coupler,” IEEE J. Quantum Electron. 18, 1580–1583 (1982).
[CrossRef]

Akhmediev, N.

N. Akhmediev and A. Ankiewicz, “Novel soliton states and bifurcation phenomena in nonlinear fiber couplers,” Phys. Rev. Lett. 70, 2395–2398 (1993).
[CrossRef] [PubMed]

Akhmediev, N. N.

A. V. Buryak and N. N. Akhmediev, “Stationary pulse propagation in N-core nonlinear fiber directional couplers,” IEEE J. Quantum Electron. 31, 682–688 (1995).
[CrossRef]

Anderson, D.

D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135–3145 (1983).
[CrossRef]

Ankiewicz, A.

N. Akhmediev and A. Ankiewicz, “Novel soliton states and bifurcation phenomena in nonlinear fiber couplers,” Phys. Rev. Lett. 70, 2395–2398 (1993).
[CrossRef] [PubMed]

Buryak, A. V.

A. V. Buryak and N. N. Akhmediev, “Stationary pulse propagation in N-core nonlinear fiber directional couplers,” IEEE J. Quantum Electron. 31, 682–688 (1995).
[CrossRef]

Chen, Y.

Chu, P. L.

Gölles, M.

I. Uzunov, R. Muschall, M. Gölles, Yu. Kivshar, B. Malomed, and F. Lederer, “Pulse switching in nonlinear fiber directional couplers,” Phys. Rev. E 51, 2527–2537 (1995).
[CrossRef]

Haus, H. A.

H. A. Haus and L. Molter-Orr, “Coupled multiple waveguide system,” IEEE J. Quantum Electron. 19, 840–844 (1983).
[CrossRef]

Jensen, S.

S. Jensen, “The nonlinear coupler,” IEEE J. Quantum Electron. 18, 1580–1583 (1982).
[CrossRef]

Kivshar, Yu.

I. Uzunov, R. Muschall, M. Gölles, Yu. Kivshar, B. Malomed, and F. Lederer, “Pulse switching in nonlinear fiber directional couplers,” Phys. Rev. E 51, 2527–2537 (1995).
[CrossRef]

Lederer, F.

I. Uzunov, R. Muschall, M. Gölles, Yu. Kivshar, B. Malomed, and F. Lederer, “Pulse switching in nonlinear fiber directional couplers,” Phys. Rev. E 51, 2527–2537 (1995).
[CrossRef]

C. Schmidt-Hattenberger, U. Trutschel, and F. Lederer, “Nonlinear switching in multiple-core couplers,” Opt. Lett. 16, 294–296 (1991).
[CrossRef] [PubMed]

Malomed, B.

I. Uzunov, R. Muschall, M. Gölles, Yu. Kivshar, B. Malomed, and F. Lederer, “Pulse switching in nonlinear fiber directional couplers,” Phys. Rev. E 51, 2527–2537 (1995).
[CrossRef]

Malomed, B. A.

Mitchell, D. J.

Molter-Orr, L.

H. A. Haus and L. Molter-Orr, “Coupled multiple waveguide system,” IEEE J. Quantum Electron. 19, 840–844 (1983).
[CrossRef]

Muschall, R.

I. Uzunov, R. Muschall, M. Gölles, Yu. Kivshar, B. Malomed, and F. Lederer, “Pulse switching in nonlinear fiber directional couplers,” Phys. Rev. E 51, 2527–2537 (1995).
[CrossRef]

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 (1998).
[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]

Peng, G. D.

Poladian, L.

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 (1998).
[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]

Rowland, D. R.

Schmidt-Hattenberger, C.

Snyder, A. W.

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, 7240–7243 (1991).
[CrossRef]

Stegeman, G. I.

J. Wilson, G. I. Stegeman, and E. M. Wright, “All-optical switching of solitons in an active nonlinear directional coupler,” Opt. Quantum Electron. 24, S1325–S1336 (1992).
[CrossRef]

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]

Trillo, S.

Trutschel, U.

Uzunov, I.

I. Uzunov, R. Muschall, M. Gölles, Yu. Kivshar, B. Malomed, and F. Lederer, “Pulse switching in nonlinear fiber directional couplers,” Phys. Rev. E 51, 2527–2537 (1995).
[CrossRef]

Wabnitz, S.

Wilson, J.

J. Wilson, G. I. Stegeman, and E. M. Wright, “All-optical switching of solitons in an active nonlinear directional coupler,” Opt. Quantum Electron. 24, S1325–S1336 (1992).
[CrossRef]

Wright, E. M.

J. Wilson, G. I. Stegeman, and E. M. Wright, “All-optical switching of solitons in an active nonlinear directional coupler,” Opt. Quantum Electron. 24, S1325–S1336 (1992).
[CrossRef]

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, 7240–7243 (1991).
[CrossRef]

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]

Wu, B.

IEEE J. Quantum Electron. (3)

S. Jensen, “The nonlinear coupler,” IEEE J. Quantum Electron. 18, 1580–1583 (1982).
[CrossRef]

A. V. Buryak and N. N. Akhmediev, “Stationary pulse propagation in N-core nonlinear fiber directional couplers,” IEEE J. Quantum Electron. 31, 682–688 (1995).
[CrossRef]

H. A. Haus and L. Molter-Orr, “Coupled multiple waveguide system,” IEEE J. Quantum Electron. 19, 840–844 (1983).
[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 (1998).
[CrossRef]

J. Appl. Phys. (1)

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, 7240–7243 (1991).
[CrossRef]

J. Opt. Soc. Am. B (2)

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. (4)

Opt. Quantum Electron. (2)

J. Wilson, G. I. Stegeman, and E. M. Wright, “All-optical switching of solitons in an active nonlinear directional coupler,” Opt. Quantum Electron. 24, S1325–S1336 (1992).
[CrossRef]

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

Phys. Rev. A (1)

D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135–3145 (1983).
[CrossRef]

Phys. Rev. E (1)

I. Uzunov, R. Muschall, M. Gölles, Yu. Kivshar, B. Malomed, and F. Lederer, “Pulse switching in nonlinear fiber directional couplers,” Phys. Rev. E 51, 2527–2537 (1995).
[CrossRef]

Phys. Rev. Lett. (1)

N. Akhmediev and A. Ankiewicz, “Novel soliton states and bifurcation phenomena in nonlinear fiber couplers,” Phys. Rev. Lett. 70, 2395–2398 (1993).
[CrossRef] [PubMed]

Other (2)

W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in C, 3rd ed. (Cambridge Univ. Press, Cambridge, UK, 1994), pp. 710–722.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, Boston, Mass., 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 (15)

Fig. 1
Fig. 1

Transmission curves of T1 as a function of the normalized input peak power p. A comparison between the results obtained from the SSFM and those obtained from the VA, for a half-beat coupler, is shown.

Fig. 2
Fig. 2

Diagram illustrating the self-routing switching operation of a twin-core fiber coupler. Pulses with input peak power p1 remain in the same core (parallel state), while pulses with lower peak powers (p2) switch to the other core (bar or cross state).

Fig. 3
Fig. 3

Evolution of the transmission coefficients (T1 for p=p1 and T2 for p=p2) along a full-beat-length twin-core coupler. These results were obtained by the SSFM.

Fig. 4
Fig. 4

Length optimization for two predefined power levels (p1 and p2). The cross-talk parameters CTj, obtained by the SSFM, are plotted against ζ, and a compromise length has been chosen.

Fig. 5
Fig. 5

Level lines of T1 for different longitudinal inclinations of the coupling coefficient. Each level line corresponds to a 0.1 increase from 0.1 to 0.9. The length of the coupler is ζC=ζH.

Fig. 6
Fig. 6

The two most used configurations of the three-core fiber coupler: (a) linear configuration, (b) circular configuration.

Fig. 7
Fig. 7

Three-core fiber coupler with a linear configuration. The transmission curves are shown as functions of the normalized input peak power p. Results were obtained by the SSFM and the VA.

Fig. 8
Fig. 8

Contour plot of the quality factor QT, for the three-core fiber coupler with κ13=0, with QT shown as a function of the coupling coefficients κ12 and κ23.

Fig. 9
Fig. 9

Contour plot of the quality factor QT, for the three-core fiber coupler with κ13=0. The quality factor is presented as a function of inclination factors m12 and m23.

Fig. 10
Fig. 10

Transmission curves for the three-core fiber coupler with m12=0.310 and m23=-0.091.

Fig. 11
Fig. 11

Pulse evolutions for the three-core fiber coupler with m12=0.310 and m23=-0.091 for (a) the first (input) core, (b) the second core, (c) the third core. The input pulse is u1(τ)=3.3 sech[3.3(τ+25)]+7.8 sech(7.8τ)+10.2 sech[10.2(τ-25)].

Fig. 12
Fig. 12

Transmission curves for the three-core fiber coupler (circular configuration) with κ=1.

Fig. 13
Fig. 13

Transmission curves for the four-core fiber coupler (linear configuration) with κ=1.

Fig. 14
Fig. 14

Transmission curves for the optimized four-core fiber coupler. The optimization point corresponds to m12=0.705, m23=0.355, and m34=-0.193.

Fig. 15
Fig. 15

Input and output profiles for the first core in a four-core linear configuration device. The left-hand pulses correspond to pOFF=12.3; the right-hand pulses, to pON=18.3.

Tables (2)

Tables Icon

Table 1 Transmission Coefficients for the Two Input Peak Powers p1 and p2 at ζC=ζH

Tables Icon

Table 2 Transmission Coefficients Tj and Cross-Talk Parameters CTj

Equations (26)

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

iujζ+122ujτ2+|uj|2uj+n=1Nκjnun=0,
τ=t-z/νgτ0
ζ=zLD=z|β2|τ02
K=0κ12κ120.
Tj(ζ)=-|uj(ζ)|2dτn=1N-|un(ζ)|2dτ.
L=j=1Ni2uj*ujζ-ujuj*ζ-12ujτ2+12|uj|4+j=1Nn=1Nκjnujun*.
uj=Ajη sech(ητ)exp[i(ψj+Cτ2)],
Qj=2Aj2,
Tj(ζ)=Aj2(ζ)n=1NAn2(ζ).
L=-Ldτ=LX+j=1NLj,
Lj=-2Aj2dψjdζ+π212η2dCdζ
-Aj23η2+C2π2η2+2η Aj43
LX=j=1Nn=1N2κjn Aj An cos(ψj-ψn)
dψjdζ=2η3Aj2-η26-C2π26η2+1Ajn=1NκjnAn cos(ψj-ψn),
dAjdζ=n=1NκjnAn sin(ψj-ψn),
dCdζ=2η3π2η-C2π2η3-j=1NAj4j=1NAj2,
dηdζ=-2Cη.
u1(ζ=0, τ)=p sech(pτ),
uj(ζ=0, τ)=0forj=2,, N,
P=pP0=p/(γLD).
QT=j=1N max [Tj(p)].
CTj[dB]=10 log10Qj(ζ)i=1,ijNQi(ζ).
κij(ζ)=κji(ζ)=κ0ij+mijζζC,
κ12=κ34=κ3,κ23=2κ.
ζH=π/(2κ),
K=0κ300κ302κ002κ0κ300κ30.

Metrics