Abstract

Nonlinear directional couplers (NLDCs) with a variable coupling coefficient (VCC) in self-focusing and self-defocusing materials are investigated. Specifically, the Gaussian type VCC NLDCs are studied in detail. The results show that the responses of the VCC NLDCs on self-focusing and self-defocusing materials are different, especially when input power is high. The coupled-mode theory can also be used to predict the characteristics of the VCC NLDC on self-focusing material, even when input power is high.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 1580–1583 (1982).
    [CrossRef]
  2. Y. Silberberg, B. G. Sfez, “All-optical phase- and power-controlled switching in nonlinear waveguide junctions,” Opt. Lett. 13, 1132–1134 (1988).
    [CrossRef] [PubMed]
  3. J. P. Sabini, N. Finlayson, G. I. Stegeman, “All-optical switching in nonlinear X junctions,” Appl. Phys. Lett. 55, 1176–1178 (1989).
    [CrossRef]
  4. C. Schmidt-Hattenberger, U. Trutschel, F. Lederer, “Nonlinear switching in multiple-core couplers,” Opt. Lett. 16, 294–296 (1991).
    [CrossRef] [PubMed]
  5. J. S. Aitchison, A. Villeneuve, G. I. Stegeman, “All-optical switching in two cascaded nonlinear directional couplers,” Opt. Lett. 20, 698–700 (1995).
    [CrossRef] [PubMed]
  6. G. J. Liu, B. M. Liang, G. L. Jin, Q. Li, “Arc-shaped waveguide switch based on the third-order nonlinear effect,” Appl. Opt. 41, 5022–5024 (2002).
    [CrossRef] [PubMed]
  7. G. J. Liu, B. M. Liang, Q. Li, G. L. Jin, “Multiple coupling length nonlinear directional couplers with variable coupling coefficient,” Opt. Commun. 218, 113–117 (2003).
    [CrossRef]
  8. Amnon Yariv and Pochi Yeh, Optical Waves in Crystals (Wiley, New York, 1984, pp. 459–469.
  9. F. J. Fraile-Pelaez, G. Assanto, “Coupled-mode equations for nonlinear directional couplers,” Appl. Opt. 29, 2216–2217 (1990).
    [CrossRef] [PubMed]
  10. Y. Chen, “Solution to full coupled wave equations of nonlinear coupled systems,” IEEE J. Quantum Electron. 25, 2149–2153 (1989).
    [CrossRef]
  11. F. Farjady, M. G. F. Wilson, P. M. Radmore, “Matrix coupled mode theory model of strongly-coupled multiwaveguide optical nonlinear directional couplers,” Opt. Quantum Electron. 33, 173–188 (2001).
    [CrossRef]
  12. W. P. Huang, “Coupled-mode theory for optical waveguides: an overview,” J. Opt. Soc. Am. A 11, 963–983 (1994).
    [CrossRef]
  13. G. R. Hadley, “Wide-angle beam propagation using Padé approximant operators,” Opt. Lett. 17, 1426–1428 (1992).
    [CrossRef]
  14. G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron. 28, 363–370 (1992).
    [CrossRef]
  15. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, 1995), pp. 42–43.
  16. G. J. Liu, B. M. Liang, Q. Li, G. L. Jin, “Switching characteristics of variable coupling coefficient nonlinear directional coupler,” IEEE. J. Lightwave Technol., submitted for publication.
  17. G. I. Stegeman, E. M. Wright, “All-optical waveguide switching,” Opt. Quantum Electron. 22, 95–122 (1990).
    [CrossRef]
  18. N. Finlayson, E. M. Wightt, C. T. Seaton, G. I. Stegeman, Y. Silberberg, “Beam propagation study of nonlinear coupling between transverse electric modes of a slab waveguide,” Appl. Phys. Lett. 50, 1562–1564 (1987).
    [CrossRef]

2003 (1)

G. J. Liu, B. M. Liang, Q. Li, G. L. Jin, “Multiple coupling length nonlinear directional couplers with variable coupling coefficient,” Opt. Commun. 218, 113–117 (2003).
[CrossRef]

2002 (1)

2001 (1)

F. Farjady, M. G. F. Wilson, P. M. Radmore, “Matrix coupled mode theory model of strongly-coupled multiwaveguide optical nonlinear directional couplers,” Opt. Quantum Electron. 33, 173–188 (2001).
[CrossRef]

1995 (1)

1994 (1)

1992 (2)

G. R. Hadley, “Wide-angle beam propagation using Padé approximant operators,” Opt. Lett. 17, 1426–1428 (1992).
[CrossRef]

G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron. 28, 363–370 (1992).
[CrossRef]

1991 (1)

1990 (2)

F. J. Fraile-Pelaez, G. Assanto, “Coupled-mode equations for nonlinear directional couplers,” Appl. Opt. 29, 2216–2217 (1990).
[CrossRef] [PubMed]

G. I. Stegeman, E. M. Wright, “All-optical waveguide switching,” Opt. Quantum Electron. 22, 95–122 (1990).
[CrossRef]

1989 (2)

Y. Chen, “Solution to full coupled wave equations of nonlinear coupled systems,” IEEE J. Quantum Electron. 25, 2149–2153 (1989).
[CrossRef]

J. P. Sabini, N. Finlayson, G. I. Stegeman, “All-optical switching in nonlinear X junctions,” Appl. Phys. Lett. 55, 1176–1178 (1989).
[CrossRef]

1988 (1)

1987 (1)

N. Finlayson, E. M. Wightt, C. T. Seaton, G. I. Stegeman, Y. Silberberg, “Beam propagation study of nonlinear coupling between transverse electric modes of a slab waveguide,” Appl. Phys. Lett. 50, 1562–1564 (1987).
[CrossRef]

1982 (1)

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

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, 1995), pp. 42–43.

Aitchison, J. S.

Assanto, G.

Chen, Y.

Y. Chen, “Solution to full coupled wave equations of nonlinear coupled systems,” IEEE J. Quantum Electron. 25, 2149–2153 (1989).
[CrossRef]

Farjady, F.

F. Farjady, M. G. F. Wilson, P. M. Radmore, “Matrix coupled mode theory model of strongly-coupled multiwaveguide optical nonlinear directional couplers,” Opt. Quantum Electron. 33, 173–188 (2001).
[CrossRef]

Finlayson, N.

J. P. Sabini, N. Finlayson, G. I. Stegeman, “All-optical switching in nonlinear X junctions,” Appl. Phys. Lett. 55, 1176–1178 (1989).
[CrossRef]

N. Finlayson, E. M. Wightt, C. T. Seaton, G. I. Stegeman, Y. Silberberg, “Beam propagation study of nonlinear coupling between transverse electric modes of a slab waveguide,” Appl. Phys. Lett. 50, 1562–1564 (1987).
[CrossRef]

Fraile-Pelaez, F. J.

Hadley, G. R.

G. R. Hadley, “Wide-angle beam propagation using Padé approximant operators,” Opt. Lett. 17, 1426–1428 (1992).
[CrossRef]

G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron. 28, 363–370 (1992).
[CrossRef]

Huang, W. P.

Jensen, S. M.

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

Jin, G. L.

G. J. Liu, B. M. Liang, Q. Li, G. L. Jin, “Multiple coupling length nonlinear directional couplers with variable coupling coefficient,” Opt. Commun. 218, 113–117 (2003).
[CrossRef]

G. J. Liu, B. M. Liang, G. L. Jin, Q. Li, “Arc-shaped waveguide switch based on the third-order nonlinear effect,” Appl. Opt. 41, 5022–5024 (2002).
[CrossRef] [PubMed]

G. J. Liu, B. M. Liang, Q. Li, G. L. Jin, “Switching characteristics of variable coupling coefficient nonlinear directional coupler,” IEEE. J. Lightwave Technol., submitted for publication.

Lederer, F.

Li, Q.

G. J. Liu, B. M. Liang, Q. Li, G. L. Jin, “Multiple coupling length nonlinear directional couplers with variable coupling coefficient,” Opt. Commun. 218, 113–117 (2003).
[CrossRef]

G. J. Liu, B. M. Liang, G. L. Jin, Q. Li, “Arc-shaped waveguide switch based on the third-order nonlinear effect,” Appl. Opt. 41, 5022–5024 (2002).
[CrossRef] [PubMed]

G. J. Liu, B. M. Liang, Q. Li, G. L. Jin, “Switching characteristics of variable coupling coefficient nonlinear directional coupler,” IEEE. J. Lightwave Technol., submitted for publication.

Liang, B. M.

G. J. Liu, B. M. Liang, Q. Li, G. L. Jin, “Multiple coupling length nonlinear directional couplers with variable coupling coefficient,” Opt. Commun. 218, 113–117 (2003).
[CrossRef]

G. J. Liu, B. M. Liang, G. L. Jin, Q. Li, “Arc-shaped waveguide switch based on the third-order nonlinear effect,” Appl. Opt. 41, 5022–5024 (2002).
[CrossRef] [PubMed]

G. J. Liu, B. M. Liang, Q. Li, G. L. Jin, “Switching characteristics of variable coupling coefficient nonlinear directional coupler,” IEEE. J. Lightwave Technol., submitted for publication.

Liu, G. J.

G. J. Liu, B. M. Liang, Q. Li, G. L. Jin, “Multiple coupling length nonlinear directional couplers with variable coupling coefficient,” Opt. Commun. 218, 113–117 (2003).
[CrossRef]

G. J. Liu, B. M. Liang, G. L. Jin, Q. Li, “Arc-shaped waveguide switch based on the third-order nonlinear effect,” Appl. Opt. 41, 5022–5024 (2002).
[CrossRef] [PubMed]

G. J. Liu, B. M. Liang, Q. Li, G. L. Jin, “Switching characteristics of variable coupling coefficient nonlinear directional coupler,” IEEE. J. Lightwave Technol., submitted for publication.

Radmore, P. M.

F. Farjady, M. G. F. Wilson, P. M. Radmore, “Matrix coupled mode theory model of strongly-coupled multiwaveguide optical nonlinear directional couplers,” Opt. Quantum Electron. 33, 173–188 (2001).
[CrossRef]

Sabini, J. P.

J. P. Sabini, N. Finlayson, G. I. Stegeman, “All-optical switching in nonlinear X junctions,” Appl. Phys. Lett. 55, 1176–1178 (1989).
[CrossRef]

Schmidt-Hattenberger, C.

Seaton, C. T.

N. Finlayson, E. M. Wightt, C. T. Seaton, G. I. Stegeman, Y. Silberberg, “Beam propagation study of nonlinear coupling between transverse electric modes of a slab waveguide,” Appl. Phys. Lett. 50, 1562–1564 (1987).
[CrossRef]

Sfez, B. G.

Silberberg, Y.

Y. Silberberg, B. G. Sfez, “All-optical phase- and power-controlled switching in nonlinear waveguide junctions,” Opt. Lett. 13, 1132–1134 (1988).
[CrossRef] [PubMed]

N. Finlayson, E. M. Wightt, C. T. Seaton, G. I. Stegeman, Y. Silberberg, “Beam propagation study of nonlinear coupling between transverse electric modes of a slab waveguide,” Appl. Phys. Lett. 50, 1562–1564 (1987).
[CrossRef]

Stegeman, G. I.

J. S. Aitchison, A. Villeneuve, G. I. Stegeman, “All-optical switching in two cascaded nonlinear directional couplers,” Opt. Lett. 20, 698–700 (1995).
[CrossRef] [PubMed]

G. I. Stegeman, E. M. Wright, “All-optical waveguide switching,” Opt. Quantum Electron. 22, 95–122 (1990).
[CrossRef]

J. P. Sabini, N. Finlayson, G. I. Stegeman, “All-optical switching in nonlinear X junctions,” Appl. Phys. Lett. 55, 1176–1178 (1989).
[CrossRef]

N. Finlayson, E. M. Wightt, C. T. Seaton, G. I. Stegeman, Y. Silberberg, “Beam propagation study of nonlinear coupling between transverse electric modes of a slab waveguide,” Appl. Phys. Lett. 50, 1562–1564 (1987).
[CrossRef]

Trutschel, U.

Villeneuve, A.

Wightt, E. M.

N. Finlayson, E. M. Wightt, C. T. Seaton, G. I. Stegeman, Y. Silberberg, “Beam propagation study of nonlinear coupling between transverse electric modes of a slab waveguide,” Appl. Phys. Lett. 50, 1562–1564 (1987).
[CrossRef]

Wilson, M. G. F.

F. Farjady, M. G. F. Wilson, P. M. Radmore, “Matrix coupled mode theory model of strongly-coupled multiwaveguide optical nonlinear directional couplers,” Opt. Quantum Electron. 33, 173–188 (2001).
[CrossRef]

Wright, E. M.

G. I. Stegeman, E. M. Wright, “All-optical waveguide switching,” Opt. Quantum Electron. 22, 95–122 (1990).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (2)

N. Finlayson, E. M. Wightt, C. T. Seaton, G. I. Stegeman, Y. Silberberg, “Beam propagation study of nonlinear coupling between transverse electric modes of a slab waveguide,” Appl. Phys. Lett. 50, 1562–1564 (1987).
[CrossRef]

J. P. Sabini, N. Finlayson, G. I. Stegeman, “All-optical switching in nonlinear X junctions,” Appl. Phys. Lett. 55, 1176–1178 (1989).
[CrossRef]

IEEE J. Quantum Electron. (3)

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

Y. Chen, “Solution to full coupled wave equations of nonlinear coupled systems,” IEEE J. Quantum Electron. 25, 2149–2153 (1989).
[CrossRef]

G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron. 28, 363–370 (1992).
[CrossRef]

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

Opt. Commun. (1)

G. J. Liu, B. M. Liang, Q. Li, G. L. Jin, “Multiple coupling length nonlinear directional couplers with variable coupling coefficient,” Opt. Commun. 218, 113–117 (2003).
[CrossRef]

Opt. Lett. (4)

Opt. Quantum Electron. (2)

G. I. Stegeman, E. M. Wright, “All-optical waveguide switching,” Opt. Quantum Electron. 22, 95–122 (1990).
[CrossRef]

F. Farjady, M. G. F. Wilson, P. M. Radmore, “Matrix coupled mode theory model of strongly-coupled multiwaveguide optical nonlinear directional couplers,” Opt. Quantum Electron. 33, 173–188 (2001).
[CrossRef]

Other (3)

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, 1995), pp. 42–43.

G. J. Liu, B. M. Liang, Q. Li, G. L. Jin, “Switching characteristics of variable coupling coefficient nonlinear directional coupler,” IEEE. J. Lightwave Technol., submitted for publication.

Amnon Yariv and Pochi Yeh, Optical Waves in Crystals (Wiley, New York, 1984, pp. 459–469.

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 (5)

Fig. 1
Fig. 1

Sketch of an arc-shaped waveguide.

Fig. 2
Fig. 2

Transmission characteristic of one-coupling-length Gaussian VCC NLDC(Δnsn0 ≈ 6%).

Fig. 3
Fig. 3

Transmission characteristic of one-coupling-length Gaussian VCC NLDC(Δnsn0 ≈ 13%).

Fig. 4
Fig. 4

Transmission characteristic of one-coupling-length Gaussian VCC NLDC (Δnsn0 ≈ 40%).

Fig. 5
Fig. 5

Transmission characteristic of multiple-coupling-length Gaussian VCC NLDC (high nonlinearity): (a) the simulation results of the CMM and the BPM of the device on self-focusing material; (b) the simulation results of the CMM and BPM of the device on self-defocusing material.

Equations (11)

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

κz=κ0 exp-z2/b2,
-iz a1=κza2+γ|a1|2a1,
-iz a2=κza1+γ|a2|2a2,
κ=2k2p exp-psβt+2/pk2+p2,
β=k0neff, k=nf2k02-β2, p=β2-ns2k02,
κ=A exp-ps,
A=2k2pβt+2/pk2+p2.
R=pb2,
s0=lnA/κ0/p.
Aeff= ξx, y2dxdy2 |ξx, Y|4dxdy,
Aeff= ξx2 dx2 |ξx|4 dx h.

Metrics