Abstract

We describe the principles underlying the operation of a nonlinear fused-tapered coupler. By analyzing a simplified model, we show that such a coupler may lead to new devices for switching and modulating optical power.

© 1993 Optical Society of America

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References

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  1. S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 1580–1583 (1982).
    [CrossRef]
  2. G. I. Stegeman, C. J. Seaton, A. C. Walker, C. N. Ironside, “Nonlinear directional couplers with integrating nonlinearities,” Opt. Commun. 61, 277–281 (1987).
    [CrossRef]
  3. S. R. Friberg, Y. Silberberg, M. R. Oliver, M. J. Andrejo, M. A. Saifi, P. W. Smith, “Ultrafast all-optical switching in a dual-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135–1136 (1987).
    [CrossRef]
  4. D. J. Mitchell, A. W. Snyder, “Modes of nonlinear couplers: building blocks for physical insight,” Opt. Lett. 14, 1143–1145 (1989).
    [CrossRef] [PubMed]
  5. J. Bures, S. Lacroix, J. Lapierre, “Analyse d'un coupleur bidirectionnel à fibres optiques monomodes fusionées,” Appl. Opt. 22, 1918–1922 (1983).
    [CrossRef] [PubMed]
  6. F. de Fornel, C. M. Ragdale, R. J. Mears, “Analysis of single-mode fused tapered fibre couplers,” Proc. Inst. Electr. Eng. Part H 131, 221–228 (1984).
  7. F. P. Payne, C. D. Hussey, M. S. Yatoki, “Modeling fused single-mode fibre couplers,” Electron. Lett. 21, 461–462 (1985).
  8. D. A. Nolan, “Multiple index passive components,” in Integrated Photonics Research Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 150.
  9. Y. Silberberg, G. I. Stegeman, “Nonlinear coupling of waveguide modes,” Appl. Phys. Lett. 50, 801–803 (1987).
    [CrossRef]
  10. G. I. Stegeman, E. M. Wright, “All-optical waveguide switching,” Opt. Quantum Electron 22, 95–122 (1990).
    [CrossRef]

1990 (1)

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

1989 (1)

1987 (3)

G. I. Stegeman, C. J. Seaton, A. C. Walker, C. N. Ironside, “Nonlinear directional couplers with integrating nonlinearities,” Opt. Commun. 61, 277–281 (1987).
[CrossRef]

S. R. Friberg, Y. Silberberg, M. R. Oliver, M. J. Andrejo, M. A. Saifi, P. W. Smith, “Ultrafast all-optical switching in a dual-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135–1136 (1987).
[CrossRef]

Y. Silberberg, G. I. Stegeman, “Nonlinear coupling of waveguide modes,” Appl. Phys. Lett. 50, 801–803 (1987).
[CrossRef]

1985 (1)

F. P. Payne, C. D. Hussey, M. S. Yatoki, “Modeling fused single-mode fibre couplers,” Electron. Lett. 21, 461–462 (1985).

1984 (1)

F. de Fornel, C. M. Ragdale, R. J. Mears, “Analysis of single-mode fused tapered fibre couplers,” Proc. Inst. Electr. Eng. Part H 131, 221–228 (1984).

1983 (1)

1982 (1)

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

Andrejo, M. J.

S. R. Friberg, Y. Silberberg, M. R. Oliver, M. J. Andrejo, M. A. Saifi, P. W. Smith, “Ultrafast all-optical switching in a dual-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135–1136 (1987).
[CrossRef]

Bures, J.

de Fornel, F.

F. de Fornel, C. M. Ragdale, R. J. Mears, “Analysis of single-mode fused tapered fibre couplers,” Proc. Inst. Electr. Eng. Part H 131, 221–228 (1984).

Friberg, S. R.

S. R. Friberg, Y. Silberberg, M. R. Oliver, M. J. Andrejo, M. A. Saifi, P. W. Smith, “Ultrafast all-optical switching in a dual-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135–1136 (1987).
[CrossRef]

Hussey, C. D.

F. P. Payne, C. D. Hussey, M. S. Yatoki, “Modeling fused single-mode fibre couplers,” Electron. Lett. 21, 461–462 (1985).

Ironside, C. N.

G. I. Stegeman, C. J. Seaton, A. C. Walker, C. N. Ironside, “Nonlinear directional couplers with integrating nonlinearities,” Opt. Commun. 61, 277–281 (1987).
[CrossRef]

Jensen, S. M.

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

Lacroix, S.

Lapierre, J.

Mears, R. J.

F. de Fornel, C. M. Ragdale, R. J. Mears, “Analysis of single-mode fused tapered fibre couplers,” Proc. Inst. Electr. Eng. Part H 131, 221–228 (1984).

Mitchell, D. J.

Nolan, D. A.

D. A. Nolan, “Multiple index passive components,” in Integrated Photonics Research Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 150.

Oliver, M. R.

S. R. Friberg, Y. Silberberg, M. R. Oliver, M. J. Andrejo, M. A. Saifi, P. W. Smith, “Ultrafast all-optical switching in a dual-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135–1136 (1987).
[CrossRef]

Payne, F. P.

F. P. Payne, C. D. Hussey, M. S. Yatoki, “Modeling fused single-mode fibre couplers,” Electron. Lett. 21, 461–462 (1985).

Ragdale, C. M.

F. de Fornel, C. M. Ragdale, R. J. Mears, “Analysis of single-mode fused tapered fibre couplers,” Proc. Inst. Electr. Eng. Part H 131, 221–228 (1984).

Saifi, M. A.

S. R. Friberg, Y. Silberberg, M. R. Oliver, M. J. Andrejo, M. A. Saifi, P. W. Smith, “Ultrafast all-optical switching in a dual-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135–1136 (1987).
[CrossRef]

Seaton, C. J.

G. I. Stegeman, C. J. Seaton, A. C. Walker, C. N. Ironside, “Nonlinear directional couplers with integrating nonlinearities,” Opt. Commun. 61, 277–281 (1987).
[CrossRef]

Silberberg, Y.

S. R. Friberg, Y. Silberberg, M. R. Oliver, M. J. Andrejo, M. A. Saifi, P. W. Smith, “Ultrafast all-optical switching in a dual-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135–1136 (1987).
[CrossRef]

Y. Silberberg, G. I. Stegeman, “Nonlinear coupling of waveguide modes,” Appl. Phys. Lett. 50, 801–803 (1987).
[CrossRef]

Smith, P. W.

S. R. Friberg, Y. Silberberg, M. R. Oliver, M. J. Andrejo, M. A. Saifi, P. W. Smith, “Ultrafast all-optical switching in a dual-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135–1136 (1987).
[CrossRef]

Snyder, A. W.

Stegeman, G. I.

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

Y. Silberberg, G. I. Stegeman, “Nonlinear coupling of waveguide modes,” Appl. Phys. Lett. 50, 801–803 (1987).
[CrossRef]

G. I. Stegeman, C. J. Seaton, A. C. Walker, C. N. Ironside, “Nonlinear directional couplers with integrating nonlinearities,” Opt. Commun. 61, 277–281 (1987).
[CrossRef]

Walker, A. C.

G. I. Stegeman, C. J. Seaton, A. C. Walker, C. N. Ironside, “Nonlinear directional couplers with integrating nonlinearities,” Opt. Commun. 61, 277–281 (1987).
[CrossRef]

Wright, E. M.

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

Yatoki, M. S.

F. P. Payne, C. D. Hussey, M. S. Yatoki, “Modeling fused single-mode fibre couplers,” Electron. Lett. 21, 461–462 (1985).

Appl. Opt. (1)

Appl. Phys. Lett. (2)

S. R. Friberg, Y. Silberberg, M. R. Oliver, M. J. Andrejo, M. A. Saifi, P. W. Smith, “Ultrafast all-optical switching in a dual-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135–1136 (1987).
[CrossRef]

Y. Silberberg, G. I. Stegeman, “Nonlinear coupling of waveguide modes,” Appl. Phys. Lett. 50, 801–803 (1987).
[CrossRef]

Electron. Lett. (1)

F. P. Payne, C. D. Hussey, M. S. Yatoki, “Modeling fused single-mode fibre couplers,” Electron. Lett. 21, 461–462 (1985).

IEEE J. Quantum Electron. (1)

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

Opt. Commun. (1)

G. I. Stegeman, C. J. Seaton, A. C. Walker, C. N. Ironside, “Nonlinear directional couplers with integrating nonlinearities,” Opt. Commun. 61, 277–281 (1987).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron (1)

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

Proc. Inst. Electr. Eng. Part H (1)

F. de Fornel, C. M. Ragdale, R. J. Mears, “Analysis of single-mode fused tapered fibre couplers,” Proc. Inst. Electr. Eng. Part H 131, 221–228 (1984).

Other (1)

D. A. Nolan, “Multiple index passive components,” in Integrated Photonics Research Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 150.

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of the nonlinear fused tapered coupler, (b) cross-section of a special single-mode fiber with an outer cladding made of highly nonlinear material, (c) coupler cross section.

Fig. 2
Fig. 2

Phase ϕ versus normalized distance Z = δβz for different values of normalized power R.

Fig. 3
Fig. 3

Phase-power portrait of the NLFC. Curves are labeled by normalized power ratio R. As the field travels down, coupler P2 and ϕ values trace out the relevant curve.

Fig. 4
Fig. 4

Fraction of output power against normalized input power R for a Z = π coupler.

Equations (9)

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E ( z ) = [ ½ a 1 ψ 1 exp ( i β 1 z ) + ½ a 2 ψ 2 exp ( i β 2 z ) ] × exp ( i ω t ) x ̂ + c . c . ,
E ( z ) = ½ A [ ψ 1 + ψ 2 exp ( i δ β z ) ] exp [ i ( β 1 z ω t ) ] x ̂ + c . c ,
E ( z ) = ½ { | a 1 ( z ) | ψ 1 + | a 2 ( z ) | ψ 2 exp [ i ϕ ( z ) ] } × exp { i [ β 1 z ω t + ϕ 1 ( z ) ] } x ̂ + c . c ,
ϕ ( z ) = δ β z + ϕ 1 ( z ) ϕ 2 ( z ) .
ψ 1 ( x , y ) = N 1 cos ( π x / 2 a ) cos ( π y / 2 b ) , ψ 2 ( x , y ) = N 2 sin ( π x / a ) cos ( π y / 2 b ) .
d a 1 d z = i C NL × [ | a 1 | 2 a 1 + 4 / 3 | a 2 | 2 a 1 + a 1 * a 2 2 exp ( i 2 δ β z ) ] , d a 2 d z = i C NL × [ | a 2 | 2 a 2 + 4 / 3 | a 1 | 2 a 2 + a 2 * a 1 2 exp ( i 2 δ β z ) ] ,
d u d z = 4 / 3 u υ sin ( 2 ϕ ) = d υ d z , d ϕ d z = δ β ( u υ ) [ 1 + 2 cos ( 2 ϕ ) ] ,
H = 4 u υ [ 1 + 2 cos ( 2 ϕ ) ] + 6 δ β ( u υ ) = 3 p 2 ,
P 4 P = 1 2 ( P 1 P 2 P 2 ) 1 / 2 cos ϕ .

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