Abstract

Propagation in a nonlinear coupler at a specified input power is like that in a linear coupler with a specified but nonsinusoidal periodic refractive index. This suggests novel schemes for reducing the switching power and leads to simple analytical expressions for ideal switches and for power-sensitive polarization beam splitters. Most importantly, we show that the critical power is reduced significantly by “freezing” a nonsinusoidal refractive index into the basic linear structure that mimics the nonlinear index above the critical power, thus biasing the nonlinear coupler.

© 1989 Optical Society of America

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References

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  1. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983), pp. 387–399, 568–574.
  2. A. W. Snyder, A. Ankiewicz, IEEE J. Lightwave Technol. LT-6, 463 (1988).
    [CrossRef]
  3. A. W. Snyder, J. Opt. Soc. Am. 62, 1267 (1972).
    [CrossRef]
  4. S. M. Jensen, IEEE Trans. Microwave Theory Tech. MTT-1, 1568 (1982).
    [CrossRef]
  5. B. Daino, G. Gregori, S. Wabnitz, J. Appl. Phys. 58, 4512 (1985).
    [CrossRef]
  6. Y. Silberberg, G. I. Stegeman, Appl. Phys. Lett. 50, 801 (1987).
    [CrossRef]
  7. A. Ankiewicz, Opt. Quantum Electron. 20, 329 (1988).
    [CrossRef]
  8. C. M. Bender, S. A. Orszag, Advanced Mathematical Methods For Scientists and Engineers (McGraw-Hill, New York, 1978).
  9. A. Ankiewicz, A. W. Snyder, X. Zheng, IEEE J. Lightwave Technol. LT-4, 1317 (1986).
    [CrossRef]
  10. A. W. Snyder, A. J. Stevenson, Opt. Lett. 11, 254 (1986).
    [CrossRef] [PubMed]

1988

A. W. Snyder, A. Ankiewicz, IEEE J. Lightwave Technol. LT-6, 463 (1988).
[CrossRef]

A. Ankiewicz, Opt. Quantum Electron. 20, 329 (1988).
[CrossRef]

1987

Y. Silberberg, G. I. Stegeman, Appl. Phys. Lett. 50, 801 (1987).
[CrossRef]

1986

A. Ankiewicz, A. W. Snyder, X. Zheng, IEEE J. Lightwave Technol. LT-4, 1317 (1986).
[CrossRef]

A. W. Snyder, A. J. Stevenson, Opt. Lett. 11, 254 (1986).
[CrossRef] [PubMed]

1985

B. Daino, G. Gregori, S. Wabnitz, J. Appl. Phys. 58, 4512 (1985).
[CrossRef]

1982

S. M. Jensen, IEEE Trans. Microwave Theory Tech. MTT-1, 1568 (1982).
[CrossRef]

1972

Ankiewicz, A.

A. W. Snyder, A. Ankiewicz, IEEE J. Lightwave Technol. LT-6, 463 (1988).
[CrossRef]

A. Ankiewicz, Opt. Quantum Electron. 20, 329 (1988).
[CrossRef]

A. Ankiewicz, A. W. Snyder, X. Zheng, IEEE J. Lightwave Technol. LT-4, 1317 (1986).
[CrossRef]

Bender, C. M.

C. M. Bender, S. A. Orszag, Advanced Mathematical Methods For Scientists and Engineers (McGraw-Hill, New York, 1978).

Daino, B.

B. Daino, G. Gregori, S. Wabnitz, J. Appl. Phys. 58, 4512 (1985).
[CrossRef]

Gregori, G.

B. Daino, G. Gregori, S. Wabnitz, J. Appl. Phys. 58, 4512 (1985).
[CrossRef]

Jensen, S. M.

S. M. Jensen, IEEE Trans. Microwave Theory Tech. MTT-1, 1568 (1982).
[CrossRef]

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983), pp. 387–399, 568–574.

Orszag, S. A.

C. M. Bender, S. A. Orszag, Advanced Mathematical Methods For Scientists and Engineers (McGraw-Hill, New York, 1978).

Silberberg, Y.

Y. Silberberg, G. I. Stegeman, Appl. Phys. Lett. 50, 801 (1987).
[CrossRef]

Snyder, A. W.

A. W. Snyder, A. Ankiewicz, IEEE J. Lightwave Technol. LT-6, 463 (1988).
[CrossRef]

A. Ankiewicz, A. W. Snyder, X. Zheng, IEEE J. Lightwave Technol. LT-4, 1317 (1986).
[CrossRef]

A. W. Snyder, A. J. Stevenson, Opt. Lett. 11, 254 (1986).
[CrossRef] [PubMed]

A. W. Snyder, J. Opt. Soc. Am. 62, 1267 (1972).
[CrossRef]

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983), pp. 387–399, 568–574.

Stegeman, G. I.

Y. Silberberg, G. I. Stegeman, Appl. Phys. Lett. 50, 801 (1987).
[CrossRef]

Stevenson, A. J.

Wabnitz, S.

B. Daino, G. Gregori, S. Wabnitz, J. Appl. Phys. 58, 4512 (1985).
[CrossRef]

Zheng, X.

A. Ankiewicz, A. W. Snyder, X. Zheng, IEEE J. Lightwave Technol. LT-4, 1317 (1986).
[CrossRef]

Appl. Phys. Lett.

Y. Silberberg, G. I. Stegeman, Appl. Phys. Lett. 50, 801 (1987).
[CrossRef]

IEEE J. Lightwave Technol.

A. Ankiewicz, A. W. Snyder, X. Zheng, IEEE J. Lightwave Technol. LT-4, 1317 (1986).
[CrossRef]

A. W. Snyder, A. Ankiewicz, IEEE J. Lightwave Technol. LT-6, 463 (1988).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

S. M. Jensen, IEEE Trans. Microwave Theory Tech. MTT-1, 1568 (1982).
[CrossRef]

J. Appl. Phys.

B. Daino, G. Gregori, S. Wabnitz, J. Appl. Phys. 58, 4512 (1985).
[CrossRef]

J. Opt. Soc. Am.

Opt. Lett.

Opt. Quantum Electron.

A. Ankiewicz, Opt. Quantum Electron. 20, 329 (1988).
[CrossRef]

Other

C. M. Bender, S. A. Orszag, Advanced Mathematical Methods For Scientists and Engineers (McGraw-Hill, New York, 1978).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983), pp. 387–399, 568–574.

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Figures (3)

Fig 1
Fig 1

(a) Physical characteristics of the coupler and input conditions. (b) The variation of power along the length of core 1 for three different input powers. (c) The output of core 1 as a function of the input power. The linear couplers have complete power transfer in a length Lc.

Fig. 2
Fig. 2

Physical parameters of dual-core fibers necessary to realize the nonlinear switch of Fig. 1(c) at P1(0) = 1.5Pc for a specified input power. For the fused quartz the Kerr constant κ = 3.16 × 10−20I m2/W. The upper horizontal scale gives the change in refractive index δn(0) caused by the input power relative to the core–cladding index difference, nconcl. The waveguide parameter V ≃ 2.4.

Fig. 3
Fig. 3

Output of core 1 as a function of the input power for the freezing-in strategy and for the conventional nonlinear coupler. In both cases the coupler length is 7Lc, where Lc is the minimum length required for complete power transfer at low power.

Equations (10)

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P 1 ( z ) = P 1 ( 0 ) [ 1 - F 2 sin 2 ( C z / F ) ] ,
F = [ 1 + ( β 1 - β 2 ) 2 / 4 C 2 ] - 1 / 2 ,
P 1 ( 0 ) P c = δ β NL ( 0 ) 4 C .
P 1 ( L ¯ ) P 1 ( 0 ) 1 - P c 2 4 P 1 2 ( 0 ) sin 2 [ q π P 1 ( 0 ) P c ] ,
a 1 = i ( β 1 + C 11 ) a 1 = C ¯ 21 a 2 ,
a 2 = i ( β 2 + C 22 ) a 2 = C ¯ 12 a 1 ,
C ¯ p q ( z ) = C p q ( z ) - N 12 C p p ( z ) ,
C p q ( z ) = k A [ n ( x , y , z ) - n p ] ψ p ψ q d A ,
P 1 ( z ) = P 1 ( 0 ) cos 2 ( π z / 2 L ) ,
L = π 2 C [ 1 + ( 3 N - 4 α ) P 1 ( 0 ) P c ] ,

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