Abstract

We point out some inconsistencies in the usual coupled-mode formulation employed to model the nonlinear behavior of symmetric directional couplers. In particular, we show that special care is required when neglecting some of the nonlinear terms in the equations.

© 1990 Optical Society of America

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References

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  1. G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, C. T. Seaton, “Third Order Nonlinear Integrated Optics,” lEEE/OSA J. Lightwave Technol. LT-6, 953–970 (1988).
    [CrossRef]
  2. S. M. Jensen, “The Nonlinear Coherent Coupler,” IEEE J. Quantum Electron. QE-18, 1580–1583 (1982).
    [CrossRef]
  3. A. Ankiewicz, “Novel Effects in Non-Linear Coupling,” Opt. Quantum Electron. 20, 329–337 (1988) and references therein.
    [CrossRef]
  4. A. Hardy, W. Streifer, “Coupled Mode Theory of Parallel Waveguides,” IEEE/OSA J. Lightwave Technol. LT-3, 1135–1146 (1985).
    [CrossRef]

1988 (2)

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, C. T. Seaton, “Third Order Nonlinear Integrated Optics,” lEEE/OSA J. Lightwave Technol. LT-6, 953–970 (1988).
[CrossRef]

A. Ankiewicz, “Novel Effects in Non-Linear Coupling,” Opt. Quantum Electron. 20, 329–337 (1988) and references therein.
[CrossRef]

1985 (1)

A. Hardy, W. Streifer, “Coupled Mode Theory of Parallel Waveguides,” IEEE/OSA J. Lightwave Technol. LT-3, 1135–1146 (1985).
[CrossRef]

1982 (1)

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

Ankiewicz, A.

A. Ankiewicz, “Novel Effects in Non-Linear Coupling,” Opt. Quantum Electron. 20, 329–337 (1988) and references therein.
[CrossRef]

Finlayson, N.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, C. T. Seaton, “Third Order Nonlinear Integrated Optics,” lEEE/OSA J. Lightwave Technol. LT-6, 953–970 (1988).
[CrossRef]

Hardy, A.

A. Hardy, W. Streifer, “Coupled Mode Theory of Parallel Waveguides,” IEEE/OSA J. Lightwave Technol. LT-3, 1135–1146 (1985).
[CrossRef]

Jensen, S. M.

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

Seaton, C. T.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, C. T. Seaton, “Third Order Nonlinear Integrated Optics,” lEEE/OSA J. Lightwave Technol. LT-6, 953–970 (1988).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, C. T. Seaton, “Third Order Nonlinear Integrated Optics,” lEEE/OSA J. Lightwave Technol. LT-6, 953–970 (1988).
[CrossRef]

Streifer, W.

A. Hardy, W. Streifer, “Coupled Mode Theory of Parallel Waveguides,” IEEE/OSA J. Lightwave Technol. LT-3, 1135–1146 (1985).
[CrossRef]

Wright, E. M.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, C. T. Seaton, “Third Order Nonlinear Integrated Optics,” lEEE/OSA J. Lightwave Technol. LT-6, 953–970 (1988).
[CrossRef]

Zanoni, R.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, C. T. Seaton, “Third Order Nonlinear Integrated Optics,” lEEE/OSA J. Lightwave Technol. LT-6, 953–970 (1988).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

IEEE/OSA J. Lightwave Technol. (1)

A. Hardy, W. Streifer, “Coupled Mode Theory of Parallel Waveguides,” IEEE/OSA J. Lightwave Technol. LT-3, 1135–1146 (1985).
[CrossRef]

lEEE/OSA J. Lightwave Technol. (1)

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, C. T. Seaton, “Third Order Nonlinear Integrated Optics,” lEEE/OSA J. Lightwave Technol. LT-6, 953–970 (1988).
[CrossRef]

Opt. Quantum Electron. (1)

A. Ankiewicz, “Novel Effects in Non-Linear Coupling,” Opt. Quantum Electron. 20, 329–337 (1988) and references therein.
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Power in the input channel vs normalized distance Z. The dashed lines represent the solution in Ref. 2, while the solid lines are obtained from Eqs. (4): Q4 = Q5 = 0.01 · Q3.

Fig. 2
Fig. 2

Same as Fig. 1 but with Q4 = Q5 = 0.1 · Q3.

Equations (9)

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

E ( r ) = A ( z ) exp ( i β z ) · E a ( x , y ) + B ( z ) exp ( i β z ) · E b ( x , y ) ,
- i d a d z = Q 2 b + ( Q 3 a 2 + 2 Q 41 b 2 ) · a + ( Q 52 b 2 + 2 Q 53 a 2 ) · b + Q 42 a * b 2 + Q 51 a 2 b * ,
- i d b d z = R 2 a + ( R 3 b 2 + 2 Q 41 a 2 ) · b + ( R 52 a 2 + 2 R 53 b 2 ) · a + R 42 a 2 b * + R 51 a * b 2 ,
Q 2 = R 2 = ω 0 4 d x d y Δ χ a · E b E a = ω 0 4 d x d y Δ χ b · E a E b ,
Q 3 = R 3 = ω 4 d x d y n 2 · E a 4 = ω 4 d x d y n 2 · E b 4 ,
Q 4 Q 41 = Q 42 = R 42 = ω 4 d x d y n 2 · E a 2 E b 2 ,
Q 5 Q 51 = Q 52 = Q 53 = R 51 = R 52 = R 53 = ω 4 d x d y n 2 · E a 3 · E b = ω 4 d x d y n 2 · E b 3 · E a ,
- i d a d z = Q 2 b + Q 3 a 2 a + Q 4 ( 2 a b 2 + a * b 2 ) + Q 5 ( a 2 b * + b 2 b + 2 a 2 b ) ,
- i d a d z = Q 2 a + Q 3 b 2 b + Q 4 ( 2 b a 2 + b * a 2 ) + Q 5 ( b 2 a * + a 2 a + 2 b 2 a ) .

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