Abstract

Poynting’s vector theorem describes power flow on twin-core couplers with arbitrary axial perturbations, both linear and nonlinear. This bypasses the coupled amplitude formulation and unifies nonlinear two-mode interactions in general.

© 1989 Optical Society of America

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References

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  1. S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
    [CrossRef]
  2. B. Daino, G. Gregori, S. Wabnitz, J. Appl. Phys. 58, 4512 (1985).
    [CrossRef]
  3. Y. Silverberg, G. I. Stegeman, Appl. Phys. Lett. 61, 1135 (1987).
  4. A. W. Snyder, W. Young, J. Opt. Soc. Am. 68, 297 (1978).
    [CrossRef]
  5. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  6. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).
  7. A. W. Snyder, Y. Chen, A. Ankiewicz, IEEE J. Lightwave Technol. 7, 1400 (1989).
    [CrossRef]
  8. R. Ulrich, Opt. Lett. 1, 109 (1977).
    [CrossRef] [PubMed]
  9. N. Minorsky, Nonlinear Oscillations (Van Nostrand, Princeton, N.J., 1962).
  10. A. W. Snyder, D. J. Mitchell, in Digest of Conference on Nonlinear Guided- Wave Phenomena (Optical Society of America, Washington, D.C., 1989), paper PD2.
  11. D. J. Mitchell, A. W. Snyder, Opt. Lett. 14, 1143 (1989).
    [CrossRef] [PubMed]

1989 (2)

A. W. Snyder, Y. Chen, A. Ankiewicz, IEEE J. Lightwave Technol. 7, 1400 (1989).
[CrossRef]

D. J. Mitchell, A. W. Snyder, Opt. Lett. 14, 1143 (1989).
[CrossRef] [PubMed]

1987 (1)

Y. Silverberg, G. I. Stegeman, Appl. Phys. Lett. 61, 1135 (1987).

1985 (1)

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

1982 (1)

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
[CrossRef]

1978 (1)

1977 (1)

Ankiewicz, A.

A. W. Snyder, Y. Chen, A. Ankiewicz, IEEE J. Lightwave Technol. 7, 1400 (1989).
[CrossRef]

Chen, Y.

A. W. Snyder, Y. Chen, A. Ankiewicz, IEEE J. Lightwave Technol. 7, 1400 (1989).
[CrossRef]

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]

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).

Jensen, S. M.

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
[CrossRef]

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Minorsky, N.

N. Minorsky, Nonlinear Oscillations (Van Nostrand, Princeton, N.J., 1962).

Mitchell, D. J.

D. J. Mitchell, A. W. Snyder, Opt. Lett. 14, 1143 (1989).
[CrossRef] [PubMed]

A. W. Snyder, D. J. Mitchell, in Digest of Conference on Nonlinear Guided- Wave Phenomena (Optical Society of America, Washington, D.C., 1989), paper PD2.

Silverberg, Y.

Y. Silverberg, G. I. Stegeman, Appl. Phys. Lett. 61, 1135 (1987).

Snyder, A. W.

A. W. Snyder, Y. Chen, A. Ankiewicz, IEEE J. Lightwave Technol. 7, 1400 (1989).
[CrossRef]

D. J. Mitchell, A. W. Snyder, Opt. Lett. 14, 1143 (1989).
[CrossRef] [PubMed]

A. W. Snyder, W. Young, J. Opt. Soc. Am. 68, 297 (1978).
[CrossRef]

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

A. W. Snyder, D. J. Mitchell, in Digest of Conference on Nonlinear Guided- Wave Phenomena (Optical Society of America, Washington, D.C., 1989), paper PD2.

Stegeman, G. I.

Y. Silverberg, G. I. Stegeman, Appl. Phys. Lett. 61, 1135 (1987).

Ulrich, R.

Wabnitz, S.

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

Young, W.

Appl. Phys. Lett. (1)

Y. Silverberg, G. I. Stegeman, Appl. Phys. Lett. 61, 1135 (1987).

IEEE J. Lightwave Technol. (1)

A. W. Snyder, Y. Chen, A. Ankiewicz, IEEE J. Lightwave Technol. 7, 1400 (1989).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
[CrossRef]

J. Appl. Phys. (1)

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

J. Opt. Soc. Am. (1)

Opt. Lett. (2)

Other (4)

N. Minorsky, Nonlinear Oscillations (Van Nostrand, Princeton, N.J., 1962).

A. W. Snyder, D. J. Mitchell, in Digest of Conference on Nonlinear Guided- Wave Phenomena (Optical Society of America, Washington, D.C., 1989), paper PD2.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).

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Equations (24)

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E ( x , y , z ) = a 1 ( z ) ψ 1 ( x , y ) + a 2 ( z ) ψ 2 ( x , y ) ,
J 2 ( x , y , z ) = i 2 k ( n cl n 1 ) E 2 ( x , y , z ) ,
P ˙ 1 ( z ) = Re A 2 J 2 E 1 * d A = C S 3 ( z ) ,
S 3 ( z ) = 2 [ P 1 ( z ) P 2 ( z ) ] 1 / 2 sin ϕ 12 ( z ) ,
C = k ( n ¯ 1 n ¯ cl ) A co ψ 1 ψ 2 d A .
E ( x , y , z ) = a + ( z ) ψ + ( x , y ) + a ( z ) ψ ( x , y ) ,
J ( x , y , z ) = i 2 k [ n ¯ ( x , y ) n ( x , y , z ) ] E ( x , y , z ) ,
P ˙ + = Re A J E + * d A ,
2 Im ( a a + * ) = S 3 ( z ) ,
2 P ± = P ± 2 ( P 1 P 2 ) 1 / 2 cos ϕ 12 ( z ) ,
P ˙ + ( z ) = 1 2 [ β 1 ( z ) β 2 ( z ) ] S 3 ( z ) ,
β i ( z ) = β ¯ + k A [ n i ( x , y , z ) n ¯ i ( x , y ) ] ψ i 2 d A ,
S 1 ( z ) = P 1 P 2 = 2 ( P + P ) 1 / 2 cos ϕ ,
S 2 ( z ) = 2 ( P 1 P 2 ) 1 / 2 cos ϕ 12 = P + P ,
S 1 2 ( z ) + S 2 2 ( z ) + S 3 2 ( z ) = P 2 .
S ˙ 1 ( z ) = ( β + β ) S 3 ( z ) ,
S ˙ 2 ( z ) = [ β 1 ( z ) β 2 ( z ) ] S 3 ( z ) .
S ˙ 3 ( z ) = ( β + β ) S 1 ( z ) + [ β 1 ( z ) β 2 ( z ) ] S 2 ( z ) .
γ ( S 1 ) + S 2 = Γ ,
γ ( S 1 ) = 0 S 1 [ β 1 ( S 1 ) β 2 ( S 1 ) ] β + β d S 1 ,
S 1 S 2 = β 1 ( S 1 ) β 2 ( S 1 ) β + β .
z p = d S 1 S ˙ 1 = 1 C min S 1 max S 1 d S 1 S 3 ,
S 3 2 = P 2 S 1 2 [ Γ γ ( S 1 ) ] 2 ,
S ¨ 1 + 2 C [ β 1 ( S 1 ) β 2 ( S 1 ) ] [ γ ( S 1 ) Γ ] + 4 C 2 S 1 = 0 ,

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