Abstract

We examine coupled-mode theory in the very-weak-coupling limit and show that in multiwaveguide systems with dissimilar waveguides the overlap integrals of the recent, more-sophisticated theory should be included to ensure accurate solutions. Using the old theory in this limit may lead to errors reaching 100% in calculated coupling length.

© 1988 Optical Society of America

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Corrections

Amos Hardy, William Streifer, and Marek Osinski, "Weak coupling of parallel waveguides: erratum," Opt. Lett. 13, 428-428 (1988)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-13-5-428

References

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  1. D. Marcuse, Light Transmission Optics (Van Nostrand, New York, 1972).
  2. H. F. Taylor, A. Yariv, Proc. IEE 62, 1044 (1974).
    [CrossRef]
  3. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983), pp. 570ff.
  4. J. K. Butler, D. E. Ackley, D. Botez, Appl. Phys. Lett. 44, 293 (1984); Erratum, Appl. Phys. Lett. 44, 935 (1984).
    [CrossRef]
  5. E. Kapon, J. Katz, A. Yariv, Opt. Lett. 9, 125 (1984); Erratum, Opt. Lett. 9, 318 (1984).
    [CrossRef] [PubMed]
  6. L. A. Molter-Orr, H. A. Haus, Appl. Opt. 24, 1260 (1985).
    [CrossRef] [PubMed]
  7. A. Hardy, W. Streifer, Opt. Lett. 10, 335 (1985).
    [CrossRef] [PubMed]
  8. A. Hardy, W. Streifer, IEEE J. Lightwave Technol. LT-3, 1135 (1985).
    [CrossRef]
  9. A. Hardy, W. Streifer, IEEE J. Lightwave Technol. LT-4, 90 (1986).
    [CrossRef]
  10. E. Marcatili, IEEE J. Quantum Electron. QE-22, 988 (1986).
    [CrossRef]
  11. E. A. J. Marcatili, L. L. Buhl, R. C. Alferness, Appl. Phys. Lett. 49, 1692 (1986).
    [CrossRef]
  12. W. Streifer, M. Osinski, A. Hardy, IEEE J. Lightwave Technol. LT-5, 1 (1987).
    [CrossRef]
  13. S.-L. Chuang, IEEE J. Lightwave Technol. LT-5, 5 (1987).
    [CrossRef]
  14. H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, IEEE J. Lightwave Technol. LT-5, 16 (1987).
    [CrossRef]
  15. S.-L. Chuang, IEEE J. Lightwave Technol. LT-5, 174 (1987).
    [CrossRef]
  16. A. Hardy, W. Streifer, IEEE J. Quantum Electron. QE-22, 528 (1986).
    [CrossRef]
  17. The elements of the third row of Eq. (12b) of Ref. 16 should read (ψ − ϕ + 2m22)/4ψ rather than (ψ − ϕ − 2m22)/4ψ as printed.

1987 (4)

W. Streifer, M. Osinski, A. Hardy, IEEE J. Lightwave Technol. LT-5, 1 (1987).
[CrossRef]

S.-L. Chuang, IEEE J. Lightwave Technol. LT-5, 5 (1987).
[CrossRef]

H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, IEEE J. Lightwave Technol. LT-5, 16 (1987).
[CrossRef]

S.-L. Chuang, IEEE J. Lightwave Technol. LT-5, 174 (1987).
[CrossRef]

1986 (4)

A. Hardy, W. Streifer, IEEE J. Quantum Electron. QE-22, 528 (1986).
[CrossRef]

A. Hardy, W. Streifer, IEEE J. Lightwave Technol. LT-4, 90 (1986).
[CrossRef]

E. Marcatili, IEEE J. Quantum Electron. QE-22, 988 (1986).
[CrossRef]

E. A. J. Marcatili, L. L. Buhl, R. C. Alferness, Appl. Phys. Lett. 49, 1692 (1986).
[CrossRef]

1985 (3)

1984 (2)

J. K. Butler, D. E. Ackley, D. Botez, Appl. Phys. Lett. 44, 293 (1984); Erratum, Appl. Phys. Lett. 44, 935 (1984).
[CrossRef]

E. Kapon, J. Katz, A. Yariv, Opt. Lett. 9, 125 (1984); Erratum, Opt. Lett. 9, 318 (1984).
[CrossRef] [PubMed]

1974 (1)

H. F. Taylor, A. Yariv, Proc. IEE 62, 1044 (1974).
[CrossRef]

Ackley, D. E.

J. K. Butler, D. E. Ackley, D. Botez, Appl. Phys. Lett. 44, 293 (1984); Erratum, Appl. Phys. Lett. 44, 935 (1984).
[CrossRef]

Alferness, R. C.

E. A. J. Marcatili, L. L. Buhl, R. C. Alferness, Appl. Phys. Lett. 49, 1692 (1986).
[CrossRef]

Botez, D.

J. K. Butler, D. E. Ackley, D. Botez, Appl. Phys. Lett. 44, 293 (1984); Erratum, Appl. Phys. Lett. 44, 935 (1984).
[CrossRef]

Buhl, L. L.

E. A. J. Marcatili, L. L. Buhl, R. C. Alferness, Appl. Phys. Lett. 49, 1692 (1986).
[CrossRef]

Butler, J. K.

J. K. Butler, D. E. Ackley, D. Botez, Appl. Phys. Lett. 44, 293 (1984); Erratum, Appl. Phys. Lett. 44, 935 (1984).
[CrossRef]

Chuang, S.-L.

S.-L. Chuang, IEEE J. Lightwave Technol. LT-5, 5 (1987).
[CrossRef]

S.-L. Chuang, IEEE J. Lightwave Technol. LT-5, 174 (1987).
[CrossRef]

Hardy, A.

W. Streifer, M. Osinski, A. Hardy, IEEE J. Lightwave Technol. LT-5, 1 (1987).
[CrossRef]

A. Hardy, W. Streifer, IEEE J. Quantum Electron. QE-22, 528 (1986).
[CrossRef]

A. Hardy, W. Streifer, IEEE J. Lightwave Technol. LT-4, 90 (1986).
[CrossRef]

A. Hardy, W. Streifer, IEEE J. Lightwave Technol. LT-3, 1135 (1985).
[CrossRef]

A. Hardy, W. Streifer, Opt. Lett. 10, 335 (1985).
[CrossRef] [PubMed]

Haus, H. A.

H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, IEEE J. Lightwave Technol. LT-5, 16 (1987).
[CrossRef]

L. A. Molter-Orr, H. A. Haus, Appl. Opt. 24, 1260 (1985).
[CrossRef] [PubMed]

Huang, W. P.

H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, IEEE J. Lightwave Technol. LT-5, 16 (1987).
[CrossRef]

Kapon, E.

Katz, J.

Kawakami, S.

H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, IEEE J. Lightwave Technol. LT-5, 16 (1987).
[CrossRef]

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983), pp. 570ff.

Marcatili, E.

E. Marcatili, IEEE J. Quantum Electron. QE-22, 988 (1986).
[CrossRef]

Marcatili, E. A. J.

E. A. J. Marcatili, L. L. Buhl, R. C. Alferness, Appl. Phys. Lett. 49, 1692 (1986).
[CrossRef]

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van Nostrand, New York, 1972).

Molter-Orr, L. A.

Osinski, M.

W. Streifer, M. Osinski, A. Hardy, IEEE J. Lightwave Technol. LT-5, 1 (1987).
[CrossRef]

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983), pp. 570ff.

Streifer, W.

W. Streifer, M. Osinski, A. Hardy, IEEE J. Lightwave Technol. LT-5, 1 (1987).
[CrossRef]

A. Hardy, W. Streifer, IEEE J. Quantum Electron. QE-22, 528 (1986).
[CrossRef]

A. Hardy, W. Streifer, IEEE J. Lightwave Technol. LT-4, 90 (1986).
[CrossRef]

A. Hardy, W. Streifer, IEEE J. Lightwave Technol. LT-3, 1135 (1985).
[CrossRef]

A. Hardy, W. Streifer, Opt. Lett. 10, 335 (1985).
[CrossRef] [PubMed]

Taylor, H. F.

H. F. Taylor, A. Yariv, Proc. IEE 62, 1044 (1974).
[CrossRef]

Whitaker, N. A.

H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, IEEE J. Lightwave Technol. LT-5, 16 (1987).
[CrossRef]

Yariv, A.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

J. K. Butler, D. E. Ackley, D. Botez, Appl. Phys. Lett. 44, 293 (1984); Erratum, Appl. Phys. Lett. 44, 935 (1984).
[CrossRef]

E. A. J. Marcatili, L. L. Buhl, R. C. Alferness, Appl. Phys. Lett. 49, 1692 (1986).
[CrossRef]

IEEE J. Lightwave Technol. (6)

W. Streifer, M. Osinski, A. Hardy, IEEE J. Lightwave Technol. LT-5, 1 (1987).
[CrossRef]

S.-L. Chuang, IEEE J. Lightwave Technol. LT-5, 5 (1987).
[CrossRef]

H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, IEEE J. Lightwave Technol. LT-5, 16 (1987).
[CrossRef]

S.-L. Chuang, IEEE J. Lightwave Technol. LT-5, 174 (1987).
[CrossRef]

A. Hardy, W. Streifer, IEEE J. Lightwave Technol. LT-3, 1135 (1985).
[CrossRef]

A. Hardy, W. Streifer, IEEE J. Lightwave Technol. LT-4, 90 (1986).
[CrossRef]

IEEE J. Quantum Electron. (2)

E. Marcatili, IEEE J. Quantum Electron. QE-22, 988 (1986).
[CrossRef]

A. Hardy, W. Streifer, IEEE J. Quantum Electron. QE-22, 528 (1986).
[CrossRef]

Opt. Lett. (2)

Proc. IEE (1)

H. F. Taylor, A. Yariv, Proc. IEE 62, 1044 (1974).
[CrossRef]

Other (3)

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983), pp. 570ff.

The elements of the third row of Eq. (12b) of Ref. 16 should read (ψ − ϕ + 2m22)/4ψ rather than (ψ − ϕ − 2m22)/4ψ as printed.

D. Marcuse, Light Transmission Optics (Van Nostrand, New York, 1972).

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Figures (2)

Fig. 1
Fig. 1

Schematic diagram of a three-waveguide coupler.

Fig. 2
Fig. 2

Field amplitude distribution for array modes of a three-waveguide system in the very-weak-coupling limit. The waveguide parameters are the same as in the example given in the text.

Equations (15)

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

E t ( x , y , z ) = m = 1 N u m ( z ) E t ( m ) ( x , y ) ,
d U d z = i ( P 1 B P + P 1 K ˜ ) U ,
d U d z = i ( B + P 1 K ) U .
p m q = z ˆ · [ E t ( q ) × H t ( m ) + E t ( m ) × H t ( q ) ] d x d y ,
κ m q = ω Δ ( q ) [ E t ( m ) E t ( q ) ( m ) 0 n 2 E z ( m ) E z ( q ) ] d x d y ,
Δ ( q ) ( x , y ) = 0 n 2 ( x , y ) ( q ) ( x , y )
( p 1 K ) 12 = κ 21 + p 12 [ β ( 1 ) β ( 2 ) ] p 12 κ 22 1 p 12 2 = κ 12 p 12 κ 22 1 p 12 2 ,
( P 1 K ) 12 = κ 12 ,
( P 1 K ) 21 = κ 21 ,
β ( 1 ) = β ( 3 ) , β ( 2 ) , zeroth order ,
κ 12 = κ 32 , κ 21 = κ 23 , p 12 = p 23 , first order ,
κ 13 = κ 31 , κ 11 = κ 33 , κ 22 , p 13 , second order ,
P 1 K = [ κ 11 p 12 κ 21 κ 12 κ 13 p 12 κ 21 κ 21 κ 22 2 p 12 κ 12 κ 21 κ 13 p 12 κ 21 κ 12 κ 11 p 12 κ 21 ] ,
σ 1 σ 2 2 κ 13 2 p 12 κ 21 + 2 κ 12 κ 21 β ( 1 ) β ( 2 )
σ 2 σ 3 β ( 1 ) β ( 2 ) .

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