Abstract

Vector coupled-mode theory is extended beyond the conventional first-order treatment. Good results are obtained from the extended theory in the case of waveguides with large index discontinuity.

© 1989 Optical Society of America

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References

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  1. A. Hardy, W. Streifer, IEEE J. Lightwave Technol. LT-3, 1135 (1985).
    [CrossRef]
  2. J. R. Qian, Electron. Lett. 22, 304 (1986).
    [CrossRef]
  3. A. Ankiewicz, A. W. Snyder, Z. H. Zheng, IEEE J. Lightwave Technol. LT-4, 1317 (1986).
    [CrossRef]
  4. H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, IEEE J. Lightwave Technol. LT-5, 16 (1987).
    [CrossRef]
  5. S.-L. Chuang, IEEE J. Lightwave Technol. LT-5, 5 (1987).
    [CrossRef]
  6. A. W. Snyder, A. Ankiewicz, IEEE J. Lightwave Technol. LT-6, 463 (1988).
    [CrossRef]
  7. A. W. Snyder, A. Ankiewicz, Electron. Lett. 22, 1237 (1986).
    [CrossRef]
  8. A. W. Snyder, A. Ankiewicz, A. Altintas, Electron. Lett. 23, 1097 (1987).
    [CrossRef]
  9. A. W. Snyder, W. R. Young, J. Opt. Soc. Am. 68, 297 (1978).
    [CrossRef]
  10. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 14 and 18.
  11. H. A. Haus, W. P. Huang, N. A. Whitaker, IEEE J. Lightwave Technol. LT-5, 1748 (1987).
    [CrossRef]
  12. A. W. Snyder, A. Ankiewicz, A. Altintas, Electron. Lett. 22, 720 (1988).
    [CrossRef]
  13. W. Streifer, Electron. Lett. 22, 718 (1988).
    [CrossRef]
  14. V. C. Vassallo, IEEE J. Lightwave Technol. 6, 294 (1988).
    [CrossRef]

1988 (4)

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

A. W. Snyder, A. Ankiewicz, A. Altintas, Electron. Lett. 22, 720 (1988).
[CrossRef]

W. Streifer, Electron. Lett. 22, 718 (1988).
[CrossRef]

V. C. Vassallo, IEEE J. Lightwave Technol. 6, 294 (1988).
[CrossRef]

1987 (4)

A. W. Snyder, A. Ankiewicz, A. Altintas, Electron. Lett. 23, 1097 (1987).
[CrossRef]

H. A. Haus, W. P. Huang, N. A. Whitaker, IEEE J. Lightwave Technol. LT-5, 1748 (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, 5 (1987).
[CrossRef]

1986 (3)

J. R. Qian, Electron. Lett. 22, 304 (1986).
[CrossRef]

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

A. W. Snyder, A. Ankiewicz, Electron. Lett. 22, 1237 (1986).
[CrossRef]

1985 (1)

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

1978 (1)

Altintas, A.

A. W. Snyder, A. Ankiewicz, A. Altintas, Electron. Lett. 22, 720 (1988).
[CrossRef]

A. W. Snyder, A. Ankiewicz, A. Altintas, Electron. Lett. 23, 1097 (1987).
[CrossRef]

Ankiewicz, A.

A. W. Snyder, A. Ankiewicz, A. Altintas, Electron. Lett. 22, 720 (1988).
[CrossRef]

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

A. W. Snyder, A. Ankiewicz, A. Altintas, Electron. Lett. 23, 1097 (1987).
[CrossRef]

A. W. Snyder, A. Ankiewicz, Electron. Lett. 22, 1237 (1986).
[CrossRef]

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

Chuang, S.-L.

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

Hardy, A.

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

Haus, H. A.

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

H. A. Haus, W. P. Huang, N. A. Whitaker, IEEE J. Lightwave Technol. LT-5, 1748 (1987).
[CrossRef]

Huang, W. P.

H. A. Haus, W. P. Huang, N. A. Whitaker, IEEE J. Lightwave Technol. LT-5, 1748 (1987).
[CrossRef]

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

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 & Hall, London, 1983), Chaps. 14 and 18.

Qian, J. R.

J. R. Qian, Electron. Lett. 22, 304 (1986).
[CrossRef]

Snyder, A. W.

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

A. W. Snyder, A. Ankiewicz, A. Altintas, Electron. Lett. 22, 720 (1988).
[CrossRef]

A. W. Snyder, A. Ankiewicz, A. Altintas, Electron. Lett. 23, 1097 (1987).
[CrossRef]

A. W. Snyder, A. Ankiewicz, Electron. Lett. 22, 1237 (1986).
[CrossRef]

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

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

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 14 and 18.

Streifer, W.

W. Streifer, Electron. Lett. 22, 718 (1988).
[CrossRef]

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

Vassallo, V. C.

V. C. Vassallo, IEEE J. Lightwave Technol. 6, 294 (1988).
[CrossRef]

Whitaker, N. A.

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

H. A. Haus, W. P. Huang, N. A. Whitaker, IEEE J. Lightwave Technol. LT-5, 1748 (1987).
[CrossRef]

Young, W. R.

Zheng, Z. H.

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

Electron. Lett. (5)

J. R. Qian, Electron. Lett. 22, 304 (1986).
[CrossRef]

A. W. Snyder, A. Ankiewicz, Electron. Lett. 22, 1237 (1986).
[CrossRef]

A. W. Snyder, A. Ankiewicz, A. Altintas, Electron. Lett. 23, 1097 (1987).
[CrossRef]

A. W. Snyder, A. Ankiewicz, A. Altintas, Electron. Lett. 22, 720 (1988).
[CrossRef]

W. Streifer, Electron. Lett. 22, 718 (1988).
[CrossRef]

IEEE J. Lightwave Technol. (7)

V. C. Vassallo, IEEE J. Lightwave Technol. 6, 294 (1988).
[CrossRef]

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

H. A. Haus, W. P. Huang, N. A. Whitaker, IEEE J. Lightwave Technol. LT-5, 1748 (1987).
[CrossRef]

A. Ankiewicz, A. W. Snyder, Z. H. Zheng, IEEE J. Lightwave Technol. LT-4, 1317 (1986).
[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, 5 (1987).
[CrossRef]

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

J. Opt. Soc. Am. (1)

Other (1)

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 14 and 18.

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Figures (2)

Fig. 1
Fig. 1

Error for the TM mode. Percentage errors in β+β are shown, where β+ and β are the propagation constants of the even and odd normal modes, respectively. The waveguide parameter V is chosen to be V = 1, where V = kρ(nco2nccl2)1/2. The distance between centers d = 4ρ, where ρ is the width of the slabs. CMT, coupled-mode theory.

Fig. 2
Fig. 2

The propagation constants βs and βa for TM modes. V = 1 and d = 4ρ. βs, always lies above βa. Note that βs of the modified coupled-mode analysis with cross power is indistinguishable from the exact analysis.

Equations (16)

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β = { ω ( μ 0 H H * + E E * ) + j [ ( T × H ) E * ( T × E ) H * ] } d a × [ ( E × H * + E * × H ) z ˆ d a ] 1 .
E = a 1 e 1 + a 2 e 2 , H = a 1 h 1 + a 2 h 2 ,
β = i , j = 1 2 a i * H i j a j i , j = 1 2 a i * P i j a j ,
H i j = P i j β j + κ i j ,
P i j = 1 4 [ e i * × h j + e j × h i * ] z ˆ d a ,
κ i j = 1 4 ω [ j ] e i * e j d a .
β j P i j a j = j H i j a j .
e 1 = e 1 + δ e 1 , e 2 = e 2 + δ e 2 ,
H i j = P i j β j + κ i j + ( β i β j ) δ P i j ,
κ i j = κ i j + 1 4 ω [ i ] δ e i * e j d a + 1 4 ω [ i ] e i * δ e j d a + 1 4 ω δ e i * δ e j d a ,
P i j = P i j + 1 4 [ δ e j * × h j + δ e j × h i * ] z ˆ d a ,
δ P i j = 1 4 δ e j × h i * z ˆ d a .
δ e x 2 = { [ ( n co n cl ) 2 1 ] e x d ρ < x d + ρ . 0 otherwise
β s β a = 2 | κ 12 | .
( β s β a ) ( P 11 + P 22 ) = [ 2 β 0 ( β a + β s ) ] ( P 12 + P 21 ) + 4 | κ 12 | ,
β a + β s = ( β s β a ) ( P 12 + P 21 ) + 2 β 0 ( P 11 + P 22 ) . + 2 ( κ 11 + κ 22 )

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