Abstract

While there have been several attempts recently to extend the accuracy of vector coupled-mode theory beyond the usual first-order expression for evanescent couplers, as yet no analytical method is available for describing the polarization properties of couplers with a large core–cladding index jump. Here we present a quasi-static approximation for couplers of low V value, where V is the usual waveguide parameter.

© 1988 Optical Society of America

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References

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  1. A. W. Snyder, J. Opt. Soc. Am. 62, 1267 (1972).
    [CrossRef]
  2. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972).
  3. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  4. A. W. Snyder, W. Young, J. Opt. Soc. Am. 68, 297 (1978).
    [CrossRef]
  5. A. Hardy, W. Streifer, IEEE J. Lightwave Technol. LT-3, 1135 (1985).
    [CrossRef]
  6. S. L. Chuang, IEEE J. Lightwave Technol. LT-5, 5 (1987).
    [CrossRef]
  7. H. A. Haus, W. P. Huang, S. Kawakami, A. Whitaker, IEEE J. Lightwave Technol. LT-5, 16 (1987).
    [CrossRef]
  8. A. W. Snyder, A. Ankiewicz, Electron. Lett. 22, 1237 (1986).
    [CrossRef]
  9. A. W. Snyder, A. Ankiewicz, A. Altintas, Electron. Lett. 23, 1097 (1987).
    [CrossRef]
  10. A. W. Snyder, A. J. Stevenson, Opt. Lett. 11, 254 (1986); A. W. Snyder, A. Ankiewicz, A. Altinas, Electron. Lett. (to be published).
    [CrossRef] [PubMed]
  11. A. Ankiewicz, A. W. Snyder, X.-H. Zheng, IEEE J. Lightwave Technol. LT-4, 1317 (1986).
    [CrossRef]
  12. A. W. Snyder, A. Ankiewicz, IEEE J. Lightwave Technol. LT-6, 463 (1988).
    [CrossRef]
  13. B. I. Bleaney, B. Bleaney, Electricity and Magnetism, 3rd ed. (Oxford U. Press, Oxford, 1978), p. 57.
  14. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  15. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

1988

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

1987

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

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

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

1986

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

A. W. Snyder, A. J. Stevenson, Opt. Lett. 11, 254 (1986); A. W. Snyder, A. Ankiewicz, A. Altinas, Electron. Lett. (to be published).
[CrossRef] [PubMed]

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

1985

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

1978

1972

Altintas, A.

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

Ankiewicz, A.

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

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

Bleaney, B.

B. I. Bleaney, B. Bleaney, Electricity and Magnetism, 3rd ed. (Oxford U. Press, Oxford, 1978), p. 57.

Bleaney, B. I.

B. I. Bleaney, B. Bleaney, Electricity and Magnetism, 3rd ed. (Oxford U. Press, Oxford, 1978), p. 57.

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, A. Whitaker, IEEE J. Lightwave Technol. LT-5, 16 (1987).
[CrossRef]

Huang, W. P.

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

Kawakami, S.

H. A. Haus, W. P. Huang, S. Kawakami, 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).

Marcuse, D.

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

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

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. 23, 1097 (1987).
[CrossRef]

A. W. Snyder, A. J. Stevenson, Opt. Lett. 11, 254 (1986); A. W. Snyder, A. Ankiewicz, A. Altinas, Electron. Lett. (to be published).
[CrossRef] [PubMed]

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

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

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

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

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

Stevenson, A. J.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Streifer, W.

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

Whitaker, A.

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

Young, W.

Zheng, X.-H.

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

Electron. Lett.

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

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

IEEE J. Lightwave Technol.

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

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

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

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

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

J. Opt. Soc. Am.

Opt. Lett.

Other

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

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

B. I. Bleaney, B. Bleaney, Electricity and Magnetism, 3rd ed. (Oxford U. Press, Oxford, 1978), p. 57.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

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Figures (1)

Fig. 1
Fig. 1

Percent error in (β+β) for TM modes of slab couplers as a function of index ratio for the standard first-order theory,2 the full perturbation theory (HS),5 and the quasi-static approximation presented here. The accuracy of these perturbation theories increases with increasing separation, so we have deliberately chosen the large value of R = 1800 and the small value of V = 0.1 to compare them when they are at their most accurate.

Equations (18)

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E ( x , y , z ) = e ( x , y ) e i β z = ( e t + z ˆ e z ) e i β z ,
e t = e ¯ t 1 + α e ¯ t 2 ( cladding ) ,
s ( Δ ) = ( n cl / n co ) 2 ( TM modes of planar waveguides )
= 2 n cl 2 / ( n co 2 + n cl 2 ) ( hybrid modes of circular cross section ) ,
h = h ¯ 1 + α h ¯ 2 ,
e z = ( 1 ) e z 1 + α ( 2 ) e z 2 ,
e = e ¯ t 1 + α e ¯ t 2 + z ˆ ( e z 1 + α e z 2 ) ( in cladding ) ,
e = e ¯ t 1 + α s 1 e ¯ t 2 + z ˆ ( e z 1 + α ( 2 ) e z 2 ) ( in core 1 ) ,
e = s 2 e ¯ t 1 + α e ¯ t 2 + z ˆ ( ( 1 ) e z 1 + α e z 2 ) ( in core 2 ) ,
β ± = β ¯ i + ω A ( ( i ) ) e ± . e ¯ i d A A ( e ± × h ¯ i * + e ¯ i * × h ± ) . d A ,
β ± = β ¯ + ± K 21 + K 11 1 ± N 12 + ( s 1 ) ( N ˜ 11 ± N ˜ 12 ) ,
K 21 = ω 0 4 ( n co 2 n cl 2 ) core 2 e 1 * · e 2 d A ,
K 11 = ω 0 4 ( n co 2 n cl 2 ) core 2 ( s | e t 1 | 2 + n cl 2 n co 2 | e z 1 | 2 ) d A ,
N 12 = 1 2 A e ¯ t 1 × h ¯ t 2 · z ˆ d A ,
N ˜ 12 = 1 4 core 2 e ¯ t 1 × h ¯ t 2 · z ˆ d A ,
N ˜ 11 = 1 4 core 2 e ¯ t 1 × h ¯ t 1 · z ˆ d A ,
d ρ ( n co / V n cl ) 2 ,
V c ( R s + 1 ) 1 / 2 ,

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