Abstract

A general variational optimization procedure is used to synthesize codirectional couplers with arbitrary sidelobe suppression down to −125 dB. Apodization shapes yielding sidelobe levels over the range of −40 dB to −75 dB are given by a single design formula. The limiting performance in terms of sidelobe suppression versus the bandwidth of passive evanescent-type couplers is found.

© 1995 Optical Society of America

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References

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  1. H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, J. Lightwave Technol. LT-5, 16 (1987).
    [Crossref]
  2. R. C. Alferness, P. S. Cross, IEEE J. Quantum Electron. QE-14, 843 (1978).
    [Crossref]
  3. H. Sakata, Opt. Lett. 17, 463 (1992).
    [Crossref] [PubMed]
  4. G.-H. Song, S.-Y. Shin, J. Opt. Soc. Am. A 2, 1905 (1985).
    [Crossref]
  5. R. Fletcher, ed., Optimization: Symposium of the Institute of Mathematics and its Applications (Academic, New York, 1969).

1992 (1)

1987 (1)

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

1985 (1)

1978 (1)

R. C. Alferness, P. S. Cross, IEEE J. Quantum Electron. QE-14, 843 (1978).
[Crossref]

Alferness, R. C.

R. C. Alferness, P. S. Cross, IEEE J. Quantum Electron. QE-14, 843 (1978).
[Crossref]

Cross, P. S.

R. C. Alferness, P. S. Cross, IEEE J. Quantum Electron. QE-14, 843 (1978).
[Crossref]

Haus, H. A.

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

Huang, W. P.

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

Kawakami, S.

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

Sakata, H.

Shin, S.-Y.

Song, G.-H.

Whitaker, N. A.

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

IEEE J. Quantum Electron. (1)

R. C. Alferness, P. S. Cross, IEEE J. Quantum Electron. QE-14, 843 (1978).
[Crossref]

J. Lightwave Technol. (1)

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

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Other (1)

R. Fletcher, ed., Optimization: Symposium of the Institute of Mathematics and its Applications (Academic, New York, 1969).

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Figures (3)

Fig. 1
Fig. 1

Discretely tapered codirectional coupler.

Fig. 2
Fig. 2

Low-sidelobe couplers: (a) spectral response, and (b) coupling-strength profiles for a uniform coupler, a −50-dB sidelobe suppressed coupler, and a −125-dB sidelobe suppressed coupler.

Fig. 3
Fig. 3

Effect of sidelobe suppression level on bandwidth. The solid curve represents the minimum passband width achievable in evanescent codirectional couplers for a desired sidelobe suppression.

Tables (1)

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Table 1 Coefficients bij Defining the Functions L i = j = 1 6 b i , j cos [ ( 2 j - 1 ) π z ]

Equations (11)

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d A 1 d z = - j κ ( z ) exp ( j Δ β z ) A 2 ,
d A 2 d z = - j κ ( z ) exp ( - j Δ β z ) A 1 .
A ( l ) = TA ( 0 ) ,
t 11 = t 22 * = cos ( S l ) - j Δ β 2 S sin ( S l ) ,
t 12 = t 21 = - j κ S sin ( S l ) ,
S = [ κ 2 + ( Δ β 2 ) 2 ] 1 / 2 ,
E ( κ ) = [ 1 ( κ ) , 2 ( κ ) , , m ( κ ) ] T .
E ( κ + Δ κ ) = E ( κ ) + ( E T ) T Δ κ + o ( Δ κ ) .
Δ κ = - α J T ( J J T ) ( - 1 ) E ( κ ) .
κ s ( z ) = L 0 ( z ) + S L 1 ( z ) + S 2 L 2 ( z ) + S 3 L 3 ( z ) + S 4 L 4 ( z ) ,
L i ( z ) = j = 1 6 b i , j cos [ ( 2 j - 1 ) π ]             ( - 0.5 < z < 0.5 ) .

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