Abstract

Synthesizing ideal windowlike spectral response in codirectional grating-assisted couplers is considered. The method of variational optimization is used to design couplers theoretically with near 100% power transfer efficiency over the passband width and with sidelobes suppressed to −40 dB. The physical role of the π-phase-reversal sections for passband flattening is explained.

© 1996 Optical Society of America

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References

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  1. R. C. Alferness, P. S. Cross, IEEE J. Quantum Electron. QE-14, 843 (1978).
    [CrossRef]
  2. G.-H. Song, S.-Y. Shin, J. Opt. Soc. Am. A 2, 1905 (1985).
  3. K. A. Winick, J. Lightwave Technol. 9, 1481 (1991).
    [CrossRef]
  4. G.-H. Song, J. Lightwave Technol. 13, 470 (1995).
    [CrossRef]
  5. B. E. Little, C. Wu, W.-P. Huang, Opt. Lett. 20, 1259 (1995).
    [CrossRef] [PubMed]
  6. W.-P. Huang, H. A. Haus, J. Lightwave Technol. 7, 920 (1989).
    [CrossRef]
  7. H. Sakata, Opt. Lett. 17, 463 (1992).
    [CrossRef] [PubMed]

1995 (2)

1992 (1)

1991 (1)

K. A. Winick, J. Lightwave Technol. 9, 1481 (1991).
[CrossRef]

1989 (1)

W.-P. Huang, H. A. Haus, J. Lightwave Technol. 7, 920 (1989).
[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.

W.-P. Huang, H. A. Haus, J. Lightwave Technol. 7, 920 (1989).
[CrossRef]

Huang, W.-P.

B. E. Little, C. Wu, W.-P. Huang, Opt. Lett. 20, 1259 (1995).
[CrossRef] [PubMed]

W.-P. Huang, H. A. Haus, J. Lightwave Technol. 7, 920 (1989).
[CrossRef]

Little, B. E.

Sakata, H.

Shin, S.-Y.

Song, G.-H.

G.-H. Song, J. Lightwave Technol. 13, 470 (1995).
[CrossRef]

G.-H. Song, S.-Y. Shin, J. Opt. Soc. Am. A 2, 1905 (1985).

Winick, K. A.

K. A. Winick, J. Lightwave Technol. 9, 1481 (1991).
[CrossRef]

Wu, C.

IEEE J. Quantum Electron (1)

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

J. Lightwave Technol. (3)

K. A. Winick, J. Lightwave Technol. 9, 1481 (1991).
[CrossRef]

G.-H. Song, J. Lightwave Technol. 13, 470 (1995).
[CrossRef]

W.-P. Huang, H. A. Haus, J. Lightwave Technol. 7, 920 (1989).
[CrossRef]

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

Opt. Lett. (2)

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Figures (3)

Fig. 1
Fig. 1

Power flow in a uniform directional coupler with a π-phase-reversal section at z = 0.75. Solid curve, phasematched signal; dashed curve, non-phase-matched signal.

Fig. 2
Fig. 2

Spectral characteristics of a uniform coupler with a π-phase-reversal section (solid curve) and for a regular uniform coupler. The coupler strength for the uniform coupler is |κ| = π/2 for a device of unit length. The coupling strength for the passband-flattened coupler is |κ| = π, and the phase reversal is placed at the normalized distance of z = 0.75 as in Fig. 1.

Fig. 3
Fig. 3

(a) Spectral characteristics of an optimized bandpass-flattened coupler with −40-dB sidelobes (solid curves) and a regular coupler with −40-dB sidelobes (dashed curves). (b) Logarithmic power scale. (c) Coupling strength profiles yielding the filter responses in (a).

Equations (8)

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

d a 1 d z = - j β 1 a 1 - j κ ( z ) a 2 ,
d a 2 d z = - j β 2 a 2 - j κ ( z ) a 1 .
A ( z ) = exp ( - j β ¯ z ) TA ( 0 ) ,
t 11 = t 22 * = cos ( S z ) - j Δ β 2 S sin ( S z ) ,
t 12 = - t 21 * = - j κ S sin ( S z ) ,
S = [ κ 2 + ( Δ β 2 ) 2 ] 1 / 2 .
E ( κ ) = [ 0 ( κ ) , 1 ( κ ) , , m ( κ ) ] T .
Δ κ = - α J T ( J J T ) - 1 E ( κ ) ,

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