Abstract

An effective and exact synthesis technique for the design of parallel-coupled ring-resonator filters with a maximally flat stop-band characteristic of any order is presented. Simple closed-form formulas determine the Q factor of each resonator and the coupling coefficients. The performances of these filters are discussed for their applications as interleavers and channel-dropping filters in wavelength-division multiplexing systems.

© 2001 Optical Society of America

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References

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  1. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis (Wiley, New York, 1999).
    [CrossRef]
  2. B. E. Little, S. T. Chu, J. V. Hryniewicz, and P. Absil, Opt. Lett. 25, 344 (2000).
    [CrossRef]
  3. G. Griffel, IEEE Photon. Technol. Lett. 12, 810 (2000).
    [CrossRef]
  4. G. L. Matthaei, L. Young, and E. M. T. Jones, in Microwave Filters, Impedance Matching Networks and Coupling Structures (McGraw-Hill, New York, 1964).
  5. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N. J., 1984).
  6. S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kokubun, IEEE Photon. Technol. Lett. 11, 1426 (1999).
    [CrossRef]

2000

1999

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kokubun, IEEE Photon. Technol. Lett. 11, 1426 (1999).
[CrossRef]

Absil, P.

Chu, S. T.

B. E. Little, S. T. Chu, J. V. Hryniewicz, and P. Absil, Opt. Lett. 25, 344 (2000).
[CrossRef]

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kokubun, IEEE Photon. Technol. Lett. 11, 1426 (1999).
[CrossRef]

Griffel, G.

G. Griffel, IEEE Photon. Technol. Lett. 12, 810 (2000).
[CrossRef]

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N. J., 1984).

Hryniewicz, J. V.

Jones, E. M. T.

G. L. Matthaei, L. Young, and E. M. T. Jones, in Microwave Filters, Impedance Matching Networks and Coupling Structures (McGraw-Hill, New York, 1964).

Kaneko, T.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kokubun, IEEE Photon. Technol. Lett. 11, 1426 (1999).
[CrossRef]

Kokubun, Y.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kokubun, IEEE Photon. Technol. Lett. 11, 1426 (1999).
[CrossRef]

Little, B. E.

B. E. Little, S. T. Chu, J. V. Hryniewicz, and P. Absil, Opt. Lett. 25, 344 (2000).
[CrossRef]

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kokubun, IEEE Photon. Technol. Lett. 11, 1426 (1999).
[CrossRef]

Madsen, C. K.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis (Wiley, New York, 1999).
[CrossRef]

Matthaei, G. L.

G. L. Matthaei, L. Young, and E. M. T. Jones, in Microwave Filters, Impedance Matching Networks and Coupling Structures (McGraw-Hill, New York, 1964).

Pan, W.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kokubun, IEEE Photon. Technol. Lett. 11, 1426 (1999).
[CrossRef]

Young, L.

G. L. Matthaei, L. Young, and E. M. T. Jones, in Microwave Filters, Impedance Matching Networks and Coupling Structures (McGraw-Hill, New York, 1964).

Zhao, J. H.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis (Wiley, New York, 1999).
[CrossRef]

IEEE Photon. Technol. Lett.

G. Griffel, IEEE Photon. Technol. Lett. 12, 810 (2000).
[CrossRef]

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kokubun, IEEE Photon. Technol. Lett. 11, 1426 (1999).
[CrossRef]

Opt. Lett.

Other

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis (Wiley, New York, 1999).
[CrossRef]

G. L. Matthaei, L. Young, and E. M. T. Jones, in Microwave Filters, Impedance Matching Networks and Coupling Structures (McGraw-Hill, New York, 1964).

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N. J., 1984).

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Figures (5)

Fig. 1
Fig. 1

Filter with parallel-coupled ring resonators.

Fig. 2
Fig. 2

Frequency responses for N=25 and FSR/B=10. Lc=Lr/100λ/4.

Fig. 3
Fig. 3

Frequency response for a fourth-order filter with FSR=100 GHz, B=20 GHz, and Lc=Lr/100λ/4.

Fig. 4
Fig. 4

Frequency response of a third-order filter with FSR/B=10 and three values of Lc (rounded to λ/4).

Fig. 5
Fig. 5

Frequency response of a fourth-order filter with FSR/B=30 and two values of Lc.

Equations (4)

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

Qq=FSR/gqB,
gq=2sin2q-12Nπ.
cq=π22Qq21+4Qq2/π212-1.
Lr=cneff FSR=cMnefff0,

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