Abstract

We have previously introduced a “compound ring resonator circuit,” in which several ring resonator (RR) cavities are coupled in a loop, and analyzed the resulting configuration with the coupling of modes in space (CMS) technique. In this work we compare the accuracy, simplicity and calculation time of three standard procedures, namely the FDTD, and the methods of coupling of modes in time (CMT) and CMS in the context of a two-dimensional (2D) complex ring resonator circuit. This provides a far more effective benchmark of the relative advantages of the methods than the analysis of far simpler structures performed by other authors. As part of these calculations, we further discuss the relationship between the power loss coefficients in the CMS and the CMT models. We verify that the CMT yields accurate and rapid results for small coupling coefficients and losses even for large waveguide circuits containing multiple rings.

© 2010 Optical Society of America

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References

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  1. M. Gad, D. Yevick, and P. Jessop, “High-speed polymer/silicon on insulator ring resonator switch,” Opt. Eng. 47, 094601-1-094601-8 (2008).
    [CrossRef]
  2. M. Gad, D. Yevick and P. Jessop, “Tunable polymer/silicon over insulator ring Resonators,” Opt. Eng. 47, 124601-1-124601-7 (2008).
    [CrossRef]
  3. M. Gad, D. Yevick, and P. Jessop, “Compound ring resonator circuit for integrated optics applications,” J. Opt. Soc. Am. A 26, 2023-2032 (2009).
    [CrossRef]
  4. C. J. Kaalund and G. D. Peng, “Pole-zero diagram approach to the design of ring resonator-based filters for photonic applications,” J. Lightwave Technol. 22, 1548-1559 (2004).
    [CrossRef]
  5. V. Van, “Dual-mode microring reflection filters,” J. Lightwave Technol. 25, 3142-3150 (2007).
    [CrossRef]
  6. I. Kiyat, A. Aydinli, and N. Dagli, “High-Q silicon-on-insulator optical rib waveguide racetrack resonators,” Opt. Express 13, 1900-1905 (2005).
    [CrossRef] [PubMed]
  7. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998-1005 (1997).
    [CrossRef]
  8. J. Saijonmaa and D. Yevick, “Beam-propagation analysis of loss in bent optical waveguides and fibers,”J. Opt. Soc. Am. 73, 1785-1791 (1983).
    [CrossRef]
  9. S. T. Chu and S. K. Chaudhuri, “A finite-difference time-domain method for the design and analysis of guided-wave optical structures,” J. Lightwave Technol. 7, 2033-2038 (1989).
    [CrossRef]
  10. L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).
  11. H. A. Haus, Waves and Fields in Optoelectronics (Prentice Hall, 1984), Chap. 7, p. 197.

2009 (1)

2008 (2)

M. Gad, D. Yevick, and P. Jessop, “High-speed polymer/silicon on insulator ring resonator switch,” Opt. Eng. 47, 094601-1-094601-8 (2008).
[CrossRef]

M. Gad, D. Yevick and P. Jessop, “Tunable polymer/silicon over insulator ring Resonators,” Opt. Eng. 47, 124601-1-124601-7 (2008).
[CrossRef]

2007 (1)

2005 (1)

2004 (1)

1997 (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

1989 (1)

S. T. Chu and S. K. Chaudhuri, “A finite-difference time-domain method for the design and analysis of guided-wave optical structures,” J. Lightwave Technol. 7, 2033-2038 (1989).
[CrossRef]

1983 (1)

Aydinli, A.

Chaudhuri, S. K.

S. T. Chu and S. K. Chaudhuri, “A finite-difference time-domain method for the design and analysis of guided-wave optical structures,” J. Lightwave Technol. 7, 2033-2038 (1989).
[CrossRef]

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

S. T. Chu and S. K. Chaudhuri, “A finite-difference time-domain method for the design and analysis of guided-wave optical structures,” J. Lightwave Technol. 7, 2033-2038 (1989).
[CrossRef]

Coldren, L. A.

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).

Corzine, S. W.

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).

Dagli, N.

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Gad, M.

M. Gad, D. Yevick, and P. Jessop, “Compound ring resonator circuit for integrated optics applications,” J. Opt. Soc. Am. A 26, 2023-2032 (2009).
[CrossRef]

M. Gad, D. Yevick, and P. Jessop, “High-speed polymer/silicon on insulator ring resonator switch,” Opt. Eng. 47, 094601-1-094601-8 (2008).
[CrossRef]

M. Gad, D. Yevick and P. Jessop, “Tunable polymer/silicon over insulator ring Resonators,” Opt. Eng. 47, 124601-1-124601-7 (2008).
[CrossRef]

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

H. A. Haus, Waves and Fields in Optoelectronics (Prentice Hall, 1984), Chap. 7, p. 197.

Jessop, P.

M. Gad, D. Yevick, and P. Jessop, “Compound ring resonator circuit for integrated optics applications,” J. Opt. Soc. Am. A 26, 2023-2032 (2009).
[CrossRef]

M. Gad, D. Yevick, and P. Jessop, “High-speed polymer/silicon on insulator ring resonator switch,” Opt. Eng. 47, 094601-1-094601-8 (2008).
[CrossRef]

M. Gad, D. Yevick and P. Jessop, “Tunable polymer/silicon over insulator ring Resonators,” Opt. Eng. 47, 124601-1-124601-7 (2008).
[CrossRef]

Kaalund, C. J.

Kiyat, I.

Laine, J.-P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Little, B. E.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Peng, G. D.

Saijonmaa, J.

Van, V.

Yevick, D.

M. Gad, D. Yevick, and P. Jessop, “Compound ring resonator circuit for integrated optics applications,” J. Opt. Soc. Am. A 26, 2023-2032 (2009).
[CrossRef]

M. Gad, D. Yevick and P. Jessop, “Tunable polymer/silicon over insulator ring Resonators,” Opt. Eng. 47, 124601-1-124601-7 (2008).
[CrossRef]

M. Gad, D. Yevick, and P. Jessop, “High-speed polymer/silicon on insulator ring resonator switch,” Opt. Eng. 47, 094601-1-094601-8 (2008).
[CrossRef]

J. Saijonmaa and D. Yevick, “Beam-propagation analysis of loss in bent optical waveguides and fibers,”J. Opt. Soc. Am. 73, 1785-1791 (1983).
[CrossRef]

J. Lightwave Technol. (4)

C. J. Kaalund and G. D. Peng, “Pole-zero diagram approach to the design of ring resonator-based filters for photonic applications,” J. Lightwave Technol. 22, 1548-1559 (2004).
[CrossRef]

V. Van, “Dual-mode microring reflection filters,” J. Lightwave Technol. 25, 3142-3150 (2007).
[CrossRef]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

S. T. Chu and S. K. Chaudhuri, “A finite-difference time-domain method for the design and analysis of guided-wave optical structures,” J. Lightwave Technol. 7, 2033-2038 (1989).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Eng. (2)

M. Gad, D. Yevick, and P. Jessop, “High-speed polymer/silicon on insulator ring resonator switch,” Opt. Eng. 47, 094601-1-094601-8 (2008).
[CrossRef]

M. Gad, D. Yevick and P. Jessop, “Tunable polymer/silicon over insulator ring Resonators,” Opt. Eng. 47, 124601-1-124601-7 (2008).
[CrossRef]

Opt. Express (1)

Other (2)

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).

H. A. Haus, Waves and Fields in Optoelectronics (Prentice Hall, 1984), Chap. 7, p. 197.

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Figures (4)

Fig. 1
Fig. 1

(a) CMS model of the compound ring resonator circuit and (b) the CMT model of the compound ring resonator circuit.

Fig. 2
Fig. 2

(a) Through-port and (b) drop-port transmission characteristics for a lossless circuit: dashed curves, by the CMT model; dotted curves, by the CMS model; and curves with circles, by the FDTD model. The small shift of results by the CMS and the CMT models is shown in the insets. The resonance wavelength corresponds to m = 19 .

Fig. 3
Fig. 3

(a) Through-port and (b) drop-port transmission characteristics for a circuit with 5% power loss per round trip: dashed curves, by the CMT model; dotted curves, by the CMS model; and curves with circles, by the FDTD model. The small shift of results by the CMS and the CMT models is shown in the insets. The resonance wavelength corresponds to m = 19 .

Fig. 4
Fig. 4

(a) Through-port and (b) drop-port transmission characteristics for a circuit with 10% power loss per round trip: dashed curves, by the CMT model; dotted curves, by the CMS model; and curves with circles by the FDTD model. The resonance wavelength corresponds to m = 19.

Equations (7)

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f = A 1 1 A 2 s ,
f T = [ f 1 f 2 f 3 f 4 ] ,
s T = [ s i 0 0 0 ] ,
A 1 = [ i Δ ω 1 + 1 τ e + 1 τ l i μ 1 0 i μ 4 i μ 1 i Δ ω 2 + 1 τ l i μ 2 0 0 i μ 2 i Δ ω 3 + 1 τ d + 1 τ l i μ 3 i μ 4 0 i μ 3 i Δ ω 4 + 1 τ l ] ,
A 2 T = [ i μ o 0 0 0 ] ,
s t = s i i μ o f 1 ,
s d = s f i μ o o f 3 ,

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