Abstract

A method for directly extracting the coupling coefficients, the resonant frequency detunings and the loss of an N th-order serially-coupled microring resonator filter from the measured power spectral responses is presented. The device parameters are obtained from the through-port complex transfer function, which is constructed from the experimentally extracted poles and zeros of the filter. We applied the method to determine the parameters of a symmetric microring doublet fabricated in the Siliconon-Insulator material platform. Simulated spectral responses using the extracted parameters showed good agreement with the measured data. The extracted parameters along with the poles and zeros of the device provide important information about the fabrication process and can be used to guide the post-fabrication trimming of high-order microring filters.

© 2008 Optical Society of America

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References

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  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 (1997).
    [CrossRef]
  2. C. K. Madsen, "Efficient architectures for exactly realizing optical filters with optimum bandpass design," IEEE Photon. Technol. Lett. 10, 1136 (1998).
    [CrossRef]
  3. V. Van, "Synthesis of elliptic optical filters using mutually-coupled microring resonators," J. Lightwave Technol. 25, 584 (2007).
    [CrossRef]
  4. G. Lenz and C. K. Madsen, "General optical all-pass filter structures for dispersion control in WDM systems," J. Lightwave Technol. 17, 1248 (1999).
    [CrossRef]
  5. F. Morichetti, A. Melloni, C. Ferrari, and M. Martinelli, "Error-free continuously-tunable delay at 10 Gbit/s in a reconfigurable on-chip delay-line," Opt. Express 16, 8395 (2008).
    [CrossRef] [PubMed]
  6. J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, "High order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320 (2000).
    [CrossRef]
  7. B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263 (2004).
    [CrossRef]
  8. T. Barwicz, M. Popovic, P. Rakich, M. Watts, H. Haus, E. Ippen, and H. Smith, "Microring-resonator-based add-drop filters in SiN: fabrication and analysis," Opt. Express 12, 1437 (2004).
    [CrossRef] [PubMed]
  9. F. Xia, M. Rooks, L. Sekaric, and Y. Vlasov, "Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects," Opt. Express 15, 11934 (2007).
    [CrossRef] [PubMed]
  10. V. Van, "Circuit-based method for synthesizing serially-coupled microring filters," J. Lightwave Technol. 24, 2912 (2006).
    [CrossRef]
  11. H. L. Liew and V. Van, "Exact realization of optical transfer functions with symmetric transmission zeros using the double-microring ladder architecture," J. Lightwave Technol. 26 (to be published).
  12. S.-L. Chuang, "Application of the strongly coupled-mode theory to integrated optical devices," IEEE J. Quantum Electron. 23, 499 (1987).
    [CrossRef]

2008 (1)

2007 (2)

2006 (1)

2004 (2)

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263 (2004).
[CrossRef]

T. Barwicz, M. Popovic, P. Rakich, M. Watts, H. Haus, E. Ippen, and H. Smith, "Microring-resonator-based add-drop filters in SiN: fabrication and analysis," Opt. Express 12, 1437 (2004).
[CrossRef] [PubMed]

2000 (1)

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, "High order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320 (2000).
[CrossRef]

1999 (1)

1998 (1)

C. K. Madsen, "Efficient architectures for exactly realizing optical filters with optimum bandpass design," IEEE Photon. Technol. Lett. 10, 1136 (1998).
[CrossRef]

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 (1997).
[CrossRef]

1987 (1)

S.-L. Chuang, "Application of the strongly coupled-mode theory to integrated optical devices," IEEE J. Quantum Electron. 23, 499 (1987).
[CrossRef]

Absil, P. P.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263 (2004).
[CrossRef]

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, "High order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320 (2000).
[CrossRef]

Barwicz, T.

Chu, S. T.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263 (2004).
[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 (1997).
[CrossRef]

Chuang, S.-L.

S.-L. Chuang, "Application of the strongly coupled-mode theory to integrated optical devices," IEEE J. Quantum Electron. 23, 499 (1987).
[CrossRef]

Ferrari, C.

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 (1997).
[CrossRef]

Gill, D.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263 (2004).
[CrossRef]

Haus, H.

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 (1997).
[CrossRef]

Ho, P.-T.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, "High order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320 (2000).
[CrossRef]

Hryniewicz, J. V.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263 (2004).
[CrossRef]

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, "High order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320 (2000).
[CrossRef]

Ippen, E.

Johnson, F. G.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263 (2004).
[CrossRef]

King, O.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263 (2004).
[CrossRef]

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 (1997).
[CrossRef]

Lenz, G.

Little, B. E.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263 (2004).
[CrossRef]

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, "High order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320 (2000).
[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 (1997).
[CrossRef]

Madsen, C. K.

G. Lenz and C. K. Madsen, "General optical all-pass filter structures for dispersion control in WDM systems," J. Lightwave Technol. 17, 1248 (1999).
[CrossRef]

C. K. Madsen, "Efficient architectures for exactly realizing optical filters with optimum bandpass design," IEEE Photon. Technol. Lett. 10, 1136 (1998).
[CrossRef]

Martinelli, M.

Melloni, A.

Morichetti, F.

Popovic, M.

Rakich, P.

Rooks, M.

Seiferth, F.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263 (2004).
[CrossRef]

Sekaric, L.

Smith, H.

Trakalo, M.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263 (2004).
[CrossRef]

Van, V.

V. Van, "Synthesis of elliptic optical filters using mutually-coupled microring resonators," J. Lightwave Technol. 25, 584 (2007).
[CrossRef]

V. Van, "Circuit-based method for synthesizing serially-coupled microring filters," J. Lightwave Technol. 24, 2912 (2006).
[CrossRef]

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263 (2004).
[CrossRef]

Vlasov, Y.

Watts, M.

Wilson, R. A.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, "High order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320 (2000).
[CrossRef]

Xia, F.

IEEE J. Quantum Electron. (1)

S.-L. Chuang, "Application of the strongly coupled-mode theory to integrated optical devices," IEEE J. Quantum Electron. 23, 499 (1987).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

C. K. Madsen, "Efficient architectures for exactly realizing optical filters with optimum bandpass design," IEEE Photon. Technol. Lett. 10, 1136 (1998).
[CrossRef]

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, "High order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320 (2000).
[CrossRef]

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263 (2004).
[CrossRef]

J. Lightwave Technol. (4)

Opt. Express (3)

Other (1)

H. L. Liew and V. Van, "Exact realization of optical transfer functions with symmetric transmission zeros using the double-microring ladder architecture," J. Lightwave Technol. 26 (to be published).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of an Nth-order serially-coupled microring filter.

Fig. 2.
Fig. 2.

(a) Schematic of a symmetric microring doublet; (b) SEM image of an SOI microring doublet; (c) SEM image of the coupling gap between the two microracetracks.

Fig. 3.
Fig. 3.

Measured (red and black dots) and simulated (green and purple solid lines) spectral responses at the drop port and through port of the microring doublet: (a) wavelength scan across two FSRs; (b) passband response at the 1.544µm center wavelength.

Fig. 4.
Fig. 4.

(a) Measured power ratios P 1 and P 2 (dots) and their least-square fourth-degree polynomial fits (solid lines); (b) pole-zero diagram showing the roots of P 1 and P 2 (black x and o), the extracted poles and zeros (red x and o) and the designed poles and zeros (blue x and o) of the microring doublet.

Tables (2)

Tables Icon

Table 1. Roots of the power ratios P 1(ω/ω c ) and P 2(ω/ω c ) and the extracted poles and zeros of the filter.

Tables Icon

Table 2. Extracted device parameters of the SOI microring doublet.

Equations (18)

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d a 1 d t = ( j ω 1 γ L γ 0 ) a 1 j μ 1 a 2 j μ 0 s i ,
d a k d t = ( j ω k γ L ) a k j μ k 1 a k 1 j μ k a k + 1 , k = 2 , 3 , N 1 ,
d a N d t = ( j ω N γ L γ N ) a N j μ N 1 a N 1 .
a 1 = j μ 0 s i s + r 1 + γ 0 + μ 1 2 s + r 2 + μ 2 2 s + r 3 + + μ N 1 2 s + r N + γ N ,
s t = s i j μ 0 a 1 ,
1 T t ( s ) = j μ 0 a 1 s i = μ 0 2 s + r 1 + γ 0 + μ 1 2 s + r 2 + μ 2 2 s + r 3 + + μ N 1 2 s + r N + γ N .
1 T t ( s ) = Q ( s ) R ( s ) Q ( s ) = μ 0 2 M ( s ) Q ( s ) ,
Q ( s ) M ( s ) = ( s + a ) + b · N ( s ) M ( s ) ,
κ k = μ k T r t , k = 0 , N ,
κ k = μ k T r t , 1 k < N 1 ,
and
α = 2 γ L v g ,
T d ( s ) = K k = 1 N ( s p k ) ,
T t ( s ) = k = 1 N ( s z k ) k = 1 N ( s p k ) ,
T d ( ω ) 2 = K 2 k = 1 N j ω p k 2 = K 2 k = 1 N ω + j p k 2 ,
T t ( ω ) 2 = k = 1 N j ω z k 2 k = 1 N j ω p k 2 = k = 1 N ω + j z k 2 k = 1 N ω + j p k 2 .
P 1 ( ω ) = 1 T d ( ω ) 2 = 1 K 2 k = 1 N ω + j p k 2 ,
P 2 ( ω ) = T t ( ω ) 2 T d ( ω ) 2 = 1 K 2 k = 1 N ω + j z k 2 ,

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