Abstract

A signal interleaver/ deinterleaver based on ring resonators is proposed and analyzed with the transfer matrix and the Z-transform techniques. The proposed structure is composed of rings connected in a closed loop and is termed a “compound ring resonator circuit.” The interleaver/deinterleaver circuit is designed to meet wavelength division multiplexing (WDM) specifications for two channels of spacing of 50GHz, a channel free spectral range of 100GHz, a crosstalk of 24dB, and a maximum dispersion of ±22psnm over a ±10GHz bandwidth at a wavelength of 1.55μm. Compared with previous circuits of this nature, this circuit possesses a smaller number of rings, a simpler design, does not require apodization, exhibits less dispersion, and offers a higher fabrication tolerance and density.

© 2009 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. (Bellingham) 47, 094601 (2008).
    [CrossRef]
  2. M. Gad, D. Yevick, and P. Jessop, “Tunable polymer/silicon over insulator ring resonators,” Opt. Eng. (Bellingham) 47, 124601 (2008).
    [CrossRef]
  3. B. E. Little and S. T. Chu, “Theory of polarization rotation and conversion in vertically coupled microresoators,” IEEE Photon. Technol. Lett. 12, 401-403 (2000).
    [CrossRef]
  4. 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]
  5. Q. Xu, J. Shakya, and M. Lipson, “Direct measurement of tunable optical delays on chip analogue to electromagnetically induced transparency,” Opt. Express 14, 6463-6468 (2006).
    [CrossRef] [PubMed]
  6. S. Darmawan, Y. M. Landobasa, and M.-K. Chin, “Polezero dynamics of high-order ring resonator filters,” J. Lightwave Technol. 25, 1568-1575 (2007).
    [CrossRef]
  7. 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]
  8. A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing (Prentice-Hall, 1989).
  9. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, 1999).
  10. C. J. Kaalund, Z. Jin, W. Li, and G.-D. Peng, “Novel optical wavelength interleaver based on symmetrically parallel-coupled and apodized ring resonator arrays,” Proc. SPIE 5206, 157-165 (2003).
    [CrossRef]
  11. V. Van, “Dual-mode microring reflection filters,” J. Lightwave Technol. 25, 3142-3150 (2007).
    [CrossRef]

2008 (2)

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

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

2007 (2)

2006 (1)

2004 (1)

2003 (1)

C. J. Kaalund, Z. Jin, W. Li, and G.-D. Peng, “Novel optical wavelength interleaver based on symmetrically parallel-coupled and apodized ring resonator arrays,” Proc. SPIE 5206, 157-165 (2003).
[CrossRef]

2000 (1)

B. E. Little and S. T. Chu, “Theory of polarization rotation and conversion in vertically coupled microresoators,” IEEE Photon. Technol. Lett. 12, 401-403 (2000).
[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, 998-1005 (1997).
[CrossRef]

Chin, M.-K.

Chu, S. T.

B. E. Little and S. T. Chu, “Theory of polarization rotation and conversion in vertically coupled microresoators,” IEEE Photon. Technol. Lett. 12, 401-403 (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, 998-1005 (1997).
[CrossRef]

Darmawan, S.

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, “High-speed polymer/silicon on insulator ring resonator switch,” Opt. Eng. (Bellingham) 47, 094601 (2008).
[CrossRef]

M. Gad, D. Yevick, and P. Jessop, “Tunable polymer/silicon over insulator ring resonators,” Opt. Eng. (Bellingham) 47, 124601 (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]

Jessop, P.

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

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

Jin, Z.

C. J. Kaalund, Z. Jin, W. Li, and G.-D. Peng, “Novel optical wavelength interleaver based on symmetrically parallel-coupled and apodized ring resonator arrays,” Proc. SPIE 5206, 157-165 (2003).
[CrossRef]

Kaalund, C. J.

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]

C. J. Kaalund, Z. Jin, W. Li, and G.-D. Peng, “Novel optical wavelength interleaver based on symmetrically parallel-coupled and apodized ring resonator arrays,” Proc. SPIE 5206, 157-165 (2003).
[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, 998-1005 (1997).
[CrossRef]

Landobasa, Y. M.

Li, W.

C. J. Kaalund, Z. Jin, W. Li, and G.-D. Peng, “Novel optical wavelength interleaver based on symmetrically parallel-coupled and apodized ring resonator arrays,” Proc. SPIE 5206, 157-165 (2003).
[CrossRef]

Lipson, M.

Little, B. E.

B. E. Little and S. T. Chu, “Theory of polarization rotation and conversion in vertically coupled microresoators,” IEEE Photon. Technol. Lett. 12, 401-403 (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, 998-1005 (1997).
[CrossRef]

Madsen, C. K.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, 1999).

Oppenheim, A. V.

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing (Prentice-Hall, 1989).

Peng, G.-D.

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]

C. J. Kaalund, Z. Jin, W. Li, and G.-D. Peng, “Novel optical wavelength interleaver based on symmetrically parallel-coupled and apodized ring resonator arrays,” Proc. SPIE 5206, 157-165 (2003).
[CrossRef]

Schafer, R. W.

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing (Prentice-Hall, 1989).

Shakya, J.

Van, V.

Xu, Q.

Yevick, D.

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

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

Zhao, J. H.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, 1999).

IEEE Photon. Technol. Lett. (1)

B. E. Little and S. T. Chu, “Theory of polarization rotation and conversion in vertically coupled microresoators,” IEEE Photon. Technol. Lett. 12, 401-403 (2000).
[CrossRef]

J. Lightwave Technol. (4)

Opt. Eng. (Bellingham) (2)

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

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

Opt. Express (1)

Proc. SPIE (1)

C. J. Kaalund, Z. Jin, W. Li, and G.-D. Peng, “Novel optical wavelength interleaver based on symmetrically parallel-coupled and apodized ring resonator arrays,” Proc. SPIE 5206, 157-165 (2003).
[CrossRef]

Other (2)

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing (Prentice-Hall, 1989).

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, 1999).

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Figures (7)

Fig. 1
Fig. 1

Compound ring resonator circuit with (a) N = 4 , (b) N = 6 ring resonators.

Fig. 2
Fig. 2

Circuit response with k o = k o o = 0.935 and k increasing from 0.5 to 0.6 in steps of 0.025. The arrows indicate increasing parameter values. The roundtrip power loss is 10%. (a) Power spectra. (b) Phase variation. (c) Normalized group delay. (d) Through port dispersion. (e) Drop port dispersion. (f) Through port pole-zero diagram. (g) Drop port pole–zero diagram.

Fig. 3
Fig. 3

Circuit response with k = 0.525 and k o = k o o increasing from 0.885 to 0.985 in steps of 0.025. The arrows indicate increasing parameter values. The roundtrip power loss is 10%. (a) Power spectra. (b) Phase variation. (c) Normalized group delay. (d) Through port dispersion. (e) Drop port dispersion. (f) Through port pole-zero diagram. (g) Drop port pole–zero diagram.

Fig. 4
Fig. 4

Circuit response with k = 0.525 and k o = k o o = 0.935 for a roundtrip power loss of 10%. (a) Power spectra. (b) Phase variation. (c) Normalized group delay. (d) Through port dispersion. (e) Drop port dispersion. (f) Through port pole-zero diagram. (g) Drop port pole–zero diagram.

Fig. 5
Fig. 5

Compound four-ring circuit attached to a single ring stage.

Fig. 6
Fig. 6

Single-ring stage response with k o = 0.952 and k o o = 0 for a roundtrip power loss of 10%. (a) Power spectra. (b) Phase variation. (c) Normalized group delay. (d) Through port dispersion. (e) Through port pole–zero diagram.

Fig. 7
Fig. 7

Drop port response with an additional single ring stage for a roundtrip power loss equal to 10%. (a) Power spectra. (b) Phase variation. (c) Normalized group delay. (d) Drop port dispersion. (e) Drop port pole–zero diagram.

Tables (1)

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Table 1 Performance of the Optimal Design in [7] Compared with Compound RR Circuit Performance

Equations (29)

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[ d o c o ] = Q o [ a o b o ] , [ d o o c o o ] = Q o o [ a o o b o o ] ,
[ d j c j ] = Q [ a j b j ] , 1 j N ,
Q o = 1 i k o [ r o 1 1 r o ] , Q o o = 1 i k o o [ r o o 1 1 r o o ] ,
Q = 1 i k [ r 1 1 r ] , k o 2 + r o 2 = 1 , k o o 2 + r o o 2 = 1 , k 2 + r 2 = 1 ,
[ a 2 j b 2 j ] = P 1 [ d 2 j 1 c 2 j 1 ] , 1 j N 2 ,
[ a 2 j + 1 b 2 j + 1 ] = P 2 [ d 2 j c 2 j ] , 1 j N 2 1
P 1 = [ 0 e i δ 1 e i δ 2 0 ] , P 2 = [ 0 e i δ 2 e i δ 1 0 ] .
b 1 = ρ 1 a 1 + τ 2 d N ,
c N = ρ 2 d N + τ 1 a 1 ,
X = [ x 1 x 2 x 3 x 4 ] ,
Y = [ y 1 y 2 y 3 y 4 ] ,
[ d N c N ] = X [ a 1 b 1 ] ,
[ a N 2 + 1 b N 2 + 1 ] = Y 1 [ a 1 b 1 ] ,
Y = Y 1 = V 1 ( P 1 Q ) U ( N 2 ) 4 ,
V 1 = [ 1 0 0 1 r o o ] ,
X = P 1 U ( N 2 ) 4 ( P 2 Q ) Y .
[ d N 2 c N 2 ] = Y 2 [ a 1 b 1 ] ,
Y = Y 2 = P 1 U N 4 ,
V 2 = [ r o o 0 0 1 ] ,
X = X 2 = P 1 U N 4 V 2 P 2 Y .
d N = b 1 e i δ 1 ,
ρ 1 = b 1 a 1 = x 1 x 2 ,
τ 1 = c N a 1 = x 3 x 1 x 4 x 2 ,
ρ 2 = c N d N = x 4 x 2 ,
τ 2 = b 1 d N = 1 x 2 .
ρ i = b 1 a 1 = ρ 1 1 τ 2 e i δ 1
τ i = c N a 1 = τ 1 + ( ρ 1 ρ 2 τ 1 τ 2 ) e i δ 1 1 τ 2 e i δ 1 .
ρ o = b o a o = r o τ i e i δ 2 1 r o τ i e i δ 2 = | ρ o | e i Φ o .
τ o = b o o a o = k o k o o ( y 3 + y 4 ρ i ) e i δ 2 τ i r o = | τ o | e i Ψ o ,

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