Abstract

A compact silicon coupled-ring modulator structure is proposed. Two rings are coupled to each other, and only one of these rings is actively driven and over-coupled to a waveguide, which enables high modulation speed. The resultant notch filter profile is steeper than that of the single ring and has exhibited a smaller resonance shift and lower driving electrical power. Simulations show that: (i) potentially 60-Gb/s non-return-to-zero (NRZ) data modulation with over 20-dB extinction ratio can be achieved by shifting the active ring by a 20 GHz resonance shift, (ii) the frequency chirp of the modulated signals can be adjusted by varying the coupling coefficient between the two rings, and (iii) dispersion tolerance at 0.5-dB power penalty is extended from 18 to 85 ps/nm, for a 40-Gb/s NRZ signal.

© 2008 Optical Society of America

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References

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  1. T. Sadagopan, S. J. Choi, K. Djordjev, and P. D. Dapkus, "Carrier-induced refractive index changes in InP-based circular microresonators for low-voltage high-speed modulation," IEEE Photon. Technol. Lett. 17, 414-416, (2005).
    [CrossRef]
  2. T. Sadagopan, S. J. Choi, S. J. Choi, P. D. Dapkus, and A. E. Bond, "High-speed, low-voltage modulation in circular WGM micro-resonators," 2004 IEEE/LEOS Summer Topical Meetings (LEOS, San Diego, Calif, 2004) MC2-3.
  3. 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]
  4. C. Li, L. Zhou, and A. W. Poon, "Silicon microring carrier-injection-based modulators/switches with tunable extinction ratios and OR-logic switching by using waveguide cross-coupling," Opt. Express 15, 5069-5076 (2007).
    [CrossRef] [PubMed]
  5. L. Zhang, J.-Y. Yang, M. Song, Y. Li, B. Zhang, R. G. Beausoleil, and A. E. Willner, "Microring-based modulation and demodulation of DPSK signal," Opt. Express 15, 11564-11569 (2007).
    [CrossRef] [PubMed]
  6. S. Manipatruni, Q. Xu, and M. Lipson, "PINIP based high-speed high-extinction ratio micron-size silicon electro-optic modulator," Opt. Express 15, 13035-13042 (2007).
    [CrossRef] [PubMed]
  7. L. Zhang, M. Song, T. Wu, L. Zou, R. G. Beausoleil and A. E. Willner, "Embedded ring resonators for micro-photonic applications," Opt. Lett.  33, to be published in issue no. 17, 2008.
  8. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett. 24, 711-713 (1999).
    [CrossRef]
  9. J. E. Heebner and R. W. Boyd, "'Slow' and 'fast' light in resonator-coupled waveguides," J. Mod. Opt. 49, 2629-2636 (2002).
    [CrossRef]
  10. C. A. Barrios, "Electrooptic modulation of multisilicon-on-insulator photonic wires," J. Lightwave Technol. 24, 2146-2155 (2006)
    [CrossRef]
  11. R. D. Kekatpure and M. L. Brongersma, "CMOS compatible high-speed electro-optical modulator," Proc. SPIE 5926, paper G1 (2005)
    [CrossRef]
  12. C. A. Barrios and M. Lipson, "Modeling and analysis of high-speed electro-optic modulation in high confinement silicon waveguides using metal-oxide-semiconductor configuration," J. Appl. Phys. 96, 6008-6015 (2004).
    [CrossRef]
  13. E. Hecht, Optics (3rd edition), (Addison Wesley Longman, Inc, 1998) Chap. 9.
  14. H. A. Haus, Waves and Fields in Optoelectronics (Prentic-Hall, Inc. Englewood Cliffs New Jersey 07632, 1984) Chap. 7.
    [CrossRef] [PubMed]
  15. Q. Xu, D. Fattal, and R. G. Beausoleil, "1.5-μm-radius high-Q silicon microring resonators," Opt. Express 16, 4309-4315 (2008).

2008 (1)

2007 (3)

2006 (1)

2005 (1)

T. Sadagopan, S. J. Choi, K. Djordjev, and P. D. Dapkus, "Carrier-induced refractive index changes in InP-based circular microresonators for low-voltage high-speed modulation," IEEE Photon. Technol. Lett. 17, 414-416, (2005).
[CrossRef]

2004 (1)

C. A. Barrios and M. Lipson, "Modeling and analysis of high-speed electro-optic modulation in high confinement silicon waveguides using metal-oxide-semiconductor configuration," J. Appl. Phys. 96, 6008-6015 (2004).
[CrossRef]

2002 (1)

J. E. Heebner and R. W. Boyd, "'Slow' and 'fast' light in resonator-coupled waveguides," J. Mod. Opt. 49, 2629-2636 (2002).
[CrossRef]

1999 (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]

Barrios, C. A.

C. A. Barrios, "Electrooptic modulation of multisilicon-on-insulator photonic wires," J. Lightwave Technol. 24, 2146-2155 (2006)
[CrossRef]

C. A. Barrios and M. Lipson, "Modeling and analysis of high-speed electro-optic modulation in high confinement silicon waveguides using metal-oxide-semiconductor configuration," J. Appl. Phys. 96, 6008-6015 (2004).
[CrossRef]

Beausoleil, R. G.

Boyd, R. W.

J. E. Heebner and R. W. Boyd, "'Slow' and 'fast' light in resonator-coupled waveguides," J. Mod. Opt. 49, 2629-2636 (2002).
[CrossRef]

Choi, S. J.

T. Sadagopan, S. J. Choi, K. Djordjev, and P. D. Dapkus, "Carrier-induced refractive index changes in InP-based circular microresonators for low-voltage high-speed modulation," IEEE Photon. Technol. Lett. 17, 414-416, (2005).
[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]

Dapkus, P. D.

T. Sadagopan, S. J. Choi, K. Djordjev, and P. D. Dapkus, "Carrier-induced refractive index changes in InP-based circular microresonators for low-voltage high-speed modulation," IEEE Photon. Technol. Lett. 17, 414-416, (2005).
[CrossRef]

Djordjev, K.

T. Sadagopan, S. J. Choi, K. Djordjev, and P. D. Dapkus, "Carrier-induced refractive index changes in InP-based circular microresonators for low-voltage high-speed modulation," IEEE Photon. Technol. Lett. 17, 414-416, (2005).
[CrossRef]

Fattal, D.

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]

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]

Heebner, J. E.

J. E. Heebner and R. W. Boyd, "'Slow' and 'fast' light in resonator-coupled waveguides," J. Mod. Opt. 49, 2629-2636 (2002).
[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]

Lee, R. K.

Li, C.

Li, Y.

Lipson, M.

S. Manipatruni, Q. Xu, and M. Lipson, "PINIP based high-speed high-extinction ratio micron-size silicon electro-optic modulator," Opt. Express 15, 13035-13042 (2007).
[CrossRef] [PubMed]

C. A. Barrios and M. Lipson, "Modeling and analysis of high-speed electro-optic modulation in high confinement silicon waveguides using metal-oxide-semiconductor configuration," J. Appl. Phys. 96, 6008-6015 (2004).
[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]

Manipatruni, S.

Poon, A. W.

Sadagopan, T.

T. Sadagopan, S. J. Choi, K. Djordjev, and P. D. Dapkus, "Carrier-induced refractive index changes in InP-based circular microresonators for low-voltage high-speed modulation," IEEE Photon. Technol. Lett. 17, 414-416, (2005).
[CrossRef]

Scherer, A.

Song, M.

Willner, A. E.

Xu, Q.

Xu, Y.

Yang, J.-Y.

Yariv, A.

Zhang, B.

Zhang, L.

Zhou, L.

IEEE Photon. Technol. Lett. (1)

T. Sadagopan, S. J. Choi, K. Djordjev, and P. D. Dapkus, "Carrier-induced refractive index changes in InP-based circular microresonators for low-voltage high-speed modulation," IEEE Photon. Technol. Lett. 17, 414-416, (2005).
[CrossRef]

J. Appl. Phys. (1)

C. A. Barrios and M. Lipson, "Modeling and analysis of high-speed electro-optic modulation in high confinement silicon waveguides using metal-oxide-semiconductor configuration," J. Appl. Phys. 96, 6008-6015 (2004).
[CrossRef]

J. Lightwave Technol. (2)

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]

C. A. Barrios, "Electrooptic modulation of multisilicon-on-insulator photonic wires," J. Lightwave Technol. 24, 2146-2155 (2006)
[CrossRef]

J. Mod. Opt. (1)

J. E. Heebner and R. W. Boyd, "'Slow' and 'fast' light in resonator-coupled waveguides," J. Mod. Opt. 49, 2629-2636 (2002).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Other (5)

R. D. Kekatpure and M. L. Brongersma, "CMOS compatible high-speed electro-optical modulator," Proc. SPIE 5926, paper G1 (2005)
[CrossRef]

E. Hecht, Optics (3rd edition), (Addison Wesley Longman, Inc, 1998) Chap. 9.

H. A. Haus, Waves and Fields in Optoelectronics (Prentic-Hall, Inc. Englewood Cliffs New Jersey 07632, 1984) Chap. 7.
[CrossRef] [PubMed]

L. Zhang, M. Song, T. Wu, L. Zou, R. G. Beausoleil and A. E. Willner, "Embedded ring resonators for micro-photonic applications," Opt. Lett.  33, to be published in issue no. 17, 2008.

T. Sadagopan, S. J. Choi, S. J. Choi, P. D. Dapkus, and A. E. Bond, "High-speed, low-voltage modulation in circular WGM micro-resonators," 2004 IEEE/LEOS Summer Topical Meetings (LEOS, San Diego, Calif, 2004) MC2-3.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Single ring modulator scheme. (b) The proposed coupled-ring modulator scheme: only the ring adjacent to waveguide is driven, which requires smaller resonance shift and enables higher modulation speed and higher extinction ratio.

Fig. 2.
Fig. 2.

Comparison among the three examples of the modulation of a 60-Gb/s NRZ signal shows that the proposed modulator requires 1/3 resonance shift (R.S.) to achieve the modulation with negligible distortion compared to the critically coupled sing ring modulator. All figures are plotted in the same scale with the same output power.

Fig. 3.
Fig. 3.

Modulation bandwidth and extinction ratio versus the ring-to-waveguide coupling coefficient κ1 for the (a) single ring and (b) coupled ring modulators.

Fig. 4.
Fig. 4.

(a) Extinction ratio versus the coupling coefficient κ2 between the inner and outer rings. Critical coupling occurs around κ2=0.013 and the extinction ratio tends to be infinite. (b) Frequency chirp is switched from negative to positive as κ2 increases.

Fig. 5.
Fig. 5.

(a) Back-to-back BER curves of the 60-Gb/s NRZ signals modulated with the single ring (linewidth=60 GHz, resonance shift=60 GHz and 20 GHz) and coupled-ring modulators (linewidth=20 GHz, resonance=20 GHz). (b) A 40-Gb/s NRZ signal under different chromatic dispersion values, where the coupled-ring modulators with different effective chirps are achieved by varying the ring–to- ring coupling coefficient κ2.

Equations (6)

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d d t a 1 = ( j ω 1 1 τ o 1 1 τ e ) a 1 + j μ 2 a 2 + j μ 1 E in
d d t a 2 = ( j ω 2 1 τ o 2 ) a 2 + j μ 2 a 1
E out = E in + j μ 1 a 1
d d t a 1 2 = 2 τ e a 1 2 2 τ o 1 a 1 2 + 2 j μ 1 · Im ( E in a 1 * )
d d t a 1 2 = 2 τ e a 1 2 2 τ o 1 a 1 2 2 j μ 2 · Im ( a 1 a 2 * ) + 2 j μ 1 · Im ( E in a 1 * )
d d t a 2 2 = 2 τ o 2 a 2 2 + 2 j μ 2 · Im ( a 1 a 2 * )

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