Abstract

We study the nonlinear distortions of a silicon ring modulator based on the carrier depletion effect for analog links. Key sources of modulation nonlinearity are identified and modeled. We find that the most important source of nonlinearity is from the pn junction itself, as opposed to the nonlinear wavelength response of the ring modulator. Spurious free dynamic range for intermodulation distortion of as high as 84 dB.Hz2/3 is obtained.

©2012 Optical Society of America

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References

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  1. H. L. R. Lira, S. Manipatruni, and M. Lipson, “Broadband hitless silicon electro-optic switch for on-chip optical networks,” Opt. Express 17(25), 22271–22280 (2009).
    [Crossref] [PubMed]
  2. P. Rabiei and W. H. Steier, “Tunable polymer double micro-ring filters,” Photon. Technol. Lett. 15(9), 1255–1257 (2003).
    [Crossref]
  3. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
    [Crossref] [PubMed]
  4. F. Y. Gardes, A. Brimont, P. Sanchis, G. Rasigade, D. Marris-Morini, L. O’Faolain, F. Dong, J. M. Fedeli, P. Dumon, L. Vivien, T. F. Krauss, G. T. Reed, and J. Martí, “High-speed modulation of a compact silicon ring resonator based on a reverse-biased pn diode,” Opt. Express 17(24), 21986–21991 (2009).
    [Crossref] [PubMed]
  5. M. Gould, T. Baehr-Jones, R. Ding, S. Huang, J. Luo, A. K.-Y. Jen, J.-M. Fedeli, M. Fournier, and M. Hochberg, “Silicon-polymer hybrid slot waveguide ring-resonator modulator,” Opt. Express 19(5), 3952–3961 (2011).
    [Crossref] [PubMed]
  6. R. A. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microw. Theory Tech. 54(2), 832–846 (2006).
    [Crossref]
  7. C. H. Cox, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the performance of RF-over-fiber links and their impact on device design,” IEEE Trans. Microw. Theory Tech. 54(2), 906–920 (2006).
    [Crossref]
  8. I. Gasulla and J. Capmany, “Analysis of the harmonic and intermodulation distortion in a multimode fiber optic link,” Opt. Express 15(15), 9366–9371 (2007).
    [Crossref] [PubMed]
  9. J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009).
    [Crossref]
  10. W. B. Bridges and J. H. Schaffner, “Distortion in linearized electrooptic modulators,” IEEE Trans. Microw. Theory Tech. 43(9), 2184–2197 (1995).
    [Crossref]
  11. S. Dubovitsky, W. H. Steier, S. Yegnanarayanan, and B. Jalali, “Analysis and improvement of Mach-Zehnder modulator linearity performance for chirped and tunable optical carriers,” J. Lightwave Technol. 20(5), 886–891 (2002).
    [Crossref]
  12. H. Tazawa and W. H. Steier, “Linearity of ring resonator-based electrooptic polymer modulator,” Electron. Lett. 41(23), 1297–1298 (2005).
    [Crossref]
  13. T. Ismail, C.-P. Liu, J. E. Mitchell, and A. J. Seeds, “High-dynamic- range wireless-over-fiber link using feed forward linearization,” J. Lightwave Technol. 25(11), 3274–3282 (2007).
    [Crossref]
  14. M. Song, L. Zhang, R. G. Beausoleil, and A. E. Willner, “Nonlinear distortion in a silicon microring-based electro-optic modulator for analog optical links,” IEEE J. Sel. Top. Quantum Electron. 16, 185–191 (2010).
  15. B. Dingel, A. Prescod, N. Madamopoulos, and R. Madabhushi, “Performance of ring resonator-based linear optical modulator (IMPACC) under Critical Coupling (CC), Over Coupling (OC), and Under Coupling (UC) conditions,” IEEE Photonics Conference (PHO) 260–261 (2011).
  16. C. Kittel, Introduction to Solid State Physics, 5th ed.(Wiley), (1976).
  17. http://www.ime.a-star.edu.sg/PPSSite/index.asp
  18. R. A. Soref and B. R. Bennet, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
    [Crossref]
  19. A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
    [Crossref]
  20. J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40(6), 726–730 (2004).
    [Crossref]

2011 (1)

2010 (1)

M. Song, L. Zhang, R. G. Beausoleil, and A. E. Willner, “Nonlinear distortion in a silicon microring-based electro-optic modulator for analog optical links,” IEEE J. Sel. Top. Quantum Electron. 16, 185–191 (2010).

2009 (3)

2007 (2)

2006 (2)

R. A. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microw. Theory Tech. 54(2), 832–846 (2006).
[Crossref]

C. H. Cox, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the performance of RF-over-fiber links and their impact on device design,” IEEE Trans. Microw. Theory Tech. 54(2), 906–920 (2006).
[Crossref]

2005 (2)

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref] [PubMed]

H. Tazawa and W. H. Steier, “Linearity of ring resonator-based electrooptic polymer modulator,” Electron. Lett. 41(23), 1297–1298 (2005).
[Crossref]

2004 (1)

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40(6), 726–730 (2004).
[Crossref]

2003 (1)

P. Rabiei and W. H. Steier, “Tunable polymer double micro-ring filters,” Photon. Technol. Lett. 15(9), 1255–1257 (2003).
[Crossref]

2002 (1)

S. Dubovitsky, W. H. Steier, S. Yegnanarayanan, and B. Jalali, “Analysis and improvement of Mach-Zehnder modulator linearity performance for chirped and tunable optical carriers,” J. Lightwave Technol. 20(5), 886–891 (2002).
[Crossref]

2000 (1)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
[Crossref]

1995 (1)

W. B. Bridges and J. H. Schaffner, “Distortion in linearized electrooptic modulators,” IEEE Trans. Microw. Theory Tech. 43(9), 2184–2197 (1995).
[Crossref]

1987 (1)

R. A. Soref and B. R. Bennet, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Ackerman, E. I.

C. H. Cox, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the performance of RF-over-fiber links and their impact on device design,” IEEE Trans. Microw. Theory Tech. 54(2), 906–920 (2006).
[Crossref]

Baehr-Jones, T.

Beausoleil, R. G.

M. Song, L. Zhang, R. G. Beausoleil, and A. E. Willner, “Nonlinear distortion in a silicon microring-based electro-optic modulator for analog optical links,” IEEE J. Sel. Top. Quantum Electron. 16, 185–191 (2010).

Bennet, B. R.

R. A. Soref and B. R. Bennet, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Betts, G. E.

C. H. Cox, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the performance of RF-over-fiber links and their impact on device design,” IEEE Trans. Microw. Theory Tech. 54(2), 906–920 (2006).
[Crossref]

Boyd, R. W.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40(6), 726–730 (2004).
[Crossref]

Bridges, W. B.

W. B. Bridges and J. H. Schaffner, “Distortion in linearized electrooptic modulators,” IEEE Trans. Microw. Theory Tech. 43(9), 2184–2197 (1995).
[Crossref]

Brimont, A.

Capmany, J.

Cox, C. H.

C. H. Cox, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the performance of RF-over-fiber links and their impact on device design,” IEEE Trans. Microw. Theory Tech. 54(2), 906–920 (2006).
[Crossref]

Ding, R.

Dong, F.

Dubovitsky, S.

S. Dubovitsky, W. H. Steier, S. Yegnanarayanan, and B. Jalali, “Analysis and improvement of Mach-Zehnder modulator linearity performance for chirped and tunable optical carriers,” J. Lightwave Technol. 20(5), 886–891 (2002).
[Crossref]

Dumon, P.

Fedeli, J. M.

Fedeli, J.-M.

Fournier, M.

Gardes, F. Y.

Gasulla, I.

Gould, M.

Heebner, J. E.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40(6), 726–730 (2004).
[Crossref]

Hochberg, M.

Huang, S.

Ismail, T.

Jackson, D. J.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40(6), 726–730 (2004).
[Crossref]

Jalali, B.

S. Dubovitsky, W. H. Steier, S. Yegnanarayanan, and B. Jalali, “Analysis and improvement of Mach-Zehnder modulator linearity performance for chirped and tunable optical carriers,” J. Lightwave Technol. 20(5), 886–891 (2002).
[Crossref]

Jen, A. K.-Y.

Krauss, T. F.

Lipson, M.

Lira, H. L. R.

Liu, C.-P.

Luo, J.

Manipatruni, S.

Marris-Morini, D.

Martí, J.

Minasian, R. A.

R. A. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microw. Theory Tech. 54(2), 832–846 (2006).
[Crossref]

Mitchell, J. E.

O’Faolain, L.

Pradhan, S.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref] [PubMed]

Prince, J. L.

C. H. Cox, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the performance of RF-over-fiber links and their impact on device design,” IEEE Trans. Microw. Theory Tech. 54(2), 906–920 (2006).
[Crossref]

Rabiei, P.

P. Rabiei and W. H. Steier, “Tunable polymer double micro-ring filters,” Photon. Technol. Lett. 15(9), 1255–1257 (2003).
[Crossref]

Rasigade, G.

Reed, G. T.

Sanchis, P.

Schaffner, J. H.

W. B. Bridges and J. H. Schaffner, “Distortion in linearized electrooptic modulators,” IEEE Trans. Microw. Theory Tech. 43(9), 2184–2197 (1995).
[Crossref]

Schmidt, B.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref] [PubMed]

Schweinsberg, A.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40(6), 726–730 (2004).
[Crossref]

Seeds, A. J.

Song, M.

M. Song, L. Zhang, R. G. Beausoleil, and A. E. Willner, “Nonlinear distortion in a silicon microring-based electro-optic modulator for analog optical links,” IEEE J. Sel. Top. Quantum Electron. 16, 185–191 (2010).

Soref, R. A.

R. A. Soref and B. R. Bennet, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Steier, W. H.

H. Tazawa and W. H. Steier, “Linearity of ring resonator-based electrooptic polymer modulator,” Electron. Lett. 41(23), 1297–1298 (2005).
[Crossref]

P. Rabiei and W. H. Steier, “Tunable polymer double micro-ring filters,” Photon. Technol. Lett. 15(9), 1255–1257 (2003).
[Crossref]

S. Dubovitsky, W. H. Steier, S. Yegnanarayanan, and B. Jalali, “Analysis and improvement of Mach-Zehnder modulator linearity performance for chirped and tunable optical carriers,” J. Lightwave Technol. 20(5), 886–891 (2002).
[Crossref]

Tazawa, H.

H. Tazawa and W. H. Steier, “Linearity of ring resonator-based electrooptic polymer modulator,” Electron. Lett. 41(23), 1297–1298 (2005).
[Crossref]

Vivien, L.

Willner, A. E.

M. Song, L. Zhang, R. G. Beausoleil, and A. E. Willner, “Nonlinear distortion in a silicon microring-based electro-optic modulator for analog optical links,” IEEE J. Sel. Top. Quantum Electron. 16, 185–191 (2010).

Wong, V.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40(6), 726–730 (2004).
[Crossref]

Xu, Q.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref] [PubMed]

Yao, J.

Yariv, A.

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
[Crossref]

Yegnanarayanan, S.

S. Dubovitsky, W. H. Steier, S. Yegnanarayanan, and B. Jalali, “Analysis and improvement of Mach-Zehnder modulator linearity performance for chirped and tunable optical carriers,” J. Lightwave Technol. 20(5), 886–891 (2002).
[Crossref]

Zhang, L.

M. Song, L. Zhang, R. G. Beausoleil, and A. E. Willner, “Nonlinear distortion in a silicon microring-based electro-optic modulator for analog optical links,” IEEE J. Sel. Top. Quantum Electron. 16, 185–191 (2010).

Electron. Lett. (2)

H. Tazawa and W. H. Steier, “Linearity of ring resonator-based electrooptic polymer modulator,” Electron. Lett. 41(23), 1297–1298 (2005).
[Crossref]

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
[Crossref]

IEEE J. Quantum Electron. (2)

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40(6), 726–730 (2004).
[Crossref]

R. A. Soref and B. R. Bennet, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

M. Song, L. Zhang, R. G. Beausoleil, and A. E. Willner, “Nonlinear distortion in a silicon microring-based electro-optic modulator for analog optical links,” IEEE J. Sel. Top. Quantum Electron. 16, 185–191 (2010).

IEEE Trans. Microw. Theory Tech. (3)

R. A. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microw. Theory Tech. 54(2), 832–846 (2006).
[Crossref]

C. H. Cox, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the performance of RF-over-fiber links and their impact on device design,” IEEE Trans. Microw. Theory Tech. 54(2), 906–920 (2006).
[Crossref]

W. B. Bridges and J. H. Schaffner, “Distortion in linearized electrooptic modulators,” IEEE Trans. Microw. Theory Tech. 43(9), 2184–2197 (1995).
[Crossref]

J. Lightwave Technol. (3)

S. Dubovitsky, W. H. Steier, S. Yegnanarayanan, and B. Jalali, “Analysis and improvement of Mach-Zehnder modulator linearity performance for chirped and tunable optical carriers,” J. Lightwave Technol. 20(5), 886–891 (2002).
[Crossref]

T. Ismail, C.-P. Liu, J. E. Mitchell, and A. J. Seeds, “High-dynamic- range wireless-over-fiber link using feed forward linearization,” J. Lightwave Technol. 25(11), 3274–3282 (2007).
[Crossref]

J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009).
[Crossref]

Nature (1)

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref] [PubMed]

Opt. Express (4)

Photon. Technol. Lett. (1)

P. Rabiei and W. H. Steier, “Tunable polymer double micro-ring filters,” Photon. Technol. Lett. 15(9), 1255–1257 (2003).
[Crossref]

Other (3)

B. Dingel, A. Prescod, N. Madamopoulos, and R. Madabhushi, “Performance of ring resonator-based linear optical modulator (IMPACC) under Critical Coupling (CC), Over Coupling (OC), and Under Coupling (UC) conditions,” IEEE Photonics Conference (PHO) 260–261 (2011).

C. Kittel, Introduction to Solid State Physics, 5th ed.(Wiley), (1976).

http://www.ime.a-star.edu.sg/PPSSite/index.asp

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Figures (7)

Fig. 1
Fig. 1 Steady state transfer function of the silicon ring modulator.

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Fig. 2
Fig. 2 Cross-section of the rib waveguides of the ring modulator.

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Fig. 3
Fig. 3 Device Layout. Optical micrograph of the ring modulator. Note that the insets with the highest magnification are renderings of the mask layout, instead of micrographs.

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Fig. 4
Fig. 4 Distribution of doping concentration in the cross-section of the device.

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Fig. 5
Fig. 5 Measured and simulated results of the effective refractive index change vs. input voltage.

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Fig. 6
Fig. 6 Detected RF power of the carrier frequency (1030 MHz) and SHD (at 2060 MHz) at 10 kHz resolution bandwidth.

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Fig. 7
Fig. 7 SFDR of the ring due to second harmonic and IMD distortion. Dots represent measured values.

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Equations (5)

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

Δn=Δ n e +Δ n h =−[ 8.8× 10 −22 ΔN+8.5× 10 −18 ( ΔP ) 0.8 ]
n eff ( t )= n eo + d n eff dV ⋅ V in ( t )+ d 2 n eff d V 2 ⋅ V in 2 ( t )+⋯
P op ( t )= P out,max ⋅[ 1− 1 1+ 4 F 2 π 2 si n 2 ( 2 π 2 ⋅r⋅ n eff ( t )⋅ f o c ) ]
I RF = R PD ⋅ P op
V in ( t )= V o1 ⋅sin( 2π f 1 t )+ V o2 ⋅sin( 2π f 2 t )

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