Abstract

The electrical nonlinearity of silicon modulators based on reversed PN junctions was found to severely limit the linearity of the modulators. This effect, however, was inadvertently neglected in previous studies. Considering the electrical nonlinearity in simulation, a 32.2 dB degradation in the CDR3 (i.e., the suppression ratio between the fundamental signal and intermodulation distortion) of the modulator was observed at a modulation speed of 12 GHz, and the spurious free dynamic range was simultaneously degraded by 17.4 dB. It was also found that the linearity of the silicon modulator could be improved by reducing the series resistance of the PN junction. The frequency dependence of the linearity due to the electrical nonlinearity was also investigated.

© 2017 Chinese Laser Press

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Corrections

17 March 2017: Corrections were made to the body text.


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References

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  1. J. Yao, “Microwave photonics,” J. Lightwave Technol. 27, 314–335 (2009).
    [Crossref]
  2. J. C. Fan, C. L. Lu, and L. G. Kazovsky, “Dynamic range requirements for microcellular personal communication systems using analog fiber-optic links,” IEEE Trans. Microwave Theory Tech. 45, 1390–1397 (1997).
    [Crossref]
  3. J. E. Roman, L. T. Nichols, and K. J. Williams, “Fiber-optic remoting of an ultrahigh dynamic range radar,” IEEE Trans. Microwave Theory Tech. 46, 2317–2323 (1998).
    [Crossref]
  4. J. Capmany, B. Ortega, and D. Pastor, “A tutorial on microwave photonic filters,” J. Lightwave Technol. 24, 201–229 (2006).
    [Crossref]
  5. C. H. Cox, E. I. Ackerman, and G. E. Betts, “Limits on the performance of RF-over-fiber links and their impact on device design,” IEEE Trans. Microwave Theory Tech. 54, 906–920 (2006).
    [Crossref]
  6. D. Marpaung, C. Roeloffzen, and R. Heideman, “Integrated microwave photonics,” Laser Photon. Rev. 7, 506–538 (2013).
    [Crossref]
  7. G. T. Reed, G. Mashanovich, and F. Y. Gardes, “Silicon optical modulators,” Nat. Photonics 4, 518–526 (2010).
    [Crossref]
  8. T. Chu, X. Xiao, H. Xu, X. Li, Z. Li, J. Yu, and Y. Yu, “High-speed silicon modulators,” in 39th European Conference and Exhibition on Optical Communication (ECOC) (2013), pp. 1–3.
  9. D. Patel, S. Ghosh, and M. Chagnon, “Design, analysis, and transmission system performance of a 41  GHz silicon photonic modulator,” Opt. Express 23, 14263–14287 (2015).
    [Crossref]
  10. A. Khilo, C. M. Sorace, and F. X. Kärtner, “Broadband linearized silicon modulator,” Opt. Express 19, 4485–4500 (2011).
    [Crossref]
  11. A. M. Gutierrez, A. Brimont, and J. Herrera, “Analytical model for calculating the nonlinear distortion in silicon-based electro-optic Mach–Zehnder modulators,” J. Lightwave Technol. 31, 3603–3613 (2013).
    [Crossref]
  12. J. Cardenas, P. A. Morton, and J. B. Khurgin, “Linearized silicon modulator based on a ring assisted Mach—Zehnder interferometer,” Opt. Express 21, 22549–22557 (2013).
    [Crossref]
  13. F. Vacondio, M. Mirshafiei, J. Basak, A. Liu, L. Liao, M. Paniccia, and L. Rusch, “Linearized silicon modulator based on a ring assisted Mach–Zehnder interferometer,” IEEE J. Sel. Top. Quantum Electron. 16, 141–148 (2010).
    [Crossref]
  14. A. Ayazi, T. Baehr-Jones, Y. Liu, A. E.-J. Lim, and M. Hochberg, “Linearity of silicon ring modulators for analog optical links,” Opt. Express 20, 13115–13122 (2012).
    [Crossref]
  15. M. Streshinsky, A. Ayazi, Z. Xuan, A. E.-J. Lim, G. Q. Lo, T. Baehr-Jones, and M. Hochberg, “Highly linear silicon traveling wave Mach–Zehnder carrier depletion modulator based on differential drive,” Opt. Express 21, 3818–3825 (2013).
    [Crossref]
  16. Y. Zhou, L. Zhou, and F. Su, “Linearity measurement and pulse amplitude modulation in a silicon single-drive push-pull Mach–Zehnder modulator,” J. Lightwave Technol. 34, 3323–3329 (2016).
    [Crossref]
  17. J. C. Pedro and N. B. Carvalho, Intermodulation Distortion in Microwave and Wireless Circuits (Artech House, 2002).
  18. S. L. Chuang, Physics of Optoelectronic Devices (Wiley, 1995).
  19. H. Xu, X. Li, X. Xiao, P. Zhou, Z. Li, J. Yu, and Y. Yu, “High-speed silicon modulator with band equalization,” Opt. Lett. 39, 4839–4842 (2014).
    [Crossref]

2016 (1)

2015 (1)

2014 (1)

2013 (4)

2012 (1)

2011 (1)

2010 (2)

G. T. Reed, G. Mashanovich, and F. Y. Gardes, “Silicon optical modulators,” Nat. Photonics 4, 518–526 (2010).
[Crossref]

F. Vacondio, M. Mirshafiei, J. Basak, A. Liu, L. Liao, M. Paniccia, and L. Rusch, “Linearized silicon modulator based on a ring assisted Mach–Zehnder interferometer,” IEEE J. Sel. Top. Quantum Electron. 16, 141–148 (2010).
[Crossref]

2009 (1)

2006 (2)

J. Capmany, B. Ortega, and D. Pastor, “A tutorial on microwave photonic filters,” J. Lightwave Technol. 24, 201–229 (2006).
[Crossref]

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

1998 (1)

J. E. Roman, L. T. Nichols, and K. J. Williams, “Fiber-optic remoting of an ultrahigh dynamic range radar,” IEEE Trans. Microwave Theory Tech. 46, 2317–2323 (1998).
[Crossref]

1997 (1)

J. C. Fan, C. L. Lu, and L. G. Kazovsky, “Dynamic range requirements for microcellular personal communication systems using analog fiber-optic links,” IEEE Trans. Microwave Theory Tech. 45, 1390–1397 (1997).
[Crossref]

Ackerman, E. I.

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

Ayazi, A.

Baehr-Jones, T.

Basak, J.

F. Vacondio, M. Mirshafiei, J. Basak, A. Liu, L. Liao, M. Paniccia, and L. Rusch, “Linearized silicon modulator based on a ring assisted Mach–Zehnder interferometer,” IEEE J. Sel. Top. Quantum Electron. 16, 141–148 (2010).
[Crossref]

Betts, G. E.

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

Brimont, A.

Capmany, J.

Cardenas, J.

Carvalho, N. B.

J. C. Pedro and N. B. Carvalho, Intermodulation Distortion in Microwave and Wireless Circuits (Artech House, 2002).

Chagnon, M.

Chu, T.

T. Chu, X. Xiao, H. Xu, X. Li, Z. Li, J. Yu, and Y. Yu, “High-speed silicon modulators,” in 39th European Conference and Exhibition on Optical Communication (ECOC) (2013), pp. 1–3.

Chuang, S. L.

S. L. Chuang, Physics of Optoelectronic Devices (Wiley, 1995).

Cox, C. H.

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

Fan, J. C.

J. C. Fan, C. L. Lu, and L. G. Kazovsky, “Dynamic range requirements for microcellular personal communication systems using analog fiber-optic links,” IEEE Trans. Microwave Theory Tech. 45, 1390–1397 (1997).
[Crossref]

Gardes, F. Y.

G. T. Reed, G. Mashanovich, and F. Y. Gardes, “Silicon optical modulators,” Nat. Photonics 4, 518–526 (2010).
[Crossref]

Ghosh, S.

Gutierrez, A. M.

Heideman, R.

D. Marpaung, C. Roeloffzen, and R. Heideman, “Integrated microwave photonics,” Laser Photon. Rev. 7, 506–538 (2013).
[Crossref]

Herrera, J.

Hochberg, M.

Kärtner, F. X.

Kazovsky, L. G.

J. C. Fan, C. L. Lu, and L. G. Kazovsky, “Dynamic range requirements for microcellular personal communication systems using analog fiber-optic links,” IEEE Trans. Microwave Theory Tech. 45, 1390–1397 (1997).
[Crossref]

Khilo, A.

Khurgin, J. B.

Li, X.

H. Xu, X. Li, X. Xiao, P. Zhou, Z. Li, J. Yu, and Y. Yu, “High-speed silicon modulator with band equalization,” Opt. Lett. 39, 4839–4842 (2014).
[Crossref]

T. Chu, X. Xiao, H. Xu, X. Li, Z. Li, J. Yu, and Y. Yu, “High-speed silicon modulators,” in 39th European Conference and Exhibition on Optical Communication (ECOC) (2013), pp. 1–3.

Li, Z.

H. Xu, X. Li, X. Xiao, P. Zhou, Z. Li, J. Yu, and Y. Yu, “High-speed silicon modulator with band equalization,” Opt. Lett. 39, 4839–4842 (2014).
[Crossref]

T. Chu, X. Xiao, H. Xu, X. Li, Z. Li, J. Yu, and Y. Yu, “High-speed silicon modulators,” in 39th European Conference and Exhibition on Optical Communication (ECOC) (2013), pp. 1–3.

Liao, L.

F. Vacondio, M. Mirshafiei, J. Basak, A. Liu, L. Liao, M. Paniccia, and L. Rusch, “Linearized silicon modulator based on a ring assisted Mach–Zehnder interferometer,” IEEE J. Sel. Top. Quantum Electron. 16, 141–148 (2010).
[Crossref]

Lim, A. E.-J.

Liu, A.

F. Vacondio, M. Mirshafiei, J. Basak, A. Liu, L. Liao, M. Paniccia, and L. Rusch, “Linearized silicon modulator based on a ring assisted Mach–Zehnder interferometer,” IEEE J. Sel. Top. Quantum Electron. 16, 141–148 (2010).
[Crossref]

Liu, Y.

Lo, G. Q.

Lu, C. L.

J. C. Fan, C. L. Lu, and L. G. Kazovsky, “Dynamic range requirements for microcellular personal communication systems using analog fiber-optic links,” IEEE Trans. Microwave Theory Tech. 45, 1390–1397 (1997).
[Crossref]

Marpaung, D.

D. Marpaung, C. Roeloffzen, and R. Heideman, “Integrated microwave photonics,” Laser Photon. Rev. 7, 506–538 (2013).
[Crossref]

Mashanovich, G.

G. T. Reed, G. Mashanovich, and F. Y. Gardes, “Silicon optical modulators,” Nat. Photonics 4, 518–526 (2010).
[Crossref]

Mirshafiei, M.

F. Vacondio, M. Mirshafiei, J. Basak, A. Liu, L. Liao, M. Paniccia, and L. Rusch, “Linearized silicon modulator based on a ring assisted Mach–Zehnder interferometer,” IEEE J. Sel. Top. Quantum Electron. 16, 141–148 (2010).
[Crossref]

Morton, P. A.

Nichols, L. T.

J. E. Roman, L. T. Nichols, and K. J. Williams, “Fiber-optic remoting of an ultrahigh dynamic range radar,” IEEE Trans. Microwave Theory Tech. 46, 2317–2323 (1998).
[Crossref]

Ortega, B.

Paniccia, M.

F. Vacondio, M. Mirshafiei, J. Basak, A. Liu, L. Liao, M. Paniccia, and L. Rusch, “Linearized silicon modulator based on a ring assisted Mach–Zehnder interferometer,” IEEE J. Sel. Top. Quantum Electron. 16, 141–148 (2010).
[Crossref]

Pastor, D.

Patel, D.

Pedro, J. C.

J. C. Pedro and N. B. Carvalho, Intermodulation Distortion in Microwave and Wireless Circuits (Artech House, 2002).

Reed, G. T.

G. T. Reed, G. Mashanovich, and F. Y. Gardes, “Silicon optical modulators,” Nat. Photonics 4, 518–526 (2010).
[Crossref]

Roeloffzen, C.

D. Marpaung, C. Roeloffzen, and R. Heideman, “Integrated microwave photonics,” Laser Photon. Rev. 7, 506–538 (2013).
[Crossref]

Roman, J. E.

J. E. Roman, L. T. Nichols, and K. J. Williams, “Fiber-optic remoting of an ultrahigh dynamic range radar,” IEEE Trans. Microwave Theory Tech. 46, 2317–2323 (1998).
[Crossref]

Rusch, L.

F. Vacondio, M. Mirshafiei, J. Basak, A. Liu, L. Liao, M. Paniccia, and L. Rusch, “Linearized silicon modulator based on a ring assisted Mach–Zehnder interferometer,” IEEE J. Sel. Top. Quantum Electron. 16, 141–148 (2010).
[Crossref]

Sorace, C. M.

Streshinsky, M.

Su, F.

Vacondio, F.

F. Vacondio, M. Mirshafiei, J. Basak, A. Liu, L. Liao, M. Paniccia, and L. Rusch, “Linearized silicon modulator based on a ring assisted Mach–Zehnder interferometer,” IEEE J. Sel. Top. Quantum Electron. 16, 141–148 (2010).
[Crossref]

Williams, K. J.

J. E. Roman, L. T. Nichols, and K. J. Williams, “Fiber-optic remoting of an ultrahigh dynamic range radar,” IEEE Trans. Microwave Theory Tech. 46, 2317–2323 (1998).
[Crossref]

Xiao, X.

H. Xu, X. Li, X. Xiao, P. Zhou, Z. Li, J. Yu, and Y. Yu, “High-speed silicon modulator with band equalization,” Opt. Lett. 39, 4839–4842 (2014).
[Crossref]

T. Chu, X. Xiao, H. Xu, X. Li, Z. Li, J. Yu, and Y. Yu, “High-speed silicon modulators,” in 39th European Conference and Exhibition on Optical Communication (ECOC) (2013), pp. 1–3.

Xu, H.

H. Xu, X. Li, X. Xiao, P. Zhou, Z. Li, J. Yu, and Y. Yu, “High-speed silicon modulator with band equalization,” Opt. Lett. 39, 4839–4842 (2014).
[Crossref]

T. Chu, X. Xiao, H. Xu, X. Li, Z. Li, J. Yu, and Y. Yu, “High-speed silicon modulators,” in 39th European Conference and Exhibition on Optical Communication (ECOC) (2013), pp. 1–3.

Xuan, Z.

Yao, J.

Yu, J.

H. Xu, X. Li, X. Xiao, P. Zhou, Z. Li, J. Yu, and Y. Yu, “High-speed silicon modulator with band equalization,” Opt. Lett. 39, 4839–4842 (2014).
[Crossref]

T. Chu, X. Xiao, H. Xu, X. Li, Z. Li, J. Yu, and Y. Yu, “High-speed silicon modulators,” in 39th European Conference and Exhibition on Optical Communication (ECOC) (2013), pp. 1–3.

Yu, Y.

H. Xu, X. Li, X. Xiao, P. Zhou, Z. Li, J. Yu, and Y. Yu, “High-speed silicon modulator with band equalization,” Opt. Lett. 39, 4839–4842 (2014).
[Crossref]

T. Chu, X. Xiao, H. Xu, X. Li, Z. Li, J. Yu, and Y. Yu, “High-speed silicon modulators,” in 39th European Conference and Exhibition on Optical Communication (ECOC) (2013), pp. 1–3.

Zhou, L.

Zhou, P.

Zhou, Y.

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

F. Vacondio, M. Mirshafiei, J. Basak, A. Liu, L. Liao, M. Paniccia, and L. Rusch, “Linearized silicon modulator based on a ring assisted Mach–Zehnder interferometer,” IEEE J. Sel. Top. Quantum Electron. 16, 141–148 (2010).
[Crossref]

IEEE Trans. Microwave Theory Tech. (3)

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

J. C. Fan, C. L. Lu, and L. G. Kazovsky, “Dynamic range requirements for microcellular personal communication systems using analog fiber-optic links,” IEEE Trans. Microwave Theory Tech. 45, 1390–1397 (1997).
[Crossref]

J. E. Roman, L. T. Nichols, and K. J. Williams, “Fiber-optic remoting of an ultrahigh dynamic range radar,” IEEE Trans. Microwave Theory Tech. 46, 2317–2323 (1998).
[Crossref]

J. Lightwave Technol. (4)

Laser Photon. Rev. (1)

D. Marpaung, C. Roeloffzen, and R. Heideman, “Integrated microwave photonics,” Laser Photon. Rev. 7, 506–538 (2013).
[Crossref]

Nat. Photonics (1)

G. T. Reed, G. Mashanovich, and F. Y. Gardes, “Silicon optical modulators,” Nat. Photonics 4, 518–526 (2010).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Other (3)

J. C. Pedro and N. B. Carvalho, Intermodulation Distortion in Microwave and Wireless Circuits (Artech House, 2002).

S. L. Chuang, Physics of Optoelectronic Devices (Wiley, 1995).

T. Chu, X. Xiao, H. Xu, X. Li, Z. Li, J. Yu, and Y. Yu, “High-speed silicon modulators,” in 39th European Conference and Exhibition on Optical Communication (ECOC) (2013), pp. 1–3.

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Figures (8)

Fig. 1.
Fig. 1. (a) Equivalent circuit for the reversed PN junction and (b) relationship between the depletion capacitance and reverse bias voltage.
Fig. 2.
Fig. 2. (a) Cross-section of a silicon phase shifter based on a vertical PN junction. (b–d) Calculated nonlinear relationships of the optical phase change, absorption coefficient change, and depletion capacitance versus the different reverse bias voltages and the fitting results.
Fig. 3.
Fig. 3. Simulated spectrum of the EN output V c ( t ) : (a) power distribution and (b) phase distribution.
Fig. 4.
Fig. 4. Composition of the spectrum of P out ( t ) .
Fig. 5.
Fig. 5. (a) Structure of the simulated MZM, (b) CDR3 under different phase biases for the nonlinear model with EN and the conventional nonlinear model without EN, and (c) SFDR results for the nonlinear model with EN and the conventional nonlinear model without EN.
Fig. 6.
Fig. 6. (a) Optimized CDR3 under different series resistances and (b) SFDR when the series resistance is 1 or 10    Ω .
Fig. 7.
Fig. 7. Normalized CDR3 versus the driving frequency (the black line shows that the linearity is frequency-independent without EN).
Fig. 8.
Fig. 8. Third nonlinear coefficient versus the phase bias.

Equations (7)

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

V in ( t ) = d ( C p ( V c ( t ) ) V c ( t ) ) d t R S + V c ( t ) ,
C p ( V c ( t ) ) = C 0 ( 1 + V c ( t ) v B ) 1 2 .
φ ( t ) = a 1 V c ( t ) + a 2 V c 2 ( t ) + a 3 V c 3 ( t ) ,
α ( t ) = b 1 V c ( t ) + b 2 V c 2 ( t ) + b 3 V c 3 ( t ) ,
P out ( t ) = c 1 ϕ ( t ) + c 2 ϕ 2 ( t ) + c 3 ϕ 3 ( t ) + d 1 α ( t ) + d 2 α 2 ( t ) + d 3 α 3 ( t ) .
P ( V ) = 1 2 exp ( α ( V ) 2 ) cos ( φ ( V ) + θ ) + 1 4 exp ( α ( V ) ) + 1 4 .
C 3 = cos θ ( 1 8 b 1 b 2 1 4 b 3 1 96 b 1 3 + 1 8 a 1 2 b 1 1 2 a 1 a 2 ) sin θ ( 1 16 a 1 b 1 2 1 4 a 1 b 2 1 4 a 2 b 1 + 1 2 a 3 1 12 a 1 3 ) + 1 4 ( b 1 b 2 b 3 1 6 b 1 3 ) .

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