Abstract

We characterize the electro-optic frequency response of a four-port traveling-wave dual-drive modulator with relatively strong coupling amongst the electrodes. We show that the electro-optic frequency response of the MZM can still be predicted with the 2×2 cascaded matrix model if the MZM is symmetric and differentially driven.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. P. Dong, L. Chen, and Y.-K. Chen, “High-speed low-voltage single-drive push-pull silicon Mach-Zehnder modulators,” Opt. Express 20(6), 6163–6169 (2012).
    [Crossref] [PubMed]
  2. D. Patel, S. Ghosh, M. Chagnon, A. Samani, V. Veerasubramanian, M. Osman, and D. V. Plant, “Design, analysis, and transmission system performance of a 41 GHz silicon photonic modulator,” Opt. Express 23(11), 14263–14287 (2015).
    [Crossref] [PubMed]
  3. A. Samani, M. Chagnon, D. Patel, V. Veerasubramanian, S. Ghosh, M. Osman, Q. Zhong, and D. V. Plant, “A Low-Voltage 35-GHz Silicon Photonic Modulator-Enabled 112-Gb/s Transmission System,” in IEEE Photon. J. 7, 3 (2015).
    [Crossref]
  4. X. Tu, K. F. Chang, T. Y. Liow, J. Song, X. Luo, L. Jia, Q. Fang, M. Yu, G. Q. Lo, P. Dong, and Y. K. Chen, “Silicon optical modulator with shield coplanar waveguide electrodes,” Opt. Express 22(19), 23724–23731 (2014).
    [Crossref] [PubMed]
  5. R. Ding, Y. Liu, Q. Li, Y. Yang, Y. Ma, K. Padmaraju, A. E. J. Lim, G. Q. Lo, K. Bergman, T. Baehr-Jones, and M. Hochberg, “Design and characterization of a 30- GHz bandwidth low-power silicon traveling-wave modulator,” Opt. Commun. 321, 124–133 (2014).
    [Crossref]
  6. G. Li, T. Mason, and P. Yu, “Analysis of segmented traveling-wave optical modulators,” J. Lightwave Technol. 22(7), 1789–1796 (2004).
    [Crossref]
  7. D. E. Bockelman and W. R. Eisenstadt, “Combined differential and common-mode scattering parameters: theory and simulation,” IEEE Trans. Microw. Theory Tech. 43(7), 1530 (1995).
    [Crossref]
  8. K. Vaz and M. Caggiano, “Measurement technique for the extraction of differential S-parameters from single-ended S-parameters,” in 27th International Spring Seminar on Electronics Technology: Meeting the Challenges of Electronics Technology Progress (IEEE 2004), pp. 313–317.
    [Crossref]
  9. A. Huynh, P. Hakansson, and S. Gong, “Mixed-mode S-parameter conversion for networks with coupled differential signals,” in Proceedings of the 37th European Microwave Conference (IEEE, 2007), pp. 238–241.
    [Crossref]
  10. W. R. Eisenstadt and Y. Eo, “S-parameter-based IC interconnect transmission line characterization,” IEEE Trans. Compon., Hybrids. Manuf. Technol 15, 4 (1992).
  11. F. Boeuf, S. Crémer, N. Vulliet, T. Pinguet, A. Mekis, G. Masini, L. Verslegers, P. Sun, A. Ayazi, N. K. Hon, S. Sahni, Y. Chi, B. Orlando, D. Ristoiu, A. Farcy, F. Leverd, L. Broussous, D. Pelissier-Tanon, C. Richard, L. Pinzelli, R. Beneyton, O. Gourhant, E. Gourvest, Y. Le-Friec, D. Monnier, P. Brun, M. Guillermet, D. Benoit, K. Haxaire, J. R. Manouvrier, S. Jan, H. Petiton, J. F. Carpentier, T. Quémerais, C. Durand, D. Gloria, M. Fourel, F. Battegay, Y. Sanchez, E. Batail, F. Baron, P. Delpech, L. Salager, P. De Dobbelaere, and B. Sautreuil, “A multi-wavelength 3D-compatible silicon photonics platform on 300mm SOI wafers for 25Gb/s applications,” 2013 IEEE International Electron Devices Meeting, Washington, DC, 2013, pp. 13.3.1–13.3.4.
    [Crossref]
  12. F. Boeuf, J. F. Carpentier, C. Baudot, P. L. Maitre, and J. R. Manouvrier, “Silicon Photonics Research and Manufacturing Using a 300-mm Wafer Platform” in Silicon Photonics III, Lorenzo Pavesi and David J. Lockwood, ed. (Springer-Verlag, 2016).
  13. D. Frickey, “Conversions between S, Z, Y, h, ABCD, and T parameters which are valid for complex source and load impedances,” IEEE Trans. Microw. Theory Tech. 42(2), 205–211 (1994).
    [Crossref]
  14. L. Chrostowski and M. Hochberg, Silicon Photonics Design (Cambridge University, 2015).

2015 (1)

2014 (2)

X. Tu, K. F. Chang, T. Y. Liow, J. Song, X. Luo, L. Jia, Q. Fang, M. Yu, G. Q. Lo, P. Dong, and Y. K. Chen, “Silicon optical modulator with shield coplanar waveguide electrodes,” Opt. Express 22(19), 23724–23731 (2014).
[Crossref] [PubMed]

R. Ding, Y. Liu, Q. Li, Y. Yang, Y. Ma, K. Padmaraju, A. E. J. Lim, G. Q. Lo, K. Bergman, T. Baehr-Jones, and M. Hochberg, “Design and characterization of a 30- GHz bandwidth low-power silicon traveling-wave modulator,” Opt. Commun. 321, 124–133 (2014).
[Crossref]

2012 (1)

2004 (1)

1995 (1)

D. E. Bockelman and W. R. Eisenstadt, “Combined differential and common-mode scattering parameters: theory and simulation,” IEEE Trans. Microw. Theory Tech. 43(7), 1530 (1995).
[Crossref]

1994 (1)

D. Frickey, “Conversions between S, Z, Y, h, ABCD, and T parameters which are valid for complex source and load impedances,” IEEE Trans. Microw. Theory Tech. 42(2), 205–211 (1994).
[Crossref]

1992 (1)

W. R. Eisenstadt and Y. Eo, “S-parameter-based IC interconnect transmission line characterization,” IEEE Trans. Compon., Hybrids. Manuf. Technol 15, 4 (1992).

Baehr-Jones, T.

R. Ding, Y. Liu, Q. Li, Y. Yang, Y. Ma, K. Padmaraju, A. E. J. Lim, G. Q. Lo, K. Bergman, T. Baehr-Jones, and M. Hochberg, “Design and characterization of a 30- GHz bandwidth low-power silicon traveling-wave modulator,” Opt. Commun. 321, 124–133 (2014).
[Crossref]

Bergman, K.

R. Ding, Y. Liu, Q. Li, Y. Yang, Y. Ma, K. Padmaraju, A. E. J. Lim, G. Q. Lo, K. Bergman, T. Baehr-Jones, and M. Hochberg, “Design and characterization of a 30- GHz bandwidth low-power silicon traveling-wave modulator,” Opt. Commun. 321, 124–133 (2014).
[Crossref]

Bockelman, D. E.

D. E. Bockelman and W. R. Eisenstadt, “Combined differential and common-mode scattering parameters: theory and simulation,” IEEE Trans. Microw. Theory Tech. 43(7), 1530 (1995).
[Crossref]

Chagnon, M.

Chang, K. F.

Chen, L.

Chen, Y. K.

Chen, Y.-K.

Ding, R.

R. Ding, Y. Liu, Q. Li, Y. Yang, Y. Ma, K. Padmaraju, A. E. J. Lim, G. Q. Lo, K. Bergman, T. Baehr-Jones, and M. Hochberg, “Design and characterization of a 30- GHz bandwidth low-power silicon traveling-wave modulator,” Opt. Commun. 321, 124–133 (2014).
[Crossref]

Dong, P.

Eisenstadt, W. R.

D. E. Bockelman and W. R. Eisenstadt, “Combined differential and common-mode scattering parameters: theory and simulation,” IEEE Trans. Microw. Theory Tech. 43(7), 1530 (1995).
[Crossref]

W. R. Eisenstadt and Y. Eo, “S-parameter-based IC interconnect transmission line characterization,” IEEE Trans. Compon., Hybrids. Manuf. Technol 15, 4 (1992).

Eo, Y.

W. R. Eisenstadt and Y. Eo, “S-parameter-based IC interconnect transmission line characterization,” IEEE Trans. Compon., Hybrids. Manuf. Technol 15, 4 (1992).

Fang, Q.

Frickey, D.

D. Frickey, “Conversions between S, Z, Y, h, ABCD, and T parameters which are valid for complex source and load impedances,” IEEE Trans. Microw. Theory Tech. 42(2), 205–211 (1994).
[Crossref]

Ghosh, S.

Gong, S.

A. Huynh, P. Hakansson, and S. Gong, “Mixed-mode S-parameter conversion for networks with coupled differential signals,” in Proceedings of the 37th European Microwave Conference (IEEE, 2007), pp. 238–241.
[Crossref]

Hakansson, P.

A. Huynh, P. Hakansson, and S. Gong, “Mixed-mode S-parameter conversion for networks with coupled differential signals,” in Proceedings of the 37th European Microwave Conference (IEEE, 2007), pp. 238–241.
[Crossref]

Hochberg, M.

R. Ding, Y. Liu, Q. Li, Y. Yang, Y. Ma, K. Padmaraju, A. E. J. Lim, G. Q. Lo, K. Bergman, T. Baehr-Jones, and M. Hochberg, “Design and characterization of a 30- GHz bandwidth low-power silicon traveling-wave modulator,” Opt. Commun. 321, 124–133 (2014).
[Crossref]

Huynh, A.

A. Huynh, P. Hakansson, and S. Gong, “Mixed-mode S-parameter conversion for networks with coupled differential signals,” in Proceedings of the 37th European Microwave Conference (IEEE, 2007), pp. 238–241.
[Crossref]

Jia, L.

Li, G.

Li, Q.

R. Ding, Y. Liu, Q. Li, Y. Yang, Y. Ma, K. Padmaraju, A. E. J. Lim, G. Q. Lo, K. Bergman, T. Baehr-Jones, and M. Hochberg, “Design and characterization of a 30- GHz bandwidth low-power silicon traveling-wave modulator,” Opt. Commun. 321, 124–133 (2014).
[Crossref]

Lim, A. E. J.

R. Ding, Y. Liu, Q. Li, Y. Yang, Y. Ma, K. Padmaraju, A. E. J. Lim, G. Q. Lo, K. Bergman, T. Baehr-Jones, and M. Hochberg, “Design and characterization of a 30- GHz bandwidth low-power silicon traveling-wave modulator,” Opt. Commun. 321, 124–133 (2014).
[Crossref]

Liow, T. Y.

Liu, Y.

R. Ding, Y. Liu, Q. Li, Y. Yang, Y. Ma, K. Padmaraju, A. E. J. Lim, G. Q. Lo, K. Bergman, T. Baehr-Jones, and M. Hochberg, “Design and characterization of a 30- GHz bandwidth low-power silicon traveling-wave modulator,” Opt. Commun. 321, 124–133 (2014).
[Crossref]

Lo, G. Q.

R. Ding, Y. Liu, Q. Li, Y. Yang, Y. Ma, K. Padmaraju, A. E. J. Lim, G. Q. Lo, K. Bergman, T. Baehr-Jones, and M. Hochberg, “Design and characterization of a 30- GHz bandwidth low-power silicon traveling-wave modulator,” Opt. Commun. 321, 124–133 (2014).
[Crossref]

X. Tu, K. F. Chang, T. Y. Liow, J. Song, X. Luo, L. Jia, Q. Fang, M. Yu, G. Q. Lo, P. Dong, and Y. K. Chen, “Silicon optical modulator with shield coplanar waveguide electrodes,” Opt. Express 22(19), 23724–23731 (2014).
[Crossref] [PubMed]

Luo, X.

Ma, Y.

R. Ding, Y. Liu, Q. Li, Y. Yang, Y. Ma, K. Padmaraju, A. E. J. Lim, G. Q. Lo, K. Bergman, T. Baehr-Jones, and M. Hochberg, “Design and characterization of a 30- GHz bandwidth low-power silicon traveling-wave modulator,” Opt. Commun. 321, 124–133 (2014).
[Crossref]

Mason, T.

Osman, M.

Padmaraju, K.

R. Ding, Y. Liu, Q. Li, Y. Yang, Y. Ma, K. Padmaraju, A. E. J. Lim, G. Q. Lo, K. Bergman, T. Baehr-Jones, and M. Hochberg, “Design and characterization of a 30- GHz bandwidth low-power silicon traveling-wave modulator,” Opt. Commun. 321, 124–133 (2014).
[Crossref]

Patel, D.

Plant, D. V.

Samani, A.

Song, J.

Tu, X.

Veerasubramanian, V.

Yang, Y.

R. Ding, Y. Liu, Q. Li, Y. Yang, Y. Ma, K. Padmaraju, A. E. J. Lim, G. Q. Lo, K. Bergman, T. Baehr-Jones, and M. Hochberg, “Design and characterization of a 30- GHz bandwidth low-power silicon traveling-wave modulator,” Opt. Commun. 321, 124–133 (2014).
[Crossref]

Yu, M.

Yu, P.

IEEE Trans. Compon., Hybrids. Manuf. Technol (1)

W. R. Eisenstadt and Y. Eo, “S-parameter-based IC interconnect transmission line characterization,” IEEE Trans. Compon., Hybrids. Manuf. Technol 15, 4 (1992).

IEEE Trans. Microw. Theory Tech. (2)

D. E. Bockelman and W. R. Eisenstadt, “Combined differential and common-mode scattering parameters: theory and simulation,” IEEE Trans. Microw. Theory Tech. 43(7), 1530 (1995).
[Crossref]

D. Frickey, “Conversions between S, Z, Y, h, ABCD, and T parameters which are valid for complex source and load impedances,” IEEE Trans. Microw. Theory Tech. 42(2), 205–211 (1994).
[Crossref]

J. Lightwave Technol. (1)

Opt. Commun. (1)

R. Ding, Y. Liu, Q. Li, Y. Yang, Y. Ma, K. Padmaraju, A. E. J. Lim, G. Q. Lo, K. Bergman, T. Baehr-Jones, and M. Hochberg, “Design and characterization of a 30- GHz bandwidth low-power silicon traveling-wave modulator,” Opt. Commun. 321, 124–133 (2014).
[Crossref]

Opt. Express (3)

Other (6)

K. Vaz and M. Caggiano, “Measurement technique for the extraction of differential S-parameters from single-ended S-parameters,” in 27th International Spring Seminar on Electronics Technology: Meeting the Challenges of Electronics Technology Progress (IEEE 2004), pp. 313–317.
[Crossref]

A. Huynh, P. Hakansson, and S. Gong, “Mixed-mode S-parameter conversion for networks with coupled differential signals,” in Proceedings of the 37th European Microwave Conference (IEEE, 2007), pp. 238–241.
[Crossref]

F. Boeuf, S. Crémer, N. Vulliet, T. Pinguet, A. Mekis, G. Masini, L. Verslegers, P. Sun, A. Ayazi, N. K. Hon, S. Sahni, Y. Chi, B. Orlando, D. Ristoiu, A. Farcy, F. Leverd, L. Broussous, D. Pelissier-Tanon, C. Richard, L. Pinzelli, R. Beneyton, O. Gourhant, E. Gourvest, Y. Le-Friec, D. Monnier, P. Brun, M. Guillermet, D. Benoit, K. Haxaire, J. R. Manouvrier, S. Jan, H. Petiton, J. F. Carpentier, T. Quémerais, C. Durand, D. Gloria, M. Fourel, F. Battegay, Y. Sanchez, E. Batail, F. Baron, P. Delpech, L. Salager, P. De Dobbelaere, and B. Sautreuil, “A multi-wavelength 3D-compatible silicon photonics platform on 300mm SOI wafers for 25Gb/s applications,” 2013 IEEE International Electron Devices Meeting, Washington, DC, 2013, pp. 13.3.1–13.3.4.
[Crossref]

F. Boeuf, J. F. Carpentier, C. Baudot, P. L. Maitre, and J. R. Manouvrier, “Silicon Photonics Research and Manufacturing Using a 300-mm Wafer Platform” in Silicon Photonics III, Lorenzo Pavesi and David J. Lockwood, ed. (Springer-Verlag, 2016).

L. Chrostowski and M. Hochberg, Silicon Photonics Design (Cambridge University, 2015).

A. Samani, M. Chagnon, D. Patel, V. Veerasubramanian, S. Ghosh, M. Osman, Q. Zhong, and D. V. Plant, “A Low-Voltage 35-GHz Silicon Photonic Modulator-Enabled 112-Gb/s Transmission System,” in IEEE Photon. J. 7, 3 (2015).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 Schematic of (a) series push-pull modulator which can be characterized by two ports, and (b) a dual-drive modulator which requires four port characterization. The dual-drive modulator shown here also has pn junction connected back-to-back and has a virtual ground at the middle due to its longitudinal symmetry. The red lines represent optical waveguides forming the MZMs.
Fig. 2
Fig. 2 Schematic of (a) a dual-drive MZM with back-to-back pn junction in reverse bias (series RC model), the RF pads and transition, and multiple nodes in the model. The source resistance is shown by RS and the termination resistance is shown by RT. (b) The schematic of one segment of the modulator showing the pn junction loaded and unloaded sections.
Fig. 3
Fig. 3 (a) The cross-section of the SOI process with a dual-drive modulator. It also depicts the electrical wall and virtual ground at the middle of the device. (b) Schematic of a fabricated dual-drive modulator with diodes connected back-to-back in series and a common bias voltage node. (c) Schematic of a fabricated dual-drive modulator with diodes connected from the signal to ground electrodes.
Fig. 4
Fig. 4 Measured E-O responses of the configurations shown in Fig. 3(b), dual-drive modulator with diodes connected back-to-back in series, and Fig, 3(c), dual-drive modulator with diodes connected from the signal to ground electrodes.
Fig. 5
Fig. 5 A summary of steps used to simulate the E-O response of differentially driven dual-drive MZMs.
Fig. 6
Fig. 6 Simulated unloaded and loaded microwave (a) attenuation, (b) phase constant, (c) effective index, (d) real part of the characteristic impedance, and (e) imaginary part of the characteristic impedance.
Fig. 7
Fig. 7 (a) Simulated differential SD2D1 100 Ω differential termination and single-ended S21 response with a 50 Ω differential termination of a 4 mm long unloaded transmission line (b) The simulated E-E responses, normalized to DC, of loaded transmission lines of different lengths with 50 Ω differential termination.
Fig. 8
Fig. 8 (a) Comparison of the simulated E-O responses with measured E-O responses, and (b) simulated and measured SD1D1 responses for differentially driven dual-drive MZMs at 4 V reverse bias and different active lengths.

Tables (1)

Tables Icon

Table 1 Measured parameters for MZMs of different lengths.

Equations (15)

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[S]=[ S 11 S 12 S 13 S 14 S 21 S 22 S 23 S 24 S 31 S 32 S 33 S 34 S 41 S 42 S 43 S 44 ]
[ S mm ]=[ S D1D1 S D1D2 S D1C1 S D1C2 S D2D1 S D2D2 S D2D1 S D2D2 S C1D1 S C1D2 S C1C1 S C1C2 S C2D1 S C2D2 S C2C1 S C2C2 ]
S D2D1 = 1 2 ( S 21 S 41 + S 43 S 23 )
S D1D1 = 1 2 ( S 11 S 31 + S 33 S 13 )
γ odd = 1 l ln[ ( 1 S D1D1 2 + S D2D1 2 2 S D2D1 ± ( S D1D1 2 S D2D1 2 +1) 2 (2 S D1D1 ) 2 (2 S D2D1 ) 2 ) 1 ]
Z 0,diff = Z ref 2 (1+ S D1D1 ) 2 S D2D1 2 (1 S D1D1 ) 2 S D2D1 2
[ V n1 I n1 ]=[ T 0,l ][ V n I n ]=[ cosh( γ odd l) Z odd sinh( γ odd l 1 Z odd sinh( γ odd l) cosh( γ odd l) ][ V n I n ]
T mod =[ 1 0 1 R mod +jω L mod + 1 jω C mod 1 ]
V S = V 0 + I 0 Z S
[ V 0 I 0 ]=[T][ V T I T ]=[ A B C D ][ V T I T ]
V T = I T Z T
V S = I T (A Z T +B+C Z T Z S +D Z S )
I T = 1 A Z T +B+C Z T Z S +D Z S
M(f)=| 2 N V S n=1 N V n ( 1 1 ω 2 L mod C mod +jω R mod C mod ) e jωn( l loaded + l unloaded )/ v O |
S D1D1 = A Z T +BC Z S * Z T D Z S * A Z T +B+C Z S Z T +D Z S

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