Abstract

We demonstrate greedy linear descent-based, basic gradient descent-based, two-point step size gradient descent-based, and two-stage optimization method-based automated control algorithms and examine their performance for use with a silicon photonic polarization receiver. With an active feedback loop control process, time-varying arbitrary polarization states from an optical fiber can be automatically adapted and stabilized to the transverse-electric (TE) mode of a single-mode silicon waveguide. Using the proposed control algorithms, we successfully realize automated adaptations for a 10 Gb/s on-off keying signal in the polarization receiver. Based on the large-signal measurement results, the control algorithms are examined and compared with regard to the iteration number and the output response. In addition, we implemented a long-duration experiment to track, adapt, and stabilize arbitrary input polarization states using the two-point step size gradient descent-based and two-stage optimization method-based control algorithms. The experimental results show that these control algorithms enable the polarization receiver to achieve real-time and continuous polarization management.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Simultaneous four-channel thermal adaptation of polarization insensitive silicon photonics WDM receiver

Robert Gatdula, Kwangwoong Kim, Argishti Melikyan, Young-Kai Chen, and Po Dong
Opt. Express 25(22) 27119-27126 (2017)

Ring resonator based polarization diversity WDM receiver

Anthony H. K. Park, Hossam Shoman, Minglei Ma, Sudip Shekhar, and Lukas Chrostowski
Opt. Express 27(5) 6147-6157 (2019)

Symmetrical polarization splitter/rotator design and application in a polarization insensitive WDM receiver

Yangjin Ma, Yang Liu, Hang Guan, Alexander Gazman, Qi Li, Ran Ding, Yunchu Li, Keren Bergman, Tom Baehr-Jones, and Michael Hochberg
Opt. Express 23(12) 16052-16062 (2015)

References

  • View by:
  • |
  • |
  • |

  1. T. Barwicz, M. R. Watts, M. A. Popović, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
    [Crossref]
  2. L. Chrostowski and M. Hochberg, Silicon photonics design: from devices to systems (Cambridge University, 2015).
  3. L. Chen, C. R. Doerr, and Y.-K. Chen, “Polarization-diversified DWDM receiver on silicon free of polarization-dependent wavelength shift,” in Optical Fiber Communication Conference, (IEEE, 2012), pp. 1–3.
  4. P. De Heyn, J. De Coster, P. Verheyen, G. Lepage, M. Pantouvaki, P. Absil, W. Bogaerts, D. Van Thourhout, and J. Van Campenhout, “Polarization-insensitive 5×20Gb/s WDM Ge receiver using compact Si ring filters with collective thermal tuning,” in Optical Fiber Communication Conference, (Optical Society of America, 2014), pp. Th4C–5.
  5. P. Dong, Y.-K. Chen, and L. L. Buhl, “Reconfigurable four-channel polarization diversity silicon photonic WDM receiver,” in Optical Fiber Communication Conference, (Optical Society of America, 2015), pp. W3A–2.
  6. Y. Ma, Y. Liu, H. Guan, A. Gazman, Q. Li, R. Ding, Y. Li, K. Bergman, T. Baehr-Jones, and M. Hochberg, “Symmetrical polarization splitter/rotator design and application in a polarization insensitive WDM receiver,” Opt. Express 23(12), 16052–16062 (2015).
    [Crossref]
  7. D. Y. Lee, X. Zheng, J. Yao, Y. Luo, J.-H. Lee, S. Lin, H. Thacker, J. Bovington, I. Shubin, S. S. Djordjevic, J. E. Cunningham, K. Raj, and A. V. Krishnamoorthy, “Error-free operation of a polarization-insensitive 4λ × 25 Gbps silicon photonic wdm receiver with closed-loop thermal stabilization of Si microrings,” Opt. Express 24(12), 13204–13209 (2016).
    [Crossref]
  8. R. Gatdula, K. Kim, A. Melikyan, Y.-K. Chen, and P. Dong, “Simultaneous four-channel thermal adaptation of polarization insensitive silicon photonics WDM receiver,” Opt. Express 25(22), 27119–27126 (2017).
    [Crossref]
  9. Y. Tan, H. Wu, and D. Dai, “Silicon-based hybrid (de) multiplexer for wavelength-/polarization-division-multiplexing,” J. Lightwave Technol. 36(11), 2051–2058 (2018).
    [Crossref]
  10. A. H. K. Park, H. Shoman, M. Ma, S. Shekhar, and L. Chrostowski, “Ring resonator based polarization diversity WDM receiver,” Opt. Express 27(5), 6147–6157 (2019).
    [Crossref]
  11. C. R. Doerr, P. J. Winzer, Y.-K. Chen, S. Chandrasekhar, M. S. Rasras, L. Chen, T.-Y. Liow, K.-W. Ang, and G.-Q. Lo, “Monolithic polarization and phase diversity coherent receiver in silicon,” J. Lightwave Technol. 28(4), 520–525 (2010).
    [Crossref]
  12. A. H. Ahmed, D. Lim, A. Elmoznine, Y. Ma, T. Huynh, C. Williams, L. Vera, Y. Liu, R. Shi, M. Streshinsky, A. Novack, R. Ding, R. Younce, J. Roman, M. Hochberg, S. Shekhar, and A. Rylyakov, “30.6 A 6V Swing 3.6% THD> 40GHz Driver with 4.5× Bandwidth Extension for a 272Gb/s Dual-Polarization 16-QAM Silicon Photonic Transmitter,” in 2019 IEEE International Solid-State Circuits Conference-(ISSCC), (IEEE, 2019), pp. 484–486.
  13. A. Melikyan, K. Kim, N. Fontaine, S. Chandrasekhar, Y.-K. Chen, and P. Dong, “Inter-polarization mixers for coherent detection of optical signals,” Opt. Express 26(14), 18523–18531 (2018).
    [Crossref]
  14. A. Melikyan, N. Kaneda, K. Kim, and P. Dong, “Inter-polarization 180-degree mixer for reception of m-ask signals,” in 2018 European Conference on Optical Communication (ECOC), (IEEE, 2018), pp. 1–3.
  15. S.-H. Kim, K. Tanizawa, Y. Shoji, G. Cong, K. Suzuki, K. Ikeda, H. Ishikawa, S. Namiki, and H. Kawashima, “Compact 2×2 polarization-diversity Si-wire switch,” Opt. Express 22(24), 29818–29826 (2014).
    [Crossref]
  16. W. D. Sacher, T. Barwicz, B. J. Taylor, and J. K. Poon, “Polarization rotator-splitters in standard active silicon photonics platforms,” Opt. Express 22(4), 3777–3786 (2014).
    [Crossref]
  17. J. N. Caspers, Y. Wang, L. Chrostowski, and M. Mojahedi, “Active polarization independent coupling to silicon photonics circuit,” in Silicon Photonics and Photonic Integrated Circuits IV, vol. 9133 (International Society for Optics and Photonics, 2014), p. 91330G.
  18. M. Ma, K. Murray, M. Ye, S. Lin, Y. Wang, Z. Lu, H. Yun, R. Hu, N. A. F. Jaeger, and L. Chrostowski, “Silicon photonic polarization receiver with automated stabilization for arbitrary input polarizations,” in CLEO: Science and Innovations, (Optical Society of America, 2016), pp. STu4G–8.
  19. P. Velha, V. Sorianello, M. Preite, G. De Angelis, T. Cassese, A. Bianchi, F. Testa, and M. Romagnoli, “Wide-band polarization controller for Si photonic integrated circuits,” Opt. Lett. 41(24), 5656–5659 (2016).
    [Crossref]
  20. H. Zhou, Y. Zhao, Y. Wei, F. Li, J. Dong, and X. Zhang, “All-in-one silicon photonic polarization processor,” Nanophotonics 8(12), 2257–2267 (2019).
    [Crossref]
  21. C. R. Doerr and L. Chen, “Monolithic PDM-DQPSK receiver in silicon,” in 36th European Conference and Exhibition on Optical Communication, (IEEE, 2010), pp. 1–3.
  22. C. R. Doerr, N. K. Fontaine, and L. L. Buhl, “PDM-DQPSK silicon receiver with integrated monitor and minimum number of controls,” IEEE Photonics Technol. Lett. 24(8), 697–699 (2012).
    [Crossref]
  23. D. A. B. Miller, “Self-configuring universal linear optical component,” Photonics Res. 1(1), 1–15 (2013).
    [Crossref]
  24. M. Ma, A. H. Park, Y. Wang, H. Shoman, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Sub-wavelength grating-assisted polarization splitter-rotators for silicon-on-insulator platforms,” Opt. Express 27(13), 17581–17591 (2019).
    [Crossref]
  25. H. Yun, W. Shi, Y. Wang, L. Chrostowski, and N. A. F. Jaeger, “2×2 adiabatic 3-dB coupler on silicon-on-insulator rib waveguides,” in Photonics North 2013, vol. 8915 (International Society for Optics and Photonics, 2013), p. 89150V.
  26. J. Barzilai and J. M. Borwein, “Two-point step size gradient methods,” IMA J. Numer. Analysis 8(1), 141–148 (1988).
    [Crossref]
  27. C. K. Madsen and J. H. Zhao, Optical filter design and analysis (Wiley, 1999).
  28. SciPy community, “Solve a nonlinear least-squares problem with bounds on the variables,” https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.least_squares.html .
  29. R. Fletcher and C. M. Reeves, “Function minimization by conjugate gradients,” The Comput. J. 7(2), 149–154 (1964).
    [Crossref]
  30. A. Ben-Israel, “A Newton-Raphson method for the solution of systems of equations,” J. Math. Analysis Appl. 15(2), 243–252 (1966).
    [Crossref]

2019 (3)

2018 (2)

2017 (1)

2016 (2)

2015 (1)

2014 (2)

2013 (1)

D. A. B. Miller, “Self-configuring universal linear optical component,” Photonics Res. 1(1), 1–15 (2013).
[Crossref]

2012 (1)

C. R. Doerr, N. K. Fontaine, and L. L. Buhl, “PDM-DQPSK silicon receiver with integrated monitor and minimum number of controls,” IEEE Photonics Technol. Lett. 24(8), 697–699 (2012).
[Crossref]

2010 (1)

2007 (1)

T. Barwicz, M. R. Watts, M. A. Popović, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

1988 (1)

J. Barzilai and J. M. Borwein, “Two-point step size gradient methods,” IMA J. Numer. Analysis 8(1), 141–148 (1988).
[Crossref]

1966 (1)

A. Ben-Israel, “A Newton-Raphson method for the solution of systems of equations,” J. Math. Analysis Appl. 15(2), 243–252 (1966).
[Crossref]

1964 (1)

R. Fletcher and C. M. Reeves, “Function minimization by conjugate gradients,” The Comput. J. 7(2), 149–154 (1964).
[Crossref]

Absil, P.

P. De Heyn, J. De Coster, P. Verheyen, G. Lepage, M. Pantouvaki, P. Absil, W. Bogaerts, D. Van Thourhout, and J. Van Campenhout, “Polarization-insensitive 5×20Gb/s WDM Ge receiver using compact Si ring filters with collective thermal tuning,” in Optical Fiber Communication Conference, (Optical Society of America, 2014), pp. Th4C–5.

Ahmed, A. H.

A. H. Ahmed, D. Lim, A. Elmoznine, Y. Ma, T. Huynh, C. Williams, L. Vera, Y. Liu, R. Shi, M. Streshinsky, A. Novack, R. Ding, R. Younce, J. Roman, M. Hochberg, S. Shekhar, and A. Rylyakov, “30.6 A 6V Swing 3.6% THD> 40GHz Driver with 4.5× Bandwidth Extension for a 272Gb/s Dual-Polarization 16-QAM Silicon Photonic Transmitter,” in 2019 IEEE International Solid-State Circuits Conference-(ISSCC), (IEEE, 2019), pp. 484–486.

Ang, K.-W.

Baehr-Jones, T.

Barwicz, T.

W. D. Sacher, T. Barwicz, B. J. Taylor, and J. K. Poon, “Polarization rotator-splitters in standard active silicon photonics platforms,” Opt. Express 22(4), 3777–3786 (2014).
[Crossref]

T. Barwicz, M. R. Watts, M. A. Popović, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

Barzilai, J.

J. Barzilai and J. M. Borwein, “Two-point step size gradient methods,” IMA J. Numer. Analysis 8(1), 141–148 (1988).
[Crossref]

Ben-Israel, A.

A. Ben-Israel, “A Newton-Raphson method for the solution of systems of equations,” J. Math. Analysis Appl. 15(2), 243–252 (1966).
[Crossref]

Bergman, K.

Bianchi, A.

Bogaerts, W.

P. De Heyn, J. De Coster, P. Verheyen, G. Lepage, M. Pantouvaki, P. Absil, W. Bogaerts, D. Van Thourhout, and J. Van Campenhout, “Polarization-insensitive 5×20Gb/s WDM Ge receiver using compact Si ring filters with collective thermal tuning,” in Optical Fiber Communication Conference, (Optical Society of America, 2014), pp. Th4C–5.

Borwein, J. M.

J. Barzilai and J. M. Borwein, “Two-point step size gradient methods,” IMA J. Numer. Analysis 8(1), 141–148 (1988).
[Crossref]

Bovington, J.

Buhl, L. L.

C. R. Doerr, N. K. Fontaine, and L. L. Buhl, “PDM-DQPSK silicon receiver with integrated monitor and minimum number of controls,” IEEE Photonics Technol. Lett. 24(8), 697–699 (2012).
[Crossref]

P. Dong, Y.-K. Chen, and L. L. Buhl, “Reconfigurable four-channel polarization diversity silicon photonic WDM receiver,” in Optical Fiber Communication Conference, (Optical Society of America, 2015), pp. W3A–2.

Caspers, J. N.

J. N. Caspers, Y. Wang, L. Chrostowski, and M. Mojahedi, “Active polarization independent coupling to silicon photonics circuit,” in Silicon Photonics and Photonic Integrated Circuits IV, vol. 9133 (International Society for Optics and Photonics, 2014), p. 91330G.

Cassese, T.

Chandrasekhar, S.

Chen, L.

C. R. Doerr, P. J. Winzer, Y.-K. Chen, S. Chandrasekhar, M. S. Rasras, L. Chen, T.-Y. Liow, K.-W. Ang, and G.-Q. Lo, “Monolithic polarization and phase diversity coherent receiver in silicon,” J. Lightwave Technol. 28(4), 520–525 (2010).
[Crossref]

C. R. Doerr and L. Chen, “Monolithic PDM-DQPSK receiver in silicon,” in 36th European Conference and Exhibition on Optical Communication, (IEEE, 2010), pp. 1–3.

L. Chen, C. R. Doerr, and Y.-K. Chen, “Polarization-diversified DWDM receiver on silicon free of polarization-dependent wavelength shift,” in Optical Fiber Communication Conference, (IEEE, 2012), pp. 1–3.

Chen, Y.-K.

Chrostowski, L.

A. H. K. Park, H. Shoman, M. Ma, S. Shekhar, and L. Chrostowski, “Ring resonator based polarization diversity WDM receiver,” Opt. Express 27(5), 6147–6157 (2019).
[Crossref]

M. Ma, A. H. Park, Y. Wang, H. Shoman, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Sub-wavelength grating-assisted polarization splitter-rotators for silicon-on-insulator platforms,” Opt. Express 27(13), 17581–17591 (2019).
[Crossref]

L. Chrostowski and M. Hochberg, Silicon photonics design: from devices to systems (Cambridge University, 2015).

M. Ma, K. Murray, M. Ye, S. Lin, Y. Wang, Z. Lu, H. Yun, R. Hu, N. A. F. Jaeger, and L. Chrostowski, “Silicon photonic polarization receiver with automated stabilization for arbitrary input polarizations,” in CLEO: Science and Innovations, (Optical Society of America, 2016), pp. STu4G–8.

J. N. Caspers, Y. Wang, L. Chrostowski, and M. Mojahedi, “Active polarization independent coupling to silicon photonics circuit,” in Silicon Photonics and Photonic Integrated Circuits IV, vol. 9133 (International Society for Optics and Photonics, 2014), p. 91330G.

H. Yun, W. Shi, Y. Wang, L. Chrostowski, and N. A. F. Jaeger, “2×2 adiabatic 3-dB coupler on silicon-on-insulator rib waveguides,” in Photonics North 2013, vol. 8915 (International Society for Optics and Photonics, 2013), p. 89150V.

Cong, G.

Cunningham, J. E.

Dai, D.

De Angelis, G.

De Coster, J.

P. De Heyn, J. De Coster, P. Verheyen, G. Lepage, M. Pantouvaki, P. Absil, W. Bogaerts, D. Van Thourhout, and J. Van Campenhout, “Polarization-insensitive 5×20Gb/s WDM Ge receiver using compact Si ring filters with collective thermal tuning,” in Optical Fiber Communication Conference, (Optical Society of America, 2014), pp. Th4C–5.

De Heyn, P.

P. De Heyn, J. De Coster, P. Verheyen, G. Lepage, M. Pantouvaki, P. Absil, W. Bogaerts, D. Van Thourhout, and J. Van Campenhout, “Polarization-insensitive 5×20Gb/s WDM Ge receiver using compact Si ring filters with collective thermal tuning,” in Optical Fiber Communication Conference, (Optical Society of America, 2014), pp. Th4C–5.

Ding, R.

Y. Ma, Y. Liu, H. Guan, A. Gazman, Q. Li, R. Ding, Y. Li, K. Bergman, T. Baehr-Jones, and M. Hochberg, “Symmetrical polarization splitter/rotator design and application in a polarization insensitive WDM receiver,” Opt. Express 23(12), 16052–16062 (2015).
[Crossref]

A. H. Ahmed, D. Lim, A. Elmoznine, Y. Ma, T. Huynh, C. Williams, L. Vera, Y. Liu, R. Shi, M. Streshinsky, A. Novack, R. Ding, R. Younce, J. Roman, M. Hochberg, S. Shekhar, and A. Rylyakov, “30.6 A 6V Swing 3.6% THD> 40GHz Driver with 4.5× Bandwidth Extension for a 272Gb/s Dual-Polarization 16-QAM Silicon Photonic Transmitter,” in 2019 IEEE International Solid-State Circuits Conference-(ISSCC), (IEEE, 2019), pp. 484–486.

Djordjevic, S. S.

Doerr, C. R.

C. R. Doerr, N. K. Fontaine, and L. L. Buhl, “PDM-DQPSK silicon receiver with integrated monitor and minimum number of controls,” IEEE Photonics Technol. Lett. 24(8), 697–699 (2012).
[Crossref]

C. R. Doerr, P. J. Winzer, Y.-K. Chen, S. Chandrasekhar, M. S. Rasras, L. Chen, T.-Y. Liow, K.-W. Ang, and G.-Q. Lo, “Monolithic polarization and phase diversity coherent receiver in silicon,” J. Lightwave Technol. 28(4), 520–525 (2010).
[Crossref]

C. R. Doerr and L. Chen, “Monolithic PDM-DQPSK receiver in silicon,” in 36th European Conference and Exhibition on Optical Communication, (IEEE, 2010), pp. 1–3.

L. Chen, C. R. Doerr, and Y.-K. Chen, “Polarization-diversified DWDM receiver on silicon free of polarization-dependent wavelength shift,” in Optical Fiber Communication Conference, (IEEE, 2012), pp. 1–3.

Dong, J.

H. Zhou, Y. Zhao, Y. Wei, F. Li, J. Dong, and X. Zhang, “All-in-one silicon photonic polarization processor,” Nanophotonics 8(12), 2257–2267 (2019).
[Crossref]

Dong, P.

A. Melikyan, K. Kim, N. Fontaine, S. Chandrasekhar, Y.-K. Chen, and P. Dong, “Inter-polarization mixers for coherent detection of optical signals,” Opt. Express 26(14), 18523–18531 (2018).
[Crossref]

R. Gatdula, K. Kim, A. Melikyan, Y.-K. Chen, and P. Dong, “Simultaneous four-channel thermal adaptation of polarization insensitive silicon photonics WDM receiver,” Opt. Express 25(22), 27119–27126 (2017).
[Crossref]

A. Melikyan, N. Kaneda, K. Kim, and P. Dong, “Inter-polarization 180-degree mixer for reception of m-ask signals,” in 2018 European Conference on Optical Communication (ECOC), (IEEE, 2018), pp. 1–3.

P. Dong, Y.-K. Chen, and L. L. Buhl, “Reconfigurable four-channel polarization diversity silicon photonic WDM receiver,” in Optical Fiber Communication Conference, (Optical Society of America, 2015), pp. W3A–2.

Elmoznine, A.

A. H. Ahmed, D. Lim, A. Elmoznine, Y. Ma, T. Huynh, C. Williams, L. Vera, Y. Liu, R. Shi, M. Streshinsky, A. Novack, R. Ding, R. Younce, J. Roman, M. Hochberg, S. Shekhar, and A. Rylyakov, “30.6 A 6V Swing 3.6% THD> 40GHz Driver with 4.5× Bandwidth Extension for a 272Gb/s Dual-Polarization 16-QAM Silicon Photonic Transmitter,” in 2019 IEEE International Solid-State Circuits Conference-(ISSCC), (IEEE, 2019), pp. 484–486.

Fletcher, R.

R. Fletcher and C. M. Reeves, “Function minimization by conjugate gradients,” The Comput. J. 7(2), 149–154 (1964).
[Crossref]

Fontaine, N.

Fontaine, N. K.

C. R. Doerr, N. K. Fontaine, and L. L. Buhl, “PDM-DQPSK silicon receiver with integrated monitor and minimum number of controls,” IEEE Photonics Technol. Lett. 24(8), 697–699 (2012).
[Crossref]

Gatdula, R.

Gazman, A.

Guan, H.

Hochberg, M.

Y. Ma, Y. Liu, H. Guan, A. Gazman, Q. Li, R. Ding, Y. Li, K. Bergman, T. Baehr-Jones, and M. Hochberg, “Symmetrical polarization splitter/rotator design and application in a polarization insensitive WDM receiver,” Opt. Express 23(12), 16052–16062 (2015).
[Crossref]

A. H. Ahmed, D. Lim, A. Elmoznine, Y. Ma, T. Huynh, C. Williams, L. Vera, Y. Liu, R. Shi, M. Streshinsky, A. Novack, R. Ding, R. Younce, J. Roman, M. Hochberg, S. Shekhar, and A. Rylyakov, “30.6 A 6V Swing 3.6% THD> 40GHz Driver with 4.5× Bandwidth Extension for a 272Gb/s Dual-Polarization 16-QAM Silicon Photonic Transmitter,” in 2019 IEEE International Solid-State Circuits Conference-(ISSCC), (IEEE, 2019), pp. 484–486.

L. Chrostowski and M. Hochberg, Silicon photonics design: from devices to systems (Cambridge University, 2015).

Hu, R.

M. Ma, K. Murray, M. Ye, S. Lin, Y. Wang, Z. Lu, H. Yun, R. Hu, N. A. F. Jaeger, and L. Chrostowski, “Silicon photonic polarization receiver with automated stabilization for arbitrary input polarizations,” in CLEO: Science and Innovations, (Optical Society of America, 2016), pp. STu4G–8.

Huynh, T.

A. H. Ahmed, D. Lim, A. Elmoznine, Y. Ma, T. Huynh, C. Williams, L. Vera, Y. Liu, R. Shi, M. Streshinsky, A. Novack, R. Ding, R. Younce, J. Roman, M. Hochberg, S. Shekhar, and A. Rylyakov, “30.6 A 6V Swing 3.6% THD> 40GHz Driver with 4.5× Bandwidth Extension for a 272Gb/s Dual-Polarization 16-QAM Silicon Photonic Transmitter,” in 2019 IEEE International Solid-State Circuits Conference-(ISSCC), (IEEE, 2019), pp. 484–486.

Ikeda, K.

Ippen, E. P.

T. Barwicz, M. R. Watts, M. A. Popović, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

Ishikawa, H.

Jaeger, N. A. F.

M. Ma, A. H. Park, Y. Wang, H. Shoman, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Sub-wavelength grating-assisted polarization splitter-rotators for silicon-on-insulator platforms,” Opt. Express 27(13), 17581–17591 (2019).
[Crossref]

H. Yun, W. Shi, Y. Wang, L. Chrostowski, and N. A. F. Jaeger, “2×2 adiabatic 3-dB coupler on silicon-on-insulator rib waveguides,” in Photonics North 2013, vol. 8915 (International Society for Optics and Photonics, 2013), p. 89150V.

M. Ma, K. Murray, M. Ye, S. Lin, Y. Wang, Z. Lu, H. Yun, R. Hu, N. A. F. Jaeger, and L. Chrostowski, “Silicon photonic polarization receiver with automated stabilization for arbitrary input polarizations,” in CLEO: Science and Innovations, (Optical Society of America, 2016), pp. STu4G–8.

Kaneda, N.

A. Melikyan, N. Kaneda, K. Kim, and P. Dong, “Inter-polarization 180-degree mixer for reception of m-ask signals,” in 2018 European Conference on Optical Communication (ECOC), (IEEE, 2018), pp. 1–3.

Kärtner, F. X.

T. Barwicz, M. R. Watts, M. A. Popović, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

Kawashima, H.

Kim, K.

Kim, S.-H.

Krishnamoorthy, A. V.

Lee, D. Y.

Lee, J.-H.

Lepage, G.

P. De Heyn, J. De Coster, P. Verheyen, G. Lepage, M. Pantouvaki, P. Absil, W. Bogaerts, D. Van Thourhout, and J. Van Campenhout, “Polarization-insensitive 5×20Gb/s WDM Ge receiver using compact Si ring filters with collective thermal tuning,” in Optical Fiber Communication Conference, (Optical Society of America, 2014), pp. Th4C–5.

Li, F.

H. Zhou, Y. Zhao, Y. Wei, F. Li, J. Dong, and X. Zhang, “All-in-one silicon photonic polarization processor,” Nanophotonics 8(12), 2257–2267 (2019).
[Crossref]

Li, Q.

Li, Y.

Lim, D.

A. H. Ahmed, D. Lim, A. Elmoznine, Y. Ma, T. Huynh, C. Williams, L. Vera, Y. Liu, R. Shi, M. Streshinsky, A. Novack, R. Ding, R. Younce, J. Roman, M. Hochberg, S. Shekhar, and A. Rylyakov, “30.6 A 6V Swing 3.6% THD> 40GHz Driver with 4.5× Bandwidth Extension for a 272Gb/s Dual-Polarization 16-QAM Silicon Photonic Transmitter,” in 2019 IEEE International Solid-State Circuits Conference-(ISSCC), (IEEE, 2019), pp. 484–486.

Lin, S.

D. Y. Lee, X. Zheng, J. Yao, Y. Luo, J.-H. Lee, S. Lin, H. Thacker, J. Bovington, I. Shubin, S. S. Djordjevic, J. E. Cunningham, K. Raj, and A. V. Krishnamoorthy, “Error-free operation of a polarization-insensitive 4λ × 25 Gbps silicon photonic wdm receiver with closed-loop thermal stabilization of Si microrings,” Opt. Express 24(12), 13204–13209 (2016).
[Crossref]

M. Ma, K. Murray, M. Ye, S. Lin, Y. Wang, Z. Lu, H. Yun, R. Hu, N. A. F. Jaeger, and L. Chrostowski, “Silicon photonic polarization receiver with automated stabilization for arbitrary input polarizations,” in CLEO: Science and Innovations, (Optical Society of America, 2016), pp. STu4G–8.

Liow, T.-Y.

Liu, Y.

Y. Ma, Y. Liu, H. Guan, A. Gazman, Q. Li, R. Ding, Y. Li, K. Bergman, T. Baehr-Jones, and M. Hochberg, “Symmetrical polarization splitter/rotator design and application in a polarization insensitive WDM receiver,” Opt. Express 23(12), 16052–16062 (2015).
[Crossref]

A. H. Ahmed, D. Lim, A. Elmoznine, Y. Ma, T. Huynh, C. Williams, L. Vera, Y. Liu, R. Shi, M. Streshinsky, A. Novack, R. Ding, R. Younce, J. Roman, M. Hochberg, S. Shekhar, and A. Rylyakov, “30.6 A 6V Swing 3.6% THD> 40GHz Driver with 4.5× Bandwidth Extension for a 272Gb/s Dual-Polarization 16-QAM Silicon Photonic Transmitter,” in 2019 IEEE International Solid-State Circuits Conference-(ISSCC), (IEEE, 2019), pp. 484–486.

Lo, G.-Q.

Lu, Z.

M. Ma, K. Murray, M. Ye, S. Lin, Y. Wang, Z. Lu, H. Yun, R. Hu, N. A. F. Jaeger, and L. Chrostowski, “Silicon photonic polarization receiver with automated stabilization for arbitrary input polarizations,” in CLEO: Science and Innovations, (Optical Society of America, 2016), pp. STu4G–8.

Luo, Y.

Ma, M.

M. Ma, A. H. Park, Y. Wang, H. Shoman, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Sub-wavelength grating-assisted polarization splitter-rotators for silicon-on-insulator platforms,” Opt. Express 27(13), 17581–17591 (2019).
[Crossref]

A. H. K. Park, H. Shoman, M. Ma, S. Shekhar, and L. Chrostowski, “Ring resonator based polarization diversity WDM receiver,” Opt. Express 27(5), 6147–6157 (2019).
[Crossref]

M. Ma, K. Murray, M. Ye, S. Lin, Y. Wang, Z. Lu, H. Yun, R. Hu, N. A. F. Jaeger, and L. Chrostowski, “Silicon photonic polarization receiver with automated stabilization for arbitrary input polarizations,” in CLEO: Science and Innovations, (Optical Society of America, 2016), pp. STu4G–8.

Ma, Y.

Y. Ma, Y. Liu, H. Guan, A. Gazman, Q. Li, R. Ding, Y. Li, K. Bergman, T. Baehr-Jones, and M. Hochberg, “Symmetrical polarization splitter/rotator design and application in a polarization insensitive WDM receiver,” Opt. Express 23(12), 16052–16062 (2015).
[Crossref]

A. H. Ahmed, D. Lim, A. Elmoznine, Y. Ma, T. Huynh, C. Williams, L. Vera, Y. Liu, R. Shi, M. Streshinsky, A. Novack, R. Ding, R. Younce, J. Roman, M. Hochberg, S. Shekhar, and A. Rylyakov, “30.6 A 6V Swing 3.6% THD> 40GHz Driver with 4.5× Bandwidth Extension for a 272Gb/s Dual-Polarization 16-QAM Silicon Photonic Transmitter,” in 2019 IEEE International Solid-State Circuits Conference-(ISSCC), (IEEE, 2019), pp. 484–486.

Madsen, C. K.

C. K. Madsen and J. H. Zhao, Optical filter design and analysis (Wiley, 1999).

Melikyan, A.

Miller, D. A. B.

D. A. B. Miller, “Self-configuring universal linear optical component,” Photonics Res. 1(1), 1–15 (2013).
[Crossref]

Mojahedi, M.

J. N. Caspers, Y. Wang, L. Chrostowski, and M. Mojahedi, “Active polarization independent coupling to silicon photonics circuit,” in Silicon Photonics and Photonic Integrated Circuits IV, vol. 9133 (International Society for Optics and Photonics, 2014), p. 91330G.

Murray, K.

M. Ma, K. Murray, M. Ye, S. Lin, Y. Wang, Z. Lu, H. Yun, R. Hu, N. A. F. Jaeger, and L. Chrostowski, “Silicon photonic polarization receiver with automated stabilization for arbitrary input polarizations,” in CLEO: Science and Innovations, (Optical Society of America, 2016), pp. STu4G–8.

Namiki, S.

Novack, A.

A. H. Ahmed, D. Lim, A. Elmoznine, Y. Ma, T. Huynh, C. Williams, L. Vera, Y. Liu, R. Shi, M. Streshinsky, A. Novack, R. Ding, R. Younce, J. Roman, M. Hochberg, S. Shekhar, and A. Rylyakov, “30.6 A 6V Swing 3.6% THD> 40GHz Driver with 4.5× Bandwidth Extension for a 272Gb/s Dual-Polarization 16-QAM Silicon Photonic Transmitter,” in 2019 IEEE International Solid-State Circuits Conference-(ISSCC), (IEEE, 2019), pp. 484–486.

Pantouvaki, M.

P. De Heyn, J. De Coster, P. Verheyen, G. Lepage, M. Pantouvaki, P. Absil, W. Bogaerts, D. Van Thourhout, and J. Van Campenhout, “Polarization-insensitive 5×20Gb/s WDM Ge receiver using compact Si ring filters with collective thermal tuning,” in Optical Fiber Communication Conference, (Optical Society of America, 2014), pp. Th4C–5.

Park, A. H.

Park, A. H. K.

Poon, J. K.

Popovic, M. A.

T. Barwicz, M. R. Watts, M. A. Popović, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

Preite, M.

Raj, K.

Rakich, P. T.

T. Barwicz, M. R. Watts, M. A. Popović, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

Rasras, M. S.

Reeves, C. M.

R. Fletcher and C. M. Reeves, “Function minimization by conjugate gradients,” The Comput. J. 7(2), 149–154 (1964).
[Crossref]

Romagnoli, M.

Roman, J.

A. H. Ahmed, D. Lim, A. Elmoznine, Y. Ma, T. Huynh, C. Williams, L. Vera, Y. Liu, R. Shi, M. Streshinsky, A. Novack, R. Ding, R. Younce, J. Roman, M. Hochberg, S. Shekhar, and A. Rylyakov, “30.6 A 6V Swing 3.6% THD> 40GHz Driver with 4.5× Bandwidth Extension for a 272Gb/s Dual-Polarization 16-QAM Silicon Photonic Transmitter,” in 2019 IEEE International Solid-State Circuits Conference-(ISSCC), (IEEE, 2019), pp. 484–486.

Rylyakov, A.

A. H. Ahmed, D. Lim, A. Elmoznine, Y. Ma, T. Huynh, C. Williams, L. Vera, Y. Liu, R. Shi, M. Streshinsky, A. Novack, R. Ding, R. Younce, J. Roman, M. Hochberg, S. Shekhar, and A. Rylyakov, “30.6 A 6V Swing 3.6% THD> 40GHz Driver with 4.5× Bandwidth Extension for a 272Gb/s Dual-Polarization 16-QAM Silicon Photonic Transmitter,” in 2019 IEEE International Solid-State Circuits Conference-(ISSCC), (IEEE, 2019), pp. 484–486.

Sacher, W. D.

Shekhar, S.

A. H. K. Park, H. Shoman, M. Ma, S. Shekhar, and L. Chrostowski, “Ring resonator based polarization diversity WDM receiver,” Opt. Express 27(5), 6147–6157 (2019).
[Crossref]

A. H. Ahmed, D. Lim, A. Elmoznine, Y. Ma, T. Huynh, C. Williams, L. Vera, Y. Liu, R. Shi, M. Streshinsky, A. Novack, R. Ding, R. Younce, J. Roman, M. Hochberg, S. Shekhar, and A. Rylyakov, “30.6 A 6V Swing 3.6% THD> 40GHz Driver with 4.5× Bandwidth Extension for a 272Gb/s Dual-Polarization 16-QAM Silicon Photonic Transmitter,” in 2019 IEEE International Solid-State Circuits Conference-(ISSCC), (IEEE, 2019), pp. 484–486.

Shi, R.

A. H. Ahmed, D. Lim, A. Elmoznine, Y. Ma, T. Huynh, C. Williams, L. Vera, Y. Liu, R. Shi, M. Streshinsky, A. Novack, R. Ding, R. Younce, J. Roman, M. Hochberg, S. Shekhar, and A. Rylyakov, “30.6 A 6V Swing 3.6% THD> 40GHz Driver with 4.5× Bandwidth Extension for a 272Gb/s Dual-Polarization 16-QAM Silicon Photonic Transmitter,” in 2019 IEEE International Solid-State Circuits Conference-(ISSCC), (IEEE, 2019), pp. 484–486.

Shi, W.

H. Yun, W. Shi, Y. Wang, L. Chrostowski, and N. A. F. Jaeger, “2×2 adiabatic 3-dB coupler on silicon-on-insulator rib waveguides,” in Photonics North 2013, vol. 8915 (International Society for Optics and Photonics, 2013), p. 89150V.

Shoji, Y.

Shoman, H.

Shubin, I.

Smith, H. I.

T. Barwicz, M. R. Watts, M. A. Popović, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

Socci, L.

T. Barwicz, M. R. Watts, M. A. Popović, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

Sorianello, V.

Streshinsky, M.

A. H. Ahmed, D. Lim, A. Elmoznine, Y. Ma, T. Huynh, C. Williams, L. Vera, Y. Liu, R. Shi, M. Streshinsky, A. Novack, R. Ding, R. Younce, J. Roman, M. Hochberg, S. Shekhar, and A. Rylyakov, “30.6 A 6V Swing 3.6% THD> 40GHz Driver with 4.5× Bandwidth Extension for a 272Gb/s Dual-Polarization 16-QAM Silicon Photonic Transmitter,” in 2019 IEEE International Solid-State Circuits Conference-(ISSCC), (IEEE, 2019), pp. 484–486.

Suzuki, K.

Tan, Y.

Tanizawa, K.

Taylor, B. J.

Testa, F.

Thacker, H.

Van Campenhout, J.

P. De Heyn, J. De Coster, P. Verheyen, G. Lepage, M. Pantouvaki, P. Absil, W. Bogaerts, D. Van Thourhout, and J. Van Campenhout, “Polarization-insensitive 5×20Gb/s WDM Ge receiver using compact Si ring filters with collective thermal tuning,” in Optical Fiber Communication Conference, (Optical Society of America, 2014), pp. Th4C–5.

Van Thourhout, D.

P. De Heyn, J. De Coster, P. Verheyen, G. Lepage, M. Pantouvaki, P. Absil, W. Bogaerts, D. Van Thourhout, and J. Van Campenhout, “Polarization-insensitive 5×20Gb/s WDM Ge receiver using compact Si ring filters with collective thermal tuning,” in Optical Fiber Communication Conference, (Optical Society of America, 2014), pp. Th4C–5.

Velha, P.

Vera, L.

A. H. Ahmed, D. Lim, A. Elmoznine, Y. Ma, T. Huynh, C. Williams, L. Vera, Y. Liu, R. Shi, M. Streshinsky, A. Novack, R. Ding, R. Younce, J. Roman, M. Hochberg, S. Shekhar, and A. Rylyakov, “30.6 A 6V Swing 3.6% THD> 40GHz Driver with 4.5× Bandwidth Extension for a 272Gb/s Dual-Polarization 16-QAM Silicon Photonic Transmitter,” in 2019 IEEE International Solid-State Circuits Conference-(ISSCC), (IEEE, 2019), pp. 484–486.

Verheyen, P.

P. De Heyn, J. De Coster, P. Verheyen, G. Lepage, M. Pantouvaki, P. Absil, W. Bogaerts, D. Van Thourhout, and J. Van Campenhout, “Polarization-insensitive 5×20Gb/s WDM Ge receiver using compact Si ring filters with collective thermal tuning,” in Optical Fiber Communication Conference, (Optical Society of America, 2014), pp. Th4C–5.

Wang, Y.

M. Ma, A. H. Park, Y. Wang, H. Shoman, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Sub-wavelength grating-assisted polarization splitter-rotators for silicon-on-insulator platforms,” Opt. Express 27(13), 17581–17591 (2019).
[Crossref]

J. N. Caspers, Y. Wang, L. Chrostowski, and M. Mojahedi, “Active polarization independent coupling to silicon photonics circuit,” in Silicon Photonics and Photonic Integrated Circuits IV, vol. 9133 (International Society for Optics and Photonics, 2014), p. 91330G.

M. Ma, K. Murray, M. Ye, S. Lin, Y. Wang, Z. Lu, H. Yun, R. Hu, N. A. F. Jaeger, and L. Chrostowski, “Silicon photonic polarization receiver with automated stabilization for arbitrary input polarizations,” in CLEO: Science and Innovations, (Optical Society of America, 2016), pp. STu4G–8.

H. Yun, W. Shi, Y. Wang, L. Chrostowski, and N. A. F. Jaeger, “2×2 adiabatic 3-dB coupler on silicon-on-insulator rib waveguides,” in Photonics North 2013, vol. 8915 (International Society for Optics and Photonics, 2013), p. 89150V.

Watts, M. R.

T. Barwicz, M. R. Watts, M. A. Popović, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

Wei, Y.

H. Zhou, Y. Zhao, Y. Wei, F. Li, J. Dong, and X. Zhang, “All-in-one silicon photonic polarization processor,” Nanophotonics 8(12), 2257–2267 (2019).
[Crossref]

Williams, C.

A. H. Ahmed, D. Lim, A. Elmoznine, Y. Ma, T. Huynh, C. Williams, L. Vera, Y. Liu, R. Shi, M. Streshinsky, A. Novack, R. Ding, R. Younce, J. Roman, M. Hochberg, S. Shekhar, and A. Rylyakov, “30.6 A 6V Swing 3.6% THD> 40GHz Driver with 4.5× Bandwidth Extension for a 272Gb/s Dual-Polarization 16-QAM Silicon Photonic Transmitter,” in 2019 IEEE International Solid-State Circuits Conference-(ISSCC), (IEEE, 2019), pp. 484–486.

Winzer, P. J.

Wu, H.

Yao, J.

Ye, M.

M. Ma, K. Murray, M. Ye, S. Lin, Y. Wang, Z. Lu, H. Yun, R. Hu, N. A. F. Jaeger, and L. Chrostowski, “Silicon photonic polarization receiver with automated stabilization for arbitrary input polarizations,” in CLEO: Science and Innovations, (Optical Society of America, 2016), pp. STu4G–8.

Younce, R.

A. H. Ahmed, D. Lim, A. Elmoznine, Y. Ma, T. Huynh, C. Williams, L. Vera, Y. Liu, R. Shi, M. Streshinsky, A. Novack, R. Ding, R. Younce, J. Roman, M. Hochberg, S. Shekhar, and A. Rylyakov, “30.6 A 6V Swing 3.6% THD> 40GHz Driver with 4.5× Bandwidth Extension for a 272Gb/s Dual-Polarization 16-QAM Silicon Photonic Transmitter,” in 2019 IEEE International Solid-State Circuits Conference-(ISSCC), (IEEE, 2019), pp. 484–486.

Yun, H.

M. Ma, K. Murray, M. Ye, S. Lin, Y. Wang, Z. Lu, H. Yun, R. Hu, N. A. F. Jaeger, and L. Chrostowski, “Silicon photonic polarization receiver with automated stabilization for arbitrary input polarizations,” in CLEO: Science and Innovations, (Optical Society of America, 2016), pp. STu4G–8.

H. Yun, W. Shi, Y. Wang, L. Chrostowski, and N. A. F. Jaeger, “2×2 adiabatic 3-dB coupler on silicon-on-insulator rib waveguides,” in Photonics North 2013, vol. 8915 (International Society for Optics and Photonics, 2013), p. 89150V.

Zhang, F.

Zhang, X.

H. Zhou, Y. Zhao, Y. Wei, F. Li, J. Dong, and X. Zhang, “All-in-one silicon photonic polarization processor,” Nanophotonics 8(12), 2257–2267 (2019).
[Crossref]

Zhao, J. H.

C. K. Madsen and J. H. Zhao, Optical filter design and analysis (Wiley, 1999).

Zhao, Y.

H. Zhou, Y. Zhao, Y. Wei, F. Li, J. Dong, and X. Zhang, “All-in-one silicon photonic polarization processor,” Nanophotonics 8(12), 2257–2267 (2019).
[Crossref]

Zheng, X.

Zhou, H.

H. Zhou, Y. Zhao, Y. Wei, F. Li, J. Dong, and X. Zhang, “All-in-one silicon photonic polarization processor,” Nanophotonics 8(12), 2257–2267 (2019).
[Crossref]

IEEE Photonics Technol. Lett. (1)

C. R. Doerr, N. K. Fontaine, and L. L. Buhl, “PDM-DQPSK silicon receiver with integrated monitor and minimum number of controls,” IEEE Photonics Technol. Lett. 24(8), 697–699 (2012).
[Crossref]

IMA J. Numer. Analysis (1)

J. Barzilai and J. M. Borwein, “Two-point step size gradient methods,” IMA J. Numer. Analysis 8(1), 141–148 (1988).
[Crossref]

J. Lightwave Technol. (2)

J. Math. Analysis Appl. (1)

A. Ben-Israel, “A Newton-Raphson method for the solution of systems of equations,” J. Math. Analysis Appl. 15(2), 243–252 (1966).
[Crossref]

Nanophotonics (1)

H. Zhou, Y. Zhao, Y. Wei, F. Li, J. Dong, and X. Zhang, “All-in-one silicon photonic polarization processor,” Nanophotonics 8(12), 2257–2267 (2019).
[Crossref]

Nat. Photonics (1)

T. Barwicz, M. R. Watts, M. A. Popović, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

Opt. Express (8)

A. H. K. Park, H. Shoman, M. Ma, S. Shekhar, and L. Chrostowski, “Ring resonator based polarization diversity WDM receiver,” Opt. Express 27(5), 6147–6157 (2019).
[Crossref]

Y. Ma, Y. Liu, H. Guan, A. Gazman, Q. Li, R. Ding, Y. Li, K. Bergman, T. Baehr-Jones, and M. Hochberg, “Symmetrical polarization splitter/rotator design and application in a polarization insensitive WDM receiver,” Opt. Express 23(12), 16052–16062 (2015).
[Crossref]

D. Y. Lee, X. Zheng, J. Yao, Y. Luo, J.-H. Lee, S. Lin, H. Thacker, J. Bovington, I. Shubin, S. S. Djordjevic, J. E. Cunningham, K. Raj, and A. V. Krishnamoorthy, “Error-free operation of a polarization-insensitive 4λ × 25 Gbps silicon photonic wdm receiver with closed-loop thermal stabilization of Si microrings,” Opt. Express 24(12), 13204–13209 (2016).
[Crossref]

R. Gatdula, K. Kim, A. Melikyan, Y.-K. Chen, and P. Dong, “Simultaneous four-channel thermal adaptation of polarization insensitive silicon photonics WDM receiver,” Opt. Express 25(22), 27119–27126 (2017).
[Crossref]

A. Melikyan, K. Kim, N. Fontaine, S. Chandrasekhar, Y.-K. Chen, and P. Dong, “Inter-polarization mixers for coherent detection of optical signals,” Opt. Express 26(14), 18523–18531 (2018).
[Crossref]

S.-H. Kim, K. Tanizawa, Y. Shoji, G. Cong, K. Suzuki, K. Ikeda, H. Ishikawa, S. Namiki, and H. Kawashima, “Compact 2×2 polarization-diversity Si-wire switch,” Opt. Express 22(24), 29818–29826 (2014).
[Crossref]

W. D. Sacher, T. Barwicz, B. J. Taylor, and J. K. Poon, “Polarization rotator-splitters in standard active silicon photonics platforms,” Opt. Express 22(4), 3777–3786 (2014).
[Crossref]

M. Ma, A. H. Park, Y. Wang, H. Shoman, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Sub-wavelength grating-assisted polarization splitter-rotators for silicon-on-insulator platforms,” Opt. Express 27(13), 17581–17591 (2019).
[Crossref]

Opt. Lett. (1)

Photonics Res. (1)

D. A. B. Miller, “Self-configuring universal linear optical component,” Photonics Res. 1(1), 1–15 (2013).
[Crossref]

The Comput. J. (1)

R. Fletcher and C. M. Reeves, “Function minimization by conjugate gradients,” The Comput. J. 7(2), 149–154 (1964).
[Crossref]

Other (12)

C. R. Doerr and L. Chen, “Monolithic PDM-DQPSK receiver in silicon,” in 36th European Conference and Exhibition on Optical Communication, (IEEE, 2010), pp. 1–3.

H. Yun, W. Shi, Y. Wang, L. Chrostowski, and N. A. F. Jaeger, “2×2 adiabatic 3-dB coupler on silicon-on-insulator rib waveguides,” in Photonics North 2013, vol. 8915 (International Society for Optics and Photonics, 2013), p. 89150V.

C. K. Madsen and J. H. Zhao, Optical filter design and analysis (Wiley, 1999).

SciPy community, “Solve a nonlinear least-squares problem with bounds on the variables,” https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.least_squares.html .

J. N. Caspers, Y. Wang, L. Chrostowski, and M. Mojahedi, “Active polarization independent coupling to silicon photonics circuit,” in Silicon Photonics and Photonic Integrated Circuits IV, vol. 9133 (International Society for Optics and Photonics, 2014), p. 91330G.

M. Ma, K. Murray, M. Ye, S. Lin, Y. Wang, Z. Lu, H. Yun, R. Hu, N. A. F. Jaeger, and L. Chrostowski, “Silicon photonic polarization receiver with automated stabilization for arbitrary input polarizations,” in CLEO: Science and Innovations, (Optical Society of America, 2016), pp. STu4G–8.

A. Melikyan, N. Kaneda, K. Kim, and P. Dong, “Inter-polarization 180-degree mixer for reception of m-ask signals,” in 2018 European Conference on Optical Communication (ECOC), (IEEE, 2018), pp. 1–3.

A. H. Ahmed, D. Lim, A. Elmoznine, Y. Ma, T. Huynh, C. Williams, L. Vera, Y. Liu, R. Shi, M. Streshinsky, A. Novack, R. Ding, R. Younce, J. Roman, M. Hochberg, S. Shekhar, and A. Rylyakov, “30.6 A 6V Swing 3.6% THD> 40GHz Driver with 4.5× Bandwidth Extension for a 272Gb/s Dual-Polarization 16-QAM Silicon Photonic Transmitter,” in 2019 IEEE International Solid-State Circuits Conference-(ISSCC), (IEEE, 2019), pp. 484–486.

L. Chrostowski and M. Hochberg, Silicon photonics design: from devices to systems (Cambridge University, 2015).

L. Chen, C. R. Doerr, and Y.-K. Chen, “Polarization-diversified DWDM receiver on silicon free of polarization-dependent wavelength shift,” in Optical Fiber Communication Conference, (IEEE, 2012), pp. 1–3.

P. De Heyn, J. De Coster, P. Verheyen, G. Lepage, M. Pantouvaki, P. Absil, W. Bogaerts, D. Van Thourhout, and J. Van Campenhout, “Polarization-insensitive 5×20Gb/s WDM Ge receiver using compact Si ring filters with collective thermal tuning,” in Optical Fiber Communication Conference, (Optical Society of America, 2014), pp. Th4C–5.

P. Dong, Y.-K. Chen, and L. L. Buhl, “Reconfigurable four-channel polarization diversity silicon photonic WDM receiver,” in Optical Fiber Communication Conference, (Optical Society of America, 2015), pp. W3A–2.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1.
Fig. 1. (a) Schematic of our polarization receiver with an arbitrary polarization input. (b) Optical micrograph of a fabricated polarization receiver.
Fig. 2.
Fig. 2. Measured optical power at the output port with various tuning powers applied to the thermal phase shifters, H1 and H2, for four input polarization ratios: (a) 100% TE mode input, (b) 100% TM mode input, (c) 50% TE and 50% TM mode input, and (d) 75% TE and 25% TM mode input.
Fig. 3.
Fig. 3. Flow diagrams illustrating (a) the GLD-based, and (b) the basic GD- and B-B GD-based minimization method for the control algorithms.
Fig. 4.
Fig. 4. Flow diagram illustrating the minimization process for the single-iteration, two-stage control algorithm: (a) an "ISTM" method for Stage 1 and (b) a dynamic minimum tracking method for Stage 2.
Fig. 5.
Fig. 5. Schematic of the experimental setup for eye diagram and BER measurements.
Fig. 6.
Fig. 6. Measurement results for four control algorithms: (a) BERs versus iteration and (b) normalized optical power at the output power and feedback ports of the PR versus iteration. Inset Fig.: Zoom-in of the measured optical power at the output port.
Fig. 7.
Fig. 7. (a) BER versus optical input power (markers for measured BERs and solid lines for the polynomial fittings) and (b) some measured eye diagrams with four different polarization states in the optical fiber. The polarization angles of the polarization state 1 - 4: 3.0 degree, 13.5 degree, 22.8 degree, and 84.6 degree.
Fig. 8.
Fig. 8. Measurement results of tracking and stabilization of continuous changed input polarization states: (a) BERs versus tracking time, a reference BER level (dash line), and optical power penalty to achieve a BER of 10−10; (b) Normalized optical power at feedback port of the PR versus tracking time; (c) Polarization angles and extinction ratios of the transmitted light in the optical fiber versus tracking time, and electric field distributions of slow-axis and fast-axis polarization state.

Equations (10)

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

α i = Δ x i Δ g i T / Δ g i 2
f ( x , h 1 , h 2 ) = E 1 ( x , h 1 , h 2 ) ,
E out ( x , h 1 , h 2 ) = [ E 1 ( x , h 1 , h 2 ) E 2 ( x , h 1 , h 2 ) ] = M ( x ) E in ( h 1 , h 2 )
Δ f = f ( x , h 1 , h 2 ) x ϵ
Δ φ = 2 π L λ 0 Δ n eff
Δ n eff = d n eff d T Δ T
Δ Q = m c h Δ T
P = Δ Q = m c h Δ T = m c h Δ n eff d n eff d T = m c h λ d n eff d T 2 π L Δ φ
P out = 0.5 ( 1 + cos ( Δ φ ) )
Δ φ = α P + β = α ( I 2 R ) + β