Abstract

We propose and fabricate a novel circuit that combines two two-dimensional (2D) grating couplers and a microring resonator (MRR). According to the polarization states, one 2D grating coupler first splits the input signals into two orthogonal paths, which co-propagate in the loop and share a common MRR, and then the two paths are combined together by the other 2D grating coupler. The proposed circuit is polarization insensitive and can be used as a polarization insensitive filter. For demonstration, the wavelength division and polarization division multiplexing (WDM-PDM) non return-to-zero differential-phase-shift-keying (NRZ-DPSK) signals can be demodulated successfully. The bit error ratio measurements show an error free operation, reflecting the good performance and the practicability.

© 2013 Optical Society of America

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2013 (1)

2012 (7)

W. H. Wu, Y. Yu, S. J. Hu, B. R. Zou, and X. L. Zhang, “All-optical format conversion for polarization and wavelength division multiplexed system,” IEEE Photon. Technol. Lett.24(18), 1606–1609 (2012).
[CrossRef]

H. Y. Jiang, L. S. Yan, J. Ye, W. Pan, B. Luo, and X. S. Yao, “PDM RZ-to-NRZ and NRZ-to-PRZ format conversions using a variable DGD element inside a polarization-diversified loop,” Opt. Lett.37(13), 2535–2537 (2012).
[CrossRef] [PubMed]

L. Xiang, Y. M. Xu, Y. Yu, and X. L. Zhang, “An ultracompact DP-QPSK demodulator based on multimode interference and photonic crystals,” J. Lightwave Technol.30(11), 1595–1601 (2012).
[CrossRef]

S. Tsunashima, F. Nakajima, Y. Nasu, R. Kasahara, Y. Nakanishi, T. Saida, T. Yamada, K. Sano, T. Hashimoto, H. Fukuyama, H. Nosaka, and K. Murata, “Silica-based, compact and variable-optical-attenuator integrated coherent receiver with stable optoelectronic coupling system,” Opt. Express20(24), 27174–27179 (2012).
[CrossRef] [PubMed]

P. Dong, C. J. Xie, L. Chen, L. L. Buhl, and Y. K. Chen, “112-Gb/s monolithic PDM-QPSK modulator in silicon,” Opt. Express20(26), B624–B629 (2012).
[CrossRef] [PubMed]

L. S. Yan, A. E. Willner, X. X. Wu, A. L. Yi, B. Antonella, Z. Y. Chen, and H. Y. Jiang, “All-optical signal processing for ultrahigh speed optical systems and networks,” J. Lightwave Technol.30(24), 3760–3770 (2012).
[CrossRef]

P. J. Winzer, “High-spectral-efficiency optical modulation formats,” J. Lightwave Technol.30(24), 3824–3835 (2012).
[CrossRef]

2011 (4)

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron.17(3), 597–608 (2011).
[CrossRef]

C. R. Doerr and T. F. Taunay, “Silicon photonics core-, wavelength-, and polarization-diversity receiver,” IEEE Photon. Technol. Lett.23(9), 597–599 (2011).
[CrossRef]

C. R. Doerr, L. Buhl, Y. Baeyens, R. Aroca, S. Chandrasekhar, X. Liu, L. Chen, and Y. K. Chen, “Packaged monolithic silicon 112-Gb/s coherent receiver,” IEEE Photon. Technol. Lett.23(12), 762–764 (2011).
[CrossRef]

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T.-C. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, S. Chandrasekhar, and Y. K. Chen, “Monolithic InP dual-polarization and dual-quadrature coherent receiver,” IEEE Photon. Technol. Lett.23(11), 694–696 (2011).
[CrossRef]

2010 (2)

2009 (1)

F. Liu, T. Wang, Z. Zhang, M. Qiu, and Y. Su, “On-chip photonic generation of ultra-wideband monocycle pulses,” Electron. Lett.45(24), 1247–1249 (2009).
[CrossRef]

2008 (1)

2007 (2)

2006 (2)

Y. Yu, X. L. Zhang, and D. X. Huang, “All-optical clock recovery from NRZ-DPSK signal,” Photon. Technol. Lett. IEEE18(22), 2356–2358 (2006).
[CrossRef]

D. X. Xu, S. Janz, and P. Cheben, “Design of polarization-insensitive ring resonators in silicon-on-insulator using MMI couplers and cladding stress engineering,” IEEE Photon. Technol. Lett.18(2), 343–345 (2006).
[CrossRef]

2003 (1)

T. Dirk, H. Chong, B. Peter, F. Lars, D. L. Rue, and B. Roel, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photon. Technol. Lett.15(9), 1249–1251 (2003).
[CrossRef]

1992 (1)

E. G. Stephen, M. F. Linn, G. P. James, and B. S. Neal, “Polarization multiplexing with solitons,” J. Lightwave Technol.10, 28–35 (1992).

Antonella, B.

Aroca, R.

C. R. Doerr, L. Buhl, Y. Baeyens, R. Aroca, S. Chandrasekhar, X. Liu, L. Chen, and Y. K. Chen, “Packaged monolithic silicon 112-Gb/s coherent receiver,” IEEE Photon. Technol. Lett.23(12), 762–764 (2011).
[CrossRef]

Baets, R.

Baeyens, Y.

C. R. Doerr, L. Buhl, Y. Baeyens, R. Aroca, S. Chandrasekhar, X. Liu, L. Chen, and Y. K. Chen, “Packaged monolithic silicon 112-Gb/s coherent receiver,” IEEE Photon. Technol. Lett.23(12), 762–764 (2011).
[CrossRef]

Beausoleil, R. G.

Bogaerts, W.

Buhl, L.

C. R. Doerr, L. Buhl, Y. Baeyens, R. Aroca, S. Chandrasekhar, X. Liu, L. Chen, and Y. K. Chen, “Packaged monolithic silicon 112-Gb/s coherent receiver,” IEEE Photon. Technol. Lett.23(12), 762–764 (2011).
[CrossRef]

Buhl, L. L.

Chandrasekhar, S.

C. R. Doerr, L. Buhl, Y. Baeyens, R. Aroca, S. Chandrasekhar, X. Liu, L. Chen, and Y. K. Chen, “Packaged monolithic silicon 112-Gb/s coherent receiver,” IEEE Photon. Technol. Lett.23(12), 762–764 (2011).
[CrossRef]

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T.-C. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, S. Chandrasekhar, and Y. K. Chen, “Monolithic InP dual-polarization and dual-quadrature coherent receiver,” IEEE Photon. Technol. Lett.23(11), 694–696 (2011).
[CrossRef]

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, and S. Chandrasekhar, “Monolithic polarization and phase diversity coherent receiver in silicon,” J. Lightwave Technol.28(4), 520–525 (2010).
[CrossRef]

Cheben, P.

D. X. Xu, S. Janz, and P. Cheben, “Design of polarization-insensitive ring resonators in silicon-on-insulator using MMI couplers and cladding stress engineering,” IEEE Photon. Technol. Lett.18(2), 343–345 (2006).
[CrossRef]

Chen, L.

P. Dong, C. J. Xie, L. Chen, L. L. Buhl, and Y. K. Chen, “112-Gb/s monolithic PDM-QPSK modulator in silicon,” Opt. Express20(26), B624–B629 (2012).
[CrossRef] [PubMed]

C. R. Doerr, L. Buhl, Y. Baeyens, R. Aroca, S. Chandrasekhar, X. Liu, L. Chen, and Y. K. Chen, “Packaged monolithic silicon 112-Gb/s coherent receiver,” IEEE Photon. Technol. Lett.23(12), 762–764 (2011).
[CrossRef]

Chen, Y. K.

P. Dong, C. J. Xie, L. Chen, L. L. Buhl, and Y. K. Chen, “112-Gb/s monolithic PDM-QPSK modulator in silicon,” Opt. Express20(26), B624–B629 (2012).
[CrossRef] [PubMed]

C. R. Doerr, L. Buhl, Y. Baeyens, R. Aroca, S. Chandrasekhar, X. Liu, L. Chen, and Y. K. Chen, “Packaged monolithic silicon 112-Gb/s coherent receiver,” IEEE Photon. Technol. Lett.23(12), 762–764 (2011).
[CrossRef]

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T.-C. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, S. Chandrasekhar, and Y. K. Chen, “Monolithic InP dual-polarization and dual-quadrature coherent receiver,” IEEE Photon. Technol. Lett.23(11), 694–696 (2011).
[CrossRef]

Chen, Z. Y.

Chong, H.

T. Dirk, H. Chong, B. Peter, F. Lars, D. L. Rue, and B. Roel, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photon. Technol. Lett.15(9), 1249–1251 (2003).
[CrossRef]

Chraplyvy, A.

A. Chraplyvy, “The coming capacity crunch,” in 35th European Conference on Optical Communication (ECOC 2009), pp. 20–24.

De Dobbelaere, P.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron.17(3), 597–608 (2011).
[CrossRef]

Ding, Y. H.

Dirk, T.

T. Dirk, H. Chong, B. Peter, F. Lars, D. L. Rue, and B. Roel, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photon. Technol. Lett.15(9), 1249–1251 (2003).
[CrossRef]

Doerr, C. R.

C. R. Doerr and T. F. Taunay, “Silicon photonics core-, wavelength-, and polarization-diversity receiver,” IEEE Photon. Technol. Lett.23(9), 597–599 (2011).
[CrossRef]

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T.-C. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, S. Chandrasekhar, and Y. K. Chen, “Monolithic InP dual-polarization and dual-quadrature coherent receiver,” IEEE Photon. Technol. Lett.23(11), 694–696 (2011).
[CrossRef]

C. R. Doerr, L. Buhl, Y. Baeyens, R. Aroca, S. Chandrasekhar, X. Liu, L. Chen, and Y. K. Chen, “Packaged monolithic silicon 112-Gb/s coherent receiver,” IEEE Photon. Technol. Lett.23(12), 762–764 (2011).
[CrossRef]

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, and S. Chandrasekhar, “Monolithic polarization and phase diversity coherent receiver in silicon,” J. Lightwave Technol.28(4), 520–525 (2010).
[CrossRef]

Dong, P.

Dumon, P.

Fukuda, H.

Fukuyama, H.

Gloeckner, S.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron.17(3), 597–608 (2011).
[CrossRef]

Hashimoto, T.

Houtsma, V.

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T.-C. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, S. Chandrasekhar, and Y. K. Chen, “Monolithic InP dual-polarization and dual-quadrature coherent receiver,” IEEE Photon. Technol. Lett.23(11), 694–696 (2011).
[CrossRef]

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, and S. Chandrasekhar, “Monolithic polarization and phase diversity coherent receiver in silicon,” J. Lightwave Technol.28(4), 520–525 (2010).
[CrossRef]

Hu, S. J.

W. H. Wu, Y. Yu, S. J. Hu, B. R. Zou, and X. L. Zhang, “All-optical format conversion for polarization and wavelength division multiplexed system,” IEEE Photon. Technol. Lett.24(18), 1606–1609 (2012).
[CrossRef]

Hu, T.

Hu, T.-C.

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T.-C. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, S. Chandrasekhar, and Y. K. Chen, “Monolithic InP dual-polarization and dual-quadrature coherent receiver,” IEEE Photon. Technol. Lett.23(11), 694–696 (2011).
[CrossRef]

Huang, D. X.

Itabashi, S.

James, G. P.

E. G. Stephen, M. F. Linn, G. P. James, and B. S. Neal, “Polarization multiplexing with solitons,” J. Lightwave Technol.10, 28–35 (1992).

Janz, S.

D. X. Xu, S. Janz, and P. Cheben, “Design of polarization-insensitive ring resonators in silicon-on-insulator using MMI couplers and cladding stress engineering,” IEEE Photon. Technol. Lett.18(2), 343–345 (2006).
[CrossRef]

Jiang, H. Y.

Kasahara, R.

Lars, F.

T. Dirk, H. Chong, B. Peter, F. Lars, D. L. Rue, and B. Roel, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photon. Technol. Lett.15(9), 1249–1251 (2003).
[CrossRef]

Li, Y. C.

Linn, M. F.

E. G. Stephen, M. F. Linn, G. P. James, and B. S. Neal, “Polarization multiplexing with solitons,” J. Lightwave Technol.10, 28–35 (1992).

Liu, F.

F. Liu, T. Wang, Z. Zhang, M. Qiu, and Y. Su, “On-chip photonic generation of ultra-wideband monocycle pulses,” Electron. Lett.45(24), 1247–1249 (2009).
[CrossRef]

Liu, L.

Liu, X.

C. R. Doerr, L. Buhl, Y. Baeyens, R. Aroca, S. Chandrasekhar, X. Liu, L. Chen, and Y. K. Chen, “Packaged monolithic silicon 112-Gb/s coherent receiver,” IEEE Photon. Technol. Lett.23(12), 762–764 (2011).
[CrossRef]

Luo, B.

Masini, G.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron.17(3), 597–608 (2011).
[CrossRef]

Mekis, A.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron.17(3), 597–608 (2011).
[CrossRef]

Murata, K.

Nakajima, F.

Nakanishi, Y.

Narasimha, A.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron.17(3), 597–608 (2011).
[CrossRef]

Nasu, Y.

Neal, B. S.

E. G. Stephen, M. F. Linn, G. P. James, and B. S. Neal, “Polarization multiplexing with solitons,” J. Lightwave Technol.10, 28–35 (1992).

Neilson, D. T.

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T.-C. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, S. Chandrasekhar, and Y. K. Chen, “Monolithic InP dual-polarization and dual-quadrature coherent receiver,” IEEE Photon. Technol. Lett.23(11), 694–696 (2011).
[CrossRef]

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, and S. Chandrasekhar, “Monolithic polarization and phase diversity coherent receiver in silicon,” J. Lightwave Technol.28(4), 520–525 (2010).
[CrossRef]

Nosaka, H.

Ou, H. Y.

Pan, W.

Peter, B.

T. Dirk, H. Chong, B. Peter, F. Lars, D. L. Rue, and B. Roel, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photon. Technol. Lett.15(9), 1249–1251 (2003).
[CrossRef]

Peucheret, C.

Pinguet, T.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron.17(3), 597–608 (2011).
[CrossRef]

Pluk, E.

Pu, M. H.

Qiu, M.

F. Liu, T. Wang, Z. Zhang, M. Qiu, and Y. Su, “On-chip photonic generation of ultra-wideband monocycle pulses,” Electron. Lett.45(24), 1247–1249 (2009).
[CrossRef]

Roel, B.

T. Dirk, H. Chong, B. Peter, F. Lars, D. L. Rue, and B. Roel, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photon. Technol. Lett.15(9), 1249–1251 (2003).
[CrossRef]

Rue, D. L.

T. Dirk, H. Chong, B. Peter, F. Lars, D. L. Rue, and B. Roel, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photon. Technol. Lett.15(9), 1249–1251 (2003).
[CrossRef]

Sahni, S.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron.17(3), 597–608 (2011).
[CrossRef]

Saida, T.

Sano, K.

Sauer, N. J.

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T.-C. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, S. Chandrasekhar, and Y. K. Chen, “Monolithic InP dual-polarization and dual-quadrature coherent receiver,” IEEE Photon. Technol. Lett.23(11), 694–696 (2011).
[CrossRef]

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, and S. Chandrasekhar, “Monolithic polarization and phase diversity coherent receiver in silicon,” J. Lightwave Technol.28(4), 520–525 (2010).
[CrossRef]

Seoane, J.

Shinojima, H.

Song, M. P.

Stephen, E. G.

E. G. Stephen, M. F. Linn, G. P. James, and B. S. Neal, “Polarization multiplexing with solitons,” J. Lightwave Technol.10, 28–35 (1992).

Su, Y.

F. Liu, T. Wang, Z. Zhang, M. Qiu, and Y. Su, “On-chip photonic generation of ultra-wideband monocycle pulses,” Electron. Lett.45(24), 1247–1249 (2009).
[CrossRef]

Taillaert, D.

Taunay, T. F.

C. R. Doerr and T. F. Taunay, “Silicon photonics core-, wavelength-, and polarization-diversity receiver,” IEEE Photon. Technol. Lett.23(9), 597–599 (2011).
[CrossRef]

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[CrossRef]

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, and S. Chandrasekhar, “Monolithic polarization and phase diversity coherent receiver in silicon,” J. Lightwave Technol.28(4), 520–525 (2010).
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C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T.-C. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, S. Chandrasekhar, and Y. K. Chen, “Monolithic InP dual-polarization and dual-quadrature coherent receiver,” IEEE Photon. Technol. Lett.23(11), 694–696 (2011).
[CrossRef]

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, and S. Chandrasekhar, “Monolithic polarization and phase diversity coherent receiver in silicon,” J. Lightwave Technol.28(4), 520–525 (2010).
[CrossRef]

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Yi, A. L.

Yu, Y.

W. H. Wu, Y. Yu, S. J. Hu, B. R. Zou, and X. L. Zhang, “All-optical format conversion for polarization and wavelength division multiplexed system,” IEEE Photon. Technol. Lett.24(18), 1606–1609 (2012).
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F. Liu, T. Wang, Z. Zhang, M. Qiu, and Y. Su, “On-chip photonic generation of ultra-wideband monocycle pulses,” Electron. Lett.45(24), 1247–1249 (2009).
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Zou, B. R.

W. H. Wu, Y. Yu, S. J. Hu, B. R. Zou, and X. L. Zhang, “All-optical format conversion for polarization and wavelength division multiplexed system,” IEEE Photon. Technol. Lett.24(18), 1606–1609 (2012).
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Electron. Lett. (1)

F. Liu, T. Wang, Z. Zhang, M. Qiu, and Y. Su, “On-chip photonic generation of ultra-wideband monocycle pulses,” Electron. Lett.45(24), 1247–1249 (2009).
[CrossRef]

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[CrossRef]

C. R. Doerr, L. Buhl, Y. Baeyens, R. Aroca, S. Chandrasekhar, X. Liu, L. Chen, and Y. K. Chen, “Packaged monolithic silicon 112-Gb/s coherent receiver,” IEEE Photon. Technol. Lett.23(12), 762–764 (2011).
[CrossRef]

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[CrossRef]

W. H. Wu, Y. Yu, S. J. Hu, B. R. Zou, and X. L. Zhang, “All-optical format conversion for polarization and wavelength division multiplexed system,” IEEE Photon. Technol. Lett.24(18), 1606–1609 (2012).
[CrossRef]

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[CrossRef]

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J. Lightwave Technol. (5)

Opt. Express (6)

Opt. Lett. (2)

Photon. Technol. Lett. IEEE (1)

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[CrossRef]

Other (3)

Lumerical Solutions, Inc., http://www.lumerical.com/ .

A. Chraplyvy, “The coming capacity crunch,” in 35th European Conference on Optical Communication (ECOC 2009), pp. 20–24.

D. Po, X. Liu, C. Sethumadhavan, L. L. Buhl, R. Aroca, Y. Baeyens, and Y. K. Chen, “224-Gb/s PDM-16-QAM modulator and receiver based on silicon photonic integrated circuits,” in National Fiber Optic Engineers Conference, (Optical Society of America, 2013), paper PDP5C.

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Figures (8)

Fig. 1
Fig. 1

Principle of the proposed circuit

Fig. 2
Fig. 2

The electric field distribution of three different input polarization states coupled into the 2D grating coupler

Fig. 3
Fig. 3

The normalized power coupled into the circuit when polarization angle varies from 0° to 90°

Fig. 4
Fig. 4

The SEM top view of (a) the layout of the fabricated circuit, (b) the 2D grating coupler, (c) the zoom in image of the holes, (d) the MRR and (e) the coupling region of the MRR

Fig. 5
Fig. 5

Measured transmission spectra of the MRR

Fig. 6
Fig. 6

The experimental setup

Fig. 7
Fig. 7

The measured spectra (a) before and (b) after the proposed circuit

Fig. 8
Fig. 8

The measured (a) eye diagram and (b) the BER curves for the demodulated signal

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