Abstract

The implementation agreement of the Optical Internet Forum for a dual polarization (DP) I/Q downconverter defines strict requirements for the phase diversity network, resulting in a negligible penalty, but does not specify the extinction ratio (ER) of the polarization beam splitters (PBS) on which the polarization diversity network is based. We propose a novel metric, based on the Frobenius norm of the Jones receiver matrix, to accurately estimate the sensitivity penalty from receiver non-idealities, stablishing a precise interface for hardware specification. Results will be numerically verified for the reception of 112 Gbps DP-QPSK signals in a realistic receiver scenario with subsequent state-of-art DSP algorithms. The proposed metric highlights the benefits of the polarization diversity scheme based on two PBS, compared to the common alternative based on a PBS and a BS, as it achieves an improvement in the receiver sensitivity of at least 3 dB for the same ER. Furthermore, this paper shows than the sensitivity penalty is negligible for an ER higher than 16 dB and that it less than 2 dB for an ER of 8 dB. These results can have an important impact in monolithically integrated DP downconverters in which practical integration of PBS with high ER is still challenging.

© 2015 Optical Society of America

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References

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  1. Optical Internetworking Forum, “Implementation agreement for integrated dual polarization intradyne coherent receivers, ” document OIF-DPC-RX-01.2 (Nov. 2013), http://www.oiforum.com/public/impagreements.html
  2. S. J. Savory, “Digital Coherent Optical Receivers: Algorithms and Subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).
    [Crossref]
  3. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008).
    [Crossref] [PubMed]
  4. I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008).
    [Crossref]
  5. J. S. Fandiño and P. Muñoz, “Manufacturing Tolerance Analysis of an MMI-Based 90° Optical Hybrid for InP Integrated Coherent Receivers,” IEEE Photon. J. 5(2), 7900512 (2013).
    [Crossref]
  6. T. Richter, M. Kroh, J. Wang, A. Theurer, C. Zawadzki, Z. Zhang, N. Keil, A. Steffan, and C. Schubert, “Integrated polarization-diversity coherent receiver on polymer PLC for QPSK and QAM signals,” in Proc. OFC 2012, pp.1–3, paper OW3G.1.
    [Crossref]
  7. H. S. Chung, S. H. Chang, and K. Kim, “Compensation of IQ mismatch in optical PDM–OFDM coherent receivers,” Opt. Fiber Technol. 16(5), 304–308 (2010).
    [Crossref]
  8. M. Morsy-Osman, M. Chagnon, X. Xu, Q. Zhuge, M. Poulin, Y. Painchaud, M. Pelletier, C. Paquet, and D. V. Plant, “Analytical and experimental performance evaluation of an integrated Si-photonic balanced coherent receiver in a colorless scenario,” Opt. Express 22(5), 5693–5730 (2014).
    [Crossref] [PubMed]
  9. D. Dai, Z. Wang, J. Peters, and J. E. Bowers, “Compact Polarization Beam Splitter Using an Asymmetrical Mach–Zehnder Interferometer Based on Silicon-on-Insulator Waveguides,” IEEE Photon. Technol. Lett. 24(8), 673–675 (2012).
    [Crossref]
  10. D. Perez-Galacho, R. Zhang, A. Ortega-Monux, R. Halir, C. Alonso-Ramos, P. Runge, K. Janiak, G. Zhou, H. G. Bach, A. G. Steffan, and I. Molina-Fernandez, “Integrated Polarization Beam Splitter for 100/400 GE Polarization Multiplexed Coherent Optical Communications,” J. Lightwave Technol. 32(3), 361–368 (2014).
    [Crossref]
  11. M. Yin, W. Yang, Y. Li, X. Wang, and H. Li, “CMOS-compatible and fabrication-tolerant MMI-based polarization beam splitter,” Opt. Commun. 335, 48–52 (2015).
    [Crossref]
  12. D. W. Kim, M. H. Lee, Y. Kim, and K. H. Kim, “Planar-type polarization beam splitter based on a bridged silicon waveguide coupler,” Opt. Express 23(2), 998–1004 (2015).
    [Crossref] [PubMed]
  13. J. Tubbax, L. Van der Perre, S. Donnay, M. Engels, M. Moonen, and H. D. Man, “Joint compensation of IQ imbalance, frequency offset and phase noise in OFDM receivers,” European Transactions on Telecommunications 15(3), 283–292 (2004).
    [Crossref]
  14. P. J. Reyes-Iglesias, I. Molina-Fernández, A. Moscoso-Mártir, and A. Ortega-Moñux, “High-performance monolithically integrated 120° downconverter with relaxed hardware constraints,” Opt. Express 20(5), 5725–5741 (2012).
    [Crossref] [PubMed]
  15. G. H. Golub, C. F. Van Loan, and JHU Matrix Computations Press, 1996.
  16. G. U. Ramos, “Roundoff error analysis of the fast Fourier transform,” Math. Comput. 25(116), 757–768 (1971).
    [Crossref]
  17. P. E. An, M. Brown, and C. J. Harris, “On the convergence rate performance of normalized least-mean-square adaptation,” IEEE Trans. Neural Netw. 6(6), 1549–1552 (1997).
    [Crossref] [PubMed]
  18. B. Zhang, C. Malouin, and T. J. Schmidt, “Towards full band colorless reception with coherent balanced receivers,” Opt. Express 20(9), 10339–10352 (2012).
    [Crossref] [PubMed]
  19. Agilent Technologies, “MIMO Performance and Condition Number in LTE Test”, Application Note 5990–4759EN, http://cp.literature.agilent.com/litweb/pdf/5990-4759EN.pdf

2015 (2)

M. Yin, W. Yang, Y. Li, X. Wang, and H. Li, “CMOS-compatible and fabrication-tolerant MMI-based polarization beam splitter,” Opt. Commun. 335, 48–52 (2015).
[Crossref]

D. W. Kim, M. H. Lee, Y. Kim, and K. H. Kim, “Planar-type polarization beam splitter based on a bridged silicon waveguide coupler,” Opt. Express 23(2), 998–1004 (2015).
[Crossref] [PubMed]

2014 (2)

2013 (1)

J. S. Fandiño and P. Muñoz, “Manufacturing Tolerance Analysis of an MMI-Based 90° Optical Hybrid for InP Integrated Coherent Receivers,” IEEE Photon. J. 5(2), 7900512 (2013).
[Crossref]

2012 (3)

2010 (2)

H. S. Chung, S. H. Chang, and K. Kim, “Compensation of IQ mismatch in optical PDM–OFDM coherent receivers,” Opt. Fiber Technol. 16(5), 304–308 (2010).
[Crossref]

S. J. Savory, “Digital Coherent Optical Receivers: Algorithms and Subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).
[Crossref]

2008 (2)

S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008).
[Crossref] [PubMed]

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008).
[Crossref]

2004 (1)

J. Tubbax, L. Van der Perre, S. Donnay, M. Engels, M. Moonen, and H. D. Man, “Joint compensation of IQ imbalance, frequency offset and phase noise in OFDM receivers,” European Transactions on Telecommunications 15(3), 283–292 (2004).
[Crossref]

1997 (1)

P. E. An, M. Brown, and C. J. Harris, “On the convergence rate performance of normalized least-mean-square adaptation,” IEEE Trans. Neural Netw. 6(6), 1549–1552 (1997).
[Crossref] [PubMed]

1971 (1)

G. U. Ramos, “Roundoff error analysis of the fast Fourier transform,” Math. Comput. 25(116), 757–768 (1971).
[Crossref]

Alonso-Ramos, C.

An, P. E.

P. E. An, M. Brown, and C. J. Harris, “On the convergence rate performance of normalized least-mean-square adaptation,” IEEE Trans. Neural Netw. 6(6), 1549–1552 (1997).
[Crossref] [PubMed]

Bach, H. G.

Bowers, J. E.

D. Dai, Z. Wang, J. Peters, and J. E. Bowers, “Compact Polarization Beam Splitter Using an Asymmetrical Mach–Zehnder Interferometer Based on Silicon-on-Insulator Waveguides,” IEEE Photon. Technol. Lett. 24(8), 673–675 (2012).
[Crossref]

Brown, M.

P. E. An, M. Brown, and C. J. Harris, “On the convergence rate performance of normalized least-mean-square adaptation,” IEEE Trans. Neural Netw. 6(6), 1549–1552 (1997).
[Crossref] [PubMed]

Chagnon, M.

Chang, S. H.

H. S. Chung, S. H. Chang, and K. Kim, “Compensation of IQ mismatch in optical PDM–OFDM coherent receivers,” Opt. Fiber Technol. 16(5), 304–308 (2010).
[Crossref]

Chung, H. S.

H. S. Chung, S. H. Chang, and K. Kim, “Compensation of IQ mismatch in optical PDM–OFDM coherent receivers,” Opt. Fiber Technol. 16(5), 304–308 (2010).
[Crossref]

Dai, D.

D. Dai, Z. Wang, J. Peters, and J. E. Bowers, “Compact Polarization Beam Splitter Using an Asymmetrical Mach–Zehnder Interferometer Based on Silicon-on-Insulator Waveguides,” IEEE Photon. Technol. Lett. 24(8), 673–675 (2012).
[Crossref]

Donnay, S.

J. Tubbax, L. Van der Perre, S. Donnay, M. Engels, M. Moonen, and H. D. Man, “Joint compensation of IQ imbalance, frequency offset and phase noise in OFDM receivers,” European Transactions on Telecommunications 15(3), 283–292 (2004).
[Crossref]

Engels, M.

J. Tubbax, L. Van der Perre, S. Donnay, M. Engels, M. Moonen, and H. D. Man, “Joint compensation of IQ imbalance, frequency offset and phase noise in OFDM receivers,” European Transactions on Telecommunications 15(3), 283–292 (2004).
[Crossref]

Fandiño, J. S.

J. S. Fandiño and P. Muñoz, “Manufacturing Tolerance Analysis of an MMI-Based 90° Optical Hybrid for InP Integrated Coherent Receivers,” IEEE Photon. J. 5(2), 7900512 (2013).
[Crossref]

Fatadin, I.

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008).
[Crossref]

Golub, G. H.

G. H. Golub, C. F. Van Loan, and JHU Matrix Computations Press, 1996.

Halir, R.

Harris, C. J.

P. E. An, M. Brown, and C. J. Harris, “On the convergence rate performance of normalized least-mean-square adaptation,” IEEE Trans. Neural Netw. 6(6), 1549–1552 (1997).
[Crossref] [PubMed]

Ives, D.

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008).
[Crossref]

Janiak, K.

Kim, D. W.

Kim, K.

H. S. Chung, S. H. Chang, and K. Kim, “Compensation of IQ mismatch in optical PDM–OFDM coherent receivers,” Opt. Fiber Technol. 16(5), 304–308 (2010).
[Crossref]

Kim, K. H.

Kim, Y.

Lee, M. H.

Li, H.

M. Yin, W. Yang, Y. Li, X. Wang, and H. Li, “CMOS-compatible and fabrication-tolerant MMI-based polarization beam splitter,” Opt. Commun. 335, 48–52 (2015).
[Crossref]

Li, Y.

M. Yin, W. Yang, Y. Li, X. Wang, and H. Li, “CMOS-compatible and fabrication-tolerant MMI-based polarization beam splitter,” Opt. Commun. 335, 48–52 (2015).
[Crossref]

Malouin, C.

Man, H. D.

J. Tubbax, L. Van der Perre, S. Donnay, M. Engels, M. Moonen, and H. D. Man, “Joint compensation of IQ imbalance, frequency offset and phase noise in OFDM receivers,” European Transactions on Telecommunications 15(3), 283–292 (2004).
[Crossref]

Matrix Computations, JHU

G. H. Golub, C. F. Van Loan, and JHU Matrix Computations Press, 1996.

Molina-Fernandez, I.

Molina-Fernández, I.

Moonen, M.

J. Tubbax, L. Van der Perre, S. Donnay, M. Engels, M. Moonen, and H. D. Man, “Joint compensation of IQ imbalance, frequency offset and phase noise in OFDM receivers,” European Transactions on Telecommunications 15(3), 283–292 (2004).
[Crossref]

Morsy-Osman, M.

Moscoso-Mártir, A.

Muñoz, P.

J. S. Fandiño and P. Muñoz, “Manufacturing Tolerance Analysis of an MMI-Based 90° Optical Hybrid for InP Integrated Coherent Receivers,” IEEE Photon. J. 5(2), 7900512 (2013).
[Crossref]

Ortega-Monux, A.

Ortega-Moñux, A.

Painchaud, Y.

Paquet, C.

Pelletier, M.

Perez-Galacho, D.

Peters, J.

D. Dai, Z. Wang, J. Peters, and J. E. Bowers, “Compact Polarization Beam Splitter Using an Asymmetrical Mach–Zehnder Interferometer Based on Silicon-on-Insulator Waveguides,” IEEE Photon. Technol. Lett. 24(8), 673–675 (2012).
[Crossref]

Plant, D. V.

Poulin, M.

Ramos, G. U.

G. U. Ramos, “Roundoff error analysis of the fast Fourier transform,” Math. Comput. 25(116), 757–768 (1971).
[Crossref]

Reyes-Iglesias, P. J.

Runge, P.

Savory, S. J.

S. J. Savory, “Digital Coherent Optical Receivers: Algorithms and Subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).
[Crossref]

S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008).
[Crossref] [PubMed]

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008).
[Crossref]

Schmidt, T. J.

Steffan, A. G.

Tubbax, J.

J. Tubbax, L. Van der Perre, S. Donnay, M. Engels, M. Moonen, and H. D. Man, “Joint compensation of IQ imbalance, frequency offset and phase noise in OFDM receivers,” European Transactions on Telecommunications 15(3), 283–292 (2004).
[Crossref]

Van der Perre, L.

J. Tubbax, L. Van der Perre, S. Donnay, M. Engels, M. Moonen, and H. D. Man, “Joint compensation of IQ imbalance, frequency offset and phase noise in OFDM receivers,” European Transactions on Telecommunications 15(3), 283–292 (2004).
[Crossref]

Van Loan, C. F.

G. H. Golub, C. F. Van Loan, and JHU Matrix Computations Press, 1996.

Wang, X.

M. Yin, W. Yang, Y. Li, X. Wang, and H. Li, “CMOS-compatible and fabrication-tolerant MMI-based polarization beam splitter,” Opt. Commun. 335, 48–52 (2015).
[Crossref]

Wang, Z.

D. Dai, Z. Wang, J. Peters, and J. E. Bowers, “Compact Polarization Beam Splitter Using an Asymmetrical Mach–Zehnder Interferometer Based on Silicon-on-Insulator Waveguides,” IEEE Photon. Technol. Lett. 24(8), 673–675 (2012).
[Crossref]

Xu, X.

Yang, W.

M. Yin, W. Yang, Y. Li, X. Wang, and H. Li, “CMOS-compatible and fabrication-tolerant MMI-based polarization beam splitter,” Opt. Commun. 335, 48–52 (2015).
[Crossref]

Yin, M.

M. Yin, W. Yang, Y. Li, X. Wang, and H. Li, “CMOS-compatible and fabrication-tolerant MMI-based polarization beam splitter,” Opt. Commun. 335, 48–52 (2015).
[Crossref]

Zhang, B.

Zhang, R.

Zhou, G.

Zhuge, Q.

European Transactions on Telecommunications (1)

J. Tubbax, L. Van der Perre, S. Donnay, M. Engels, M. Moonen, and H. D. Man, “Joint compensation of IQ imbalance, frequency offset and phase noise in OFDM receivers,” European Transactions on Telecommunications 15(3), 283–292 (2004).
[Crossref]

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

S. J. Savory, “Digital Coherent Optical Receivers: Algorithms and Subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).
[Crossref]

IEEE Photon. J. (1)

J. S. Fandiño and P. Muñoz, “Manufacturing Tolerance Analysis of an MMI-Based 90° Optical Hybrid for InP Integrated Coherent Receivers,” IEEE Photon. J. 5(2), 7900512 (2013).
[Crossref]

IEEE Photon. Technol. Lett. (2)

D. Dai, Z. Wang, J. Peters, and J. E. Bowers, “Compact Polarization Beam Splitter Using an Asymmetrical Mach–Zehnder Interferometer Based on Silicon-on-Insulator Waveguides,” IEEE Photon. Technol. Lett. 24(8), 673–675 (2012).
[Crossref]

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008).
[Crossref]

IEEE Trans. Neural Netw. (1)

P. E. An, M. Brown, and C. J. Harris, “On the convergence rate performance of normalized least-mean-square adaptation,” IEEE Trans. Neural Netw. 6(6), 1549–1552 (1997).
[Crossref] [PubMed]

J. Lightwave Technol. (1)

Math. Comput. (1)

G. U. Ramos, “Roundoff error analysis of the fast Fourier transform,” Math. Comput. 25(116), 757–768 (1971).
[Crossref]

Opt. Commun. (1)

M. Yin, W. Yang, Y. Li, X. Wang, and H. Li, “CMOS-compatible and fabrication-tolerant MMI-based polarization beam splitter,” Opt. Commun. 335, 48–52 (2015).
[Crossref]

Opt. Express (5)

Opt. Fiber Technol. (1)

H. S. Chung, S. H. Chang, and K. Kim, “Compensation of IQ mismatch in optical PDM–OFDM coherent receivers,” Opt. Fiber Technol. 16(5), 304–308 (2010).
[Crossref]

Other (4)

Optical Internetworking Forum, “Implementation agreement for integrated dual polarization intradyne coherent receivers, ” document OIF-DPC-RX-01.2 (Nov. 2013), http://www.oiforum.com/public/impagreements.html

T. Richter, M. Kroh, J. Wang, A. Theurer, C. Zawadzki, Z. Zhang, N. Keil, A. Steffan, and C. Schubert, “Integrated polarization-diversity coherent receiver on polymer PLC for QPSK and QAM signals,” in Proc. OFC 2012, pp.1–3, paper OW3G.1.
[Crossref]

G. H. Golub, C. F. Van Loan, and JHU Matrix Computations Press, 1996.

Agilent Technologies, “MIMO Performance and Condition Number in LTE Test”, Application Note 5990–4759EN, http://cp.literature.agilent.com/litweb/pdf/5990-4759EN.pdf

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Figures (5)

Fig. 1
Fig. 1 Block diagram of a DP coherent optical communication system. LO: Local Oscillator, N ¯ OE : Optoelectronic Noise, ADC: Analog-to-Digital Converter, DSP: Digital Signal Processing.
Fig. 2
Fig. 2 Functional diagram of a DP I/Q downconverter. PBS: Polarization Beam Spliter, BS3dB: 3 dB power beam Splitter, TIA: Transimpedance Amplifier.
Fig. 3
Fig. 3 BER versus signal power and estimation of the power penalty ΔPs as a function of the ER of non-ideal PBS: (a) PBS + PBS architecture (b) PBS + BS architecture.
Fig. 4
Fig. 4 Power penalty versus the ER numerically simulated and estimated from the Frobenius norm (12) in the polarization diversity schemes PBS + BS and PBS + PBS.
Fig. 5
Fig. 5 Relationship between the condition number K2 and (a) the extinction ratio (b) normalized convergence time as a function of the polarization diversity scheme.

Equations (13)

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

S ¯ in = M ¯ ¯ F · Γ ¯ tx =[ cos θ F e j φ F ·sin θ F e j φ F ·sin θ F cos θ F ]· Γ ¯ tx
S ¯ out = M ¯ ¯ S · S ¯ in + M ¯ ¯ R · S ¯ in  * + N ¯ OE
S ¯ out = M ¯ ¯ S · M ¯ ¯ F · Γ ¯ tx + N ¯ OE .
Γ ¯ rx = M ¯ ¯ DSP · S ¯ out = M ¯ ¯ DSP ·( M ¯ ¯ S · M ¯ ¯ F )· Γ ¯ tx + M ¯ ¯ DSP · N ¯ OE
Γ ¯ rx = Γ ¯ tx + ( M ¯ ¯ S · M ¯ ¯ F ) 1 · N ¯ OE .
[ I out x +j· Q out x I out y +j· Q out y ]= M ¯ ¯ S ·[ I in x +j· Q in x I in y +j· Q in y ].
J ¯ ¯ 1 =[ a 0 0 b ]=K·[ 1 0 0 10 ER / 20 ]; J ¯ ¯ 2 =[ b 0 0 a ]=K·[ 10 ER / 20 0 0 1 ]
M ¯ ¯ S | PBS+PBS = P LO 2 1 1+er [ er 1 1 er ]; M ¯ ¯ S | PBS+BS = P LO 4 1 ( 1+er ) [ er 1 1 er ]
M ¯ ¯ F = i j | m ij | 2 .
Γ ¯ rx RMS 1 2 · ( M ¯ ¯ S · M ¯ ¯ F ) 1 F · N ¯ OE RMS .
Γ ¯ rx RMS 1 2 · M ¯ ¯ S 1 F · N ¯ OE RMS .
Δ P s  ( dB )=10·log( M ¯ ¯ S 1 F 2 /2 ).
k 2 ( M ¯ ¯ )= k 2 ( M ¯ ¯ 1 )=  M ¯ ¯ 2 · M ¯ ¯ 1 2

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