Abstract

A coherent receiver based on a 120° downconverter architecture, inherited from previous approaches at the microwave and optical fields, is proposed, analyzed, numerically evaluated and compared to the conventional 90° downconverter alternative. It is shown that, due to its superior calibration procedure, the new downconverter architecture allows full compensation of the imbalances in its optical front-end thus leading to an extended dynamic range and a broader operating bandwidth than its 90° counterpart. Simulation results from monolithically integrated downconverters show that our approach can be an interesting alternative to support efficient modulation schemes such as M-QAM that is being studied as potential candidate for the next generation of optical communication systems.

© 2012 OSA

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References

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  1. Optical Internetworking Forum (OIF), “100G ultra long haul DWDM framework document,” document OIF-FD-100G-DWDM-01.0 (June 2009), http://www.oiforum.com/public/impagreements.html .
  2. Mirthe Project, “Monolithic InP-based dual polarization QPSK integrated receiver and transmitter for coherent 100–400Gb Ethernet,” http://www.ist-mirthe.eu/ .
  3. M. Nakazawa, “Ultrafast and high-spectral-density optical communications systems,” "Ultrafast and High-spectral-density optical communications systems,” in CLEO:2011—Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CThGG3.
  4. A. Sano, H. Masuda, T. Kobayashi, M. Fujiwara, K. Horikoshi, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, H. Yamazaki, Y. Sakamaki, and H. Ishii, “69.1-Tb/s (432 x 171-Gb/s) C- and extended L-band transmission over 240 km Using PDM-16-QAM modulation and digital coherent detection,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PDPB7.
  5. F. Boubal, E. Brandon, L. Buet, S. Chernikov, V. Havard, C. Heerdt, A. Hugbart, W. Idler, L. Labrunie, P. Le Roux, S. A. E. Lewis, A. Pham, L. Piriou, R. Uhel, and J. P. Blondel, “4.16 Tbit/s (104x40 Gbit/s) unrepeatered transmission over 135 km in S + C + L bands with 104 nm total bandwidth,” in 27th European Conference on Optical Communication, 2001. ECOC '01 (2001), vol. 1, pp. 58–59
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    [CrossRef]
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    [CrossRef] [PubMed]
  8. Optoplex Corportation, “2x4 QPSK mixer-polarization diversified optical hybrid,” datasheet, www.optoplex.com .
  9. A. Matiss, S. Bottacchi, J. K. Fischer, R. Ludwig, C. C. Leonhardt, C. Schmidt-Langhorst, and C. Schubert, “Performance of an integrated coherent receiver module for up to 160G DP-QPSK transmission systems,” J. Lightwave Technol. 29(7), 1026–1032 (2011).
    [CrossRef]
  10. R. Kunkel, H.-G. Bach, D. Hoffmann, C. Weinert, I. Molina-Fernandez, and R. Halir, “First monolithic InP-based 90 degrees-hybrid OEIC comprising balanced detectors for 100GE coherent frontends,” in International Conference on Indium Phosphide & Related Materials (IPRM) (2009), paper TuB2.2, pp. 167–170.
  11. 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]
  12. A. Moscoso-Martir, I. Molina-Fernandez, and A. Ortega-Monux, “Signal constellation distortion and ber degradation due to hardware impairments in six-port receivers with analog I/Q generation,” Prog. Electromagn. Res. 121, 225–247 (2011).
    [CrossRef]
  13. J. Li, R. G. Bosisio, and K. Wu, “Computer and measurement simulation of a new digital receiver operating directly at millimeter-wave frequencies,” IEEE Trans. Microw. Theory Tech. 43(12), 2766–2772 (1995).
    [CrossRef]
  14. P. Pérez-Lara, I. Molina-Fernandez, J. G. Wanguemert-Perez, and A. Rueda-Perez, “Broadband five-port direct receiver based on low-pass and high-pass phase shifters,” IEEE Trans. Microw. Theory Tech. 58(4), 849–853 (2010).
    [CrossRef]
  15. T. Pfau, S. Hoffmann, O. Adamczyk, R. Peveling, V. Herath, M. Porrmann, and R. Noé, “Coherent optical communication: towards realtime systems at 40 Gbit/s and beyond,” Opt. Express 16(2), 866–872 (2008).
    [CrossRef] [PubMed]
  16. A. B. Carlson, Communication Systems (McGraw-Hill, 1986).
  17. P. Perez-Lara, I. Molina-Fernandez, J. G. Wangüemert-Perez, and R. G. Bosisio, “Effects of hardware imperfection on six-port direct digital receivers calibrated with three and four signal standards,” IEE Proc. Microw. Antennas Propag. 153(2), 171–176 (2006).
    [CrossRef]
  18. F. M. Ghannouchi and R. G. Bosisio, “An alternative explicit six-port matrix calibration formalism using five standards,” IEEE Trans. Microw. Theory Tech. 36(3), 494–498 (1988).
    [CrossRef]
  19. R. Halir, G. Roelkens, A. Ortega-Moñux, and J. G. Wangüemert-Pérez, “High-performance 90° hybrid based on a silicon-on-insulator multimode interference coupler,” Opt. Lett. 36(2), 178–180 (2011).
    [CrossRef] [PubMed]
  20. R. Halir, A. Ortega-Moñux, I. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, D.-X. Xu, B. Lamontagne, and S. Janz, “Integrated optical six-port reflectometer in silicon-on-insulator,” J. Lightwave Technol. 27(23), 5405–5409 (2009).
    [CrossRef]
  21. R. Halir, I. Molina-Fernandez, A. Ortega-Monux, J. G. Wanguemert-Perez, D.-X. Xu, P. Cheben, and S. Janz, “A design procedure for high-performance, rib-waveguide-based multimode interference couplers in silicon-on-insulator,” J. Lightwave Technol. 26(16), 2928–2936 (2008).
    [CrossRef]
  22. P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol. 12(6), 1004–1009 (1994).
    [CrossRef]
  23. M. Seimetz, “Multi-format transmitters for coherent optical M-PSK and M-QAM transmission,” Proceedings of 2005 7th International Conference Transparent Optical Networks (2005), pp. 225–229, paper Th.B1.5

2011 (3)

2010 (1)

P. Pérez-Lara, I. Molina-Fernandez, J. G. Wanguemert-Perez, and A. Rueda-Perez, “Broadband five-port direct receiver based on low-pass and high-pass phase shifters,” IEEE Trans. Microw. Theory Tech. 58(4), 849–853 (2010).
[CrossRef]

2009 (2)

2008 (3)

2006 (1)

P. Perez-Lara, I. Molina-Fernandez, J. G. Wangüemert-Perez, and R. G. Bosisio, “Effects of hardware imperfection on six-port direct digital receivers calibrated with three and four signal standards,” IEE Proc. Microw. Antennas Propag. 153(2), 171–176 (2006).
[CrossRef]

1995 (1)

J. Li, R. G. Bosisio, and K. Wu, “Computer and measurement simulation of a new digital receiver operating directly at millimeter-wave frequencies,” IEEE Trans. Microw. Theory Tech. 43(12), 2766–2772 (1995).
[CrossRef]

1994 (1)

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol. 12(6), 1004–1009 (1994).
[CrossRef]

1988 (1)

F. M. Ghannouchi and R. G. Bosisio, “An alternative explicit six-port matrix calibration formalism using five standards,” IEEE Trans. Microw. Theory Tech. 36(3), 494–498 (1988).
[CrossRef]

1987 (1)

A. W. Davis, M. Pettitt, J. King, and S. Wright, “Phase diversity techniques for coherent optical receivers,” J. Lightwave Technol. 5(4), 561–572 (1987).
[CrossRef]

Adamczyk, O.

Bachmann, M.

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol. 12(6), 1004–1009 (1994).
[CrossRef]

Besse, P. A.

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol. 12(6), 1004–1009 (1994).
[CrossRef]

Bosisio, R. G.

P. Perez-Lara, I. Molina-Fernandez, J. G. Wangüemert-Perez, and R. G. Bosisio, “Effects of hardware imperfection on six-port direct digital receivers calibrated with three and four signal standards,” IEE Proc. Microw. Antennas Propag. 153(2), 171–176 (2006).
[CrossRef]

J. Li, R. G. Bosisio, and K. Wu, “Computer and measurement simulation of a new digital receiver operating directly at millimeter-wave frequencies,” IEEE Trans. Microw. Theory Tech. 43(12), 2766–2772 (1995).
[CrossRef]

F. M. Ghannouchi and R. G. Bosisio, “An alternative explicit six-port matrix calibration formalism using five standards,” IEEE Trans. Microw. Theory Tech. 36(3), 494–498 (1988).
[CrossRef]

Bottacchi, S.

Cheben, P.

Davis, A. W.

A. W. Davis, M. Pettitt, J. King, and S. Wright, “Phase diversity techniques for coherent optical receivers,” J. Lightwave Technol. 5(4), 561–572 (1987).
[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]

Fischer, J. K.

Ghannouchi, F. M.

F. M. Ghannouchi and R. G. Bosisio, “An alternative explicit six-port matrix calibration formalism using five standards,” IEEE Trans. Microw. Theory Tech. 36(3), 494–498 (1988).
[CrossRef]

Halir, R.

Herath, V.

Hoffmann, S.

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]

Janz, S.

King, J.

A. W. Davis, M. Pettitt, J. King, and S. Wright, “Phase diversity techniques for coherent optical receivers,” J. Lightwave Technol. 5(4), 561–572 (1987).
[CrossRef]

Lamontagne, B.

Leonhardt, C. C.

Li, J.

J. Li, R. G. Bosisio, and K. Wu, “Computer and measurement simulation of a new digital receiver operating directly at millimeter-wave frequencies,” IEEE Trans. Microw. Theory Tech. 43(12), 2766–2772 (1995).
[CrossRef]

Ludwig, R.

Matiss, A.

Melchior, H.

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol. 12(6), 1004–1009 (1994).
[CrossRef]

Molina-Fernandez, I.

A. Moscoso-Martir, I. Molina-Fernandez, and A. Ortega-Monux, “Signal constellation distortion and ber degradation due to hardware impairments in six-port receivers with analog I/Q generation,” Prog. Electromagn. Res. 121, 225–247 (2011).
[CrossRef]

P. Pérez-Lara, I. Molina-Fernandez, J. G. Wanguemert-Perez, and A. Rueda-Perez, “Broadband five-port direct receiver based on low-pass and high-pass phase shifters,” IEEE Trans. Microw. Theory Tech. 58(4), 849–853 (2010).
[CrossRef]

R. Halir, I. Molina-Fernandez, A. Ortega-Monux, J. G. Wanguemert-Perez, D.-X. Xu, P. Cheben, and S. Janz, “A design procedure for high-performance, rib-waveguide-based multimode interference couplers in silicon-on-insulator,” J. Lightwave Technol. 26(16), 2928–2936 (2008).
[CrossRef]

P. Perez-Lara, I. Molina-Fernandez, J. G. Wangüemert-Perez, and R. G. Bosisio, “Effects of hardware imperfection on six-port direct digital receivers calibrated with three and four signal standards,” IEE Proc. Microw. Antennas Propag. 153(2), 171–176 (2006).
[CrossRef]

Molina-Fernández, I.

Morin, M.

Moscoso-Martir, A.

A. Moscoso-Martir, I. Molina-Fernandez, and A. Ortega-Monux, “Signal constellation distortion and ber degradation due to hardware impairments in six-port receivers with analog I/Q generation,” Prog. Electromagn. Res. 121, 225–247 (2011).
[CrossRef]

Noé, R.

Ortega-Monux, A.

A. Moscoso-Martir, I. Molina-Fernandez, and A. Ortega-Monux, “Signal constellation distortion and ber degradation due to hardware impairments in six-port receivers with analog I/Q generation,” Prog. Electromagn. Res. 121, 225–247 (2011).
[CrossRef]

R. Halir, I. Molina-Fernandez, A. Ortega-Monux, J. G. Wanguemert-Perez, D.-X. Xu, P. Cheben, and S. Janz, “A design procedure for high-performance, rib-waveguide-based multimode interference couplers in silicon-on-insulator,” J. Lightwave Technol. 26(16), 2928–2936 (2008).
[CrossRef]

Ortega-Moñux, A.

Painchaud, Y.

Perez-Lara, P.

P. Perez-Lara, I. Molina-Fernandez, J. G. Wangüemert-Perez, and R. G. Bosisio, “Effects of hardware imperfection on six-port direct digital receivers calibrated with three and four signal standards,” IEE Proc. Microw. Antennas Propag. 153(2), 171–176 (2006).
[CrossRef]

Pérez-Lara, P.

P. Pérez-Lara, I. Molina-Fernandez, J. G. Wanguemert-Perez, and A. Rueda-Perez, “Broadband five-port direct receiver based on low-pass and high-pass phase shifters,” IEEE Trans. Microw. Theory Tech. 58(4), 849–853 (2010).
[CrossRef]

Pettitt, M.

A. W. Davis, M. Pettitt, J. King, and S. Wright, “Phase diversity techniques for coherent optical receivers,” J. Lightwave Technol. 5(4), 561–572 (1987).
[CrossRef]

Peveling, R.

Pfau, T.

Porrmann, M.

Poulin, M.

Roelkens, G.

Rueda-Perez, A.

P. Pérez-Lara, I. Molina-Fernandez, J. G. Wanguemert-Perez, and A. Rueda-Perez, “Broadband five-port direct receiver based on low-pass and high-pass phase shifters,” IEEE Trans. Microw. Theory Tech. 58(4), 849–853 (2010).
[CrossRef]

Savory, S. J.

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-Langhorst, C.

Schubert, C.

Smit, M. K.

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol. 12(6), 1004–1009 (1994).
[CrossRef]

Soldano, L. B.

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol. 12(6), 1004–1009 (1994).
[CrossRef]

Têtu, M.

Wanguemert-Perez, J. G.

P. Pérez-Lara, I. Molina-Fernandez, J. G. Wanguemert-Perez, and A. Rueda-Perez, “Broadband five-port direct receiver based on low-pass and high-pass phase shifters,” IEEE Trans. Microw. Theory Tech. 58(4), 849–853 (2010).
[CrossRef]

R. Halir, I. Molina-Fernandez, A. Ortega-Monux, J. G. Wanguemert-Perez, D.-X. Xu, P. Cheben, and S. Janz, “A design procedure for high-performance, rib-waveguide-based multimode interference couplers in silicon-on-insulator,” J. Lightwave Technol. 26(16), 2928–2936 (2008).
[CrossRef]

Wangüemert-Perez, J. G.

P. Perez-Lara, I. Molina-Fernandez, J. G. Wangüemert-Perez, and R. G. Bosisio, “Effects of hardware imperfection on six-port direct digital receivers calibrated with three and four signal standards,” IEE Proc. Microw. Antennas Propag. 153(2), 171–176 (2006).
[CrossRef]

Wangüemert-Pérez, J. G.

Wright, S.

A. W. Davis, M. Pettitt, J. King, and S. Wright, “Phase diversity techniques for coherent optical receivers,” J. Lightwave Technol. 5(4), 561–572 (1987).
[CrossRef]

Wu, K.

J. Li, R. G. Bosisio, and K. Wu, “Computer and measurement simulation of a new digital receiver operating directly at millimeter-wave frequencies,” IEEE Trans. Microw. Theory Tech. 43(12), 2766–2772 (1995).
[CrossRef]

Xu, D.-X.

IEE Proc. Microw. Antennas Propag. (1)

P. Perez-Lara, I. Molina-Fernandez, J. G. Wangüemert-Perez, and R. G. Bosisio, “Effects of hardware imperfection on six-port direct digital receivers calibrated with three and four signal standards,” IEE Proc. Microw. Antennas Propag. 153(2), 171–176 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

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. Microw. Theory Tech. (3)

F. M. Ghannouchi and R. G. Bosisio, “An alternative explicit six-port matrix calibration formalism using five standards,” IEEE Trans. Microw. Theory Tech. 36(3), 494–498 (1988).
[CrossRef]

J. Li, R. G. Bosisio, and K. Wu, “Computer and measurement simulation of a new digital receiver operating directly at millimeter-wave frequencies,” IEEE Trans. Microw. Theory Tech. 43(12), 2766–2772 (1995).
[CrossRef]

P. Pérez-Lara, I. Molina-Fernandez, J. G. Wanguemert-Perez, and A. Rueda-Perez, “Broadband five-port direct receiver based on low-pass and high-pass phase shifters,” IEEE Trans. Microw. Theory Tech. 58(4), 849–853 (2010).
[CrossRef]

J. Lightwave Technol. (5)

Opt. Express (2)

Opt. Lett. (1)

Prog. Electromagn. Res. (1)

A. Moscoso-Martir, I. Molina-Fernandez, and A. Ortega-Monux, “Signal constellation distortion and ber degradation due to hardware impairments in six-port receivers with analog I/Q generation,” Prog. Electromagn. Res. 121, 225–247 (2011).
[CrossRef]

Other (9)

R. Kunkel, H.-G. Bach, D. Hoffmann, C. Weinert, I. Molina-Fernandez, and R. Halir, “First monolithic InP-based 90 degrees-hybrid OEIC comprising balanced detectors for 100GE coherent frontends,” in International Conference on Indium Phosphide & Related Materials (IPRM) (2009), paper TuB2.2, pp. 167–170.

Optical Internetworking Forum (OIF), “100G ultra long haul DWDM framework document,” document OIF-FD-100G-DWDM-01.0 (June 2009), http://www.oiforum.com/public/impagreements.html .

Mirthe Project, “Monolithic InP-based dual polarization QPSK integrated receiver and transmitter for coherent 100–400Gb Ethernet,” http://www.ist-mirthe.eu/ .

M. Nakazawa, “Ultrafast and high-spectral-density optical communications systems,” "Ultrafast and High-spectral-density optical communications systems,” in CLEO:2011—Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CThGG3.

A. Sano, H. Masuda, T. Kobayashi, M. Fujiwara, K. Horikoshi, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, H. Yamazaki, Y. Sakamaki, and H. Ishii, “69.1-Tb/s (432 x 171-Gb/s) C- and extended L-band transmission over 240 km Using PDM-16-QAM modulation and digital coherent detection,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PDPB7.

F. Boubal, E. Brandon, L. Buet, S. Chernikov, V. Havard, C. Heerdt, A. Hugbart, W. Idler, L. Labrunie, P. Le Roux, S. A. E. Lewis, A. Pham, L. Piriou, R. Uhel, and J. P. Blondel, “4.16 Tbit/s (104x40 Gbit/s) unrepeatered transmission over 135 km in S + C + L bands with 104 nm total bandwidth,” in 27th European Conference on Optical Communication, 2001. ECOC '01 (2001), vol. 1, pp. 58–59

M. Seimetz, “Multi-format transmitters for coherent optical M-PSK and M-QAM transmission,” Proceedings of 2005 7th International Conference Transparent Optical Networks (2005), pp. 225–229, paper Th.B1.5

A. B. Carlson, Communication Systems (McGraw-Hill, 1986).

Optoplex Corportation, “2x4 QPSK mixer-polarization diversified optical hybrid,” datasheet, www.optoplex.com .

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Figures (12)

Fig. 1
Fig. 1

90° hybrid coherent receiver.

Fig. 2
Fig. 2

64-QAM constellation distortion for an unbalanced 90° hybrid coherent receiver under ASE noise: (a) linear impairments (γ = 0) causing non-zero DC offset (α≠0), rotation and imbalance of reference axes (u≠j·v); (b) non-linear impairment (γ≠0, α = 0, u = -j·v).

Fig. 3
Fig. 3

BER performance versus signal power for different LO power for 56 Gbps (a) 64-QAM and (b) 256-QAM transmission, considering an ideal coherent receiver with noise sources (Be = Rs, R = 0.89 A/W).

Fig. 4
Fig. 4

120° coherent receiver.

Fig. 5
Fig. 5

Amplitude (left) and phase imbalance (right) of 2x4 MMI 90° hybrid (in plane mode) obtained from electromagnetic modeling.

Fig. 6
Fig. 6

Amplitude (left) and phase imbalance (right) of 2x3 MMI 120° coupler (in plane mode) obtained from electromagnetic modeling.

Fig. 7
Fig. 7

BER performance versus Ps in 90° downconverter for different PLO when noise sources and hardware impairments are considered for 64-QAM and 256-QAM at central operation wavelength (top) and at the upper limit of the L-band (bottom).

Fig. 8
Fig. 8

Corrected 64-QAM following GSOP in 90° downconverter at the upper limit of the L-band for 10 dBm LO power when Ps/PLO ratio is (a) −20 dB (left) and (b) −5 dB (right).

Fig. 9
Fig. 9

BER performance versus Ps in 120° downconverter for different PLO when noise sources and hardware impairments are considered for 64-QAM and 256-QAM at central operation wavelength (top) and at the upper limit of the L-band (bottom).

Fig. 10
Fig. 10

Corrected 64-QAM constellation following linear calibration for the 120° downconverter at the upper limit of the L-band for 10 dBm LO power when Ps/PLO ratio is (a) −20 dB (left) and (b) −5 dB (right)

Fig. 11
Fig. 11

Transmitted/demodulated 16-QAM constellation (down) and amplitude eye diagram (up) for 10 dBm LO power when incoming OSNR is fixed for BER = 10−12 in a noiseless ideal coherent receiver at the upper limit of the L-band.

Fig. 12
Fig. 12

BER performance versus wavelength for the 90° (top) and 120° (bottom) downconverters for different signal to LO power ratios (LO power fixed to 10 dBm except in the insets where signal and LO power are equal to 0 dBm) under 64-QAM and 256-QAM modulation.

Tables (2)

Tables Icon

Table 1 Parameters Derived in [12] to Characterize 90° Hybrid Integrated Coherent Receiver

Tables Icon

Table 2 Parameters to Characterize 120° Coherent Receiver

Equations (30)

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

e s ( t ) =Re{ e ˜ s e j ω o t }
e LO ( t )=Re{ e ˜ LO e j ω o t }
e ˜ s = P s ( I+jQ )+ n ASE
i i = R i | S i1 e ˜ s + S i2 e ˜ LO | 2 ; i=3, ..., 6.
i i = R i | S i1 | 2 P LO [ | q i | 2 + | Γ s | 2 2Re( q i * Γ s ) ] ; i=3, ..., 6.
[ i I i Q ]=[ i 3 i 4 i 5 i 6 ]=[ α I α Q ]+[ γ I γ Q ][ I 2 + Q 2 ]+[ u I u Q v I v Q ][ I Q ]
i I =R P LO P s I=R P LO Re( e ˜ s ) i Q =R P LO P s Q=R P LO Im( e ˜ s )
| i s | 2 = | R P LO e ˜ s | 2 = R 2 P LO P s
i noiseI 2 = i noiseQ 2 = i ASELO 2 + 1 2 i shot 2 = R 2 P LO N B ASE e 2 +qR B e ( P s + P LO )
1 SNR = i noiseI 2 + i noiseQ 2 | i s | 2 = 1 OSNR + 2q B e R ( 1 P LO + 1 P s )
BER= 1 log 2 M { 1 [ 1( 1 1 M )erfc( 3 2(M1) SNR ) ] 2 }
i i = R i | S i1 e ˜ s + S i2 e ˜ LO | 2 ; i=3, ..., 5.
i i = R i | S i1 | 2 P LO | Γ s q i | 2 ; i=3, ..., 5.
[ i 3 i 4 i 5 ]=[ α 1 α 2 α 3 ]+[ γ 1 γ 2 γ 3 ][ I 2 + Q 2 ]+[ u 1I u 1Q u 2I u 2Q u 3I u 3Q ][ I Q ]
i I = i=3,4,5 A Ii i i + C I i Q = i=3,4,5 A Qi i i + C Q
i 35 = R 3 { P LO + P s +2 P LO Re( e ˜ s e j120º ) }= R 3 { P LO + P s P LO P s [ I 3 Q ] } i 4 = R 3 { P LO + P s +2 P LO P s I }
i I =0.5 i 3 + i 4 0.5 i 5 =R P LO P s I=R P LO Re( e ˜ s ) i Q = 3 2 ( i 3 i 5 )=R P LO P s Q=R P LO Im( e ˜ s )
i shot 2 =2q B e i =2qR B e ( P s + P LO )
i sho t i 2 =2q B e i i = i shot 2 k ; i=3, ..., k+2
i RIN_i 2 =RI N B e i i 2 ; i=3, ..., k+2
i TIA 2 = i TIAI 2 = i TIAQ 2 = i TIAi 2 = α TIA 2 B e
i I =R P LO Re( e ˜ s + n ASE )+ i shot3 i shot4 + i TIAI =R P LO Re( e ˜ s )+ i noiseI i Q =R P LO Im( e ˜ s + n ASE )+ i shot5 i shot6 + i TIAQ =R P LO Im( e ˜ s )+ i noiseQ
i noiseI = i ASEILO + i shot3 i shot4 + i TIAI i noiseQ = i ASEQLO + i shot5 i shot6 + i TIAQ
i ASELO 2 = i ASEILO 2 = i ASEQLO 2 = R 2 P LO n ASE 2 2 = R 2 P LO N B ASE e 2
i noiseI 2 = i noiseQ 2 = i ASELO 2 +2 i sho t i 2 + i TIA 2
i noiseI 2 = i noiseQ 2 = i ASELO 2 + 1 2 i shot 2 = R 2 P LO N B ASE e 2 +qR B e ( P s + P LO )
{ P LO + P s +2 P LO Re( ( e ˜ s + n ASE ) e j120º )+2Re( e ˜ s * n s ) }+ i sho t 5 3 + i RI N 5 3 + i TI A 5 3 i 4 = R 3 { P LO + P s +2 P LO Re( e ˜ s + n ASE )+2Re( e ˜ s * n s ) }+ i shot4 + i RIN4 + i TIA4
i I =0.5 i 3 + i 4 0.5 i 5 =R P LO Re( e ˜ s )+ i noiseI i Q = 3 2 ( i 3 i 5 )=R P LO Im( e ˜ s )+ i noiseQ
i noiseI = i ASEILO 0.5 ( i shot3 + i shot5 + i TIA3 + i TIA5 )+ i shot4 + i TIA4 i noiseQ = i ASEQLO + 3 2 ( i shot3 i shot5 + i TIA3 i TIA5 )
i noiseI 2 = i noiseQ 2 = i ASELO 2 + 3 2 i sho t i 2 = i ASELO 2 + 1 2 i shot 2

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