Abstract

An all-optical channel aggregation from two lower bit rate OOK and MPSK to a higher bit rate 2M-ary PSK signal based on cross phase modulation (XPM) effect and corresponding de-aggregation to recover the two original signals by phase sensitive amplification (PSA) are proposed and demonstrated aimed to improve efficient use of the fiber and transponder resources in elastic optical networking (EON). Moreover, for the PSA-based de-aggregation scheme, a black-box device to extract the phase locked pump is also designed to realize the desired phase-locking relationship for practical application. Both 20-Gbps aggregated QPSK signal (M=2) and 30-Gbps aggregated 8PSK signal (M=4) as examples are studied respectively. The feasibility and tunability of the scheme have been confirmed by the input-output constellations and waveforms. The phase noise (PN) of recovered B/QPSK signal and amplitude standard deviation (ASD) of recovered OOK signal over the varying optical signal-to-noise ratio (OSNR) of the Q/8PSK signal affected by the link noise are studied and analyzed. Based on the same link noise environment, the two system bit-error rate (BER) performance are also investigated and the corresponding OSNRs for error-free signal recovery are given respectively. Finally, some potential application scenarios are discussed based on the same setup.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  16. L. Pan, H. Wang, and Y. Ji, “All-optical deaggregation from 8PSK to 3×BPSK based on FWM in HNLF,” Appl. Opt. 58(5), 1246–1252 (2019).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  23. S. K. Ibrahim, S. Sygletos, R. Weerasuriya, and A. D. Ellis, “Novel real-time homodyne coherent receiver using a feed-forward based carrier extraction scheme for phase modulated signals,” Opt. Express 19(9), 8320–8326 (2011).
    [Crossref]
  24. R. Weerasuriya, S. Sygletos, S. K. Ibrahim, R. Phelan, J. O’Carroll, B. Kelly, J. O’Gorman, and A. D. Ellis, “Generation of frequency symmetric signals from a BPSK input for phase sensitive amplification,” in Optical Fiber Communication Conference, (Optical Society of America, 2010), p. OWT6.
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    [Crossref]

2019 (5)

Y. F. Ji, H. X. Wang, J. B. Cui, M. T. Yu, Z. T. Yang, and L. Bai, “All-optical signal processing technologies in flexible optical networks,” Photonic Netw. Commun. 38(1), 14–36 (2019).
[Crossref]

H. Liu, H. Wang, J. Cui, and Y. Ji, “Design of all-optical modulation format converter from one 8PSK to two QPSK signals based on phase sensitive amplification in elastic optical network,” IEEE Access 7, 51379–51385 (2019).
[Crossref]

L. Pan, H. Wang, and Y. Ji, “All-optical deaggregation from 8PSK to 3×BPSK based on FWM in HNLF,” Appl. Opt. 58(5), 1246–1252 (2019).
[Crossref]

J. Cui, G. Lu, H. Wang, and Y. Ji, “On-chip optical vector quadrature de-multiplexer proposal for QAM de-aggregation by single bi-directional SOA-based phase-sensitive amplifier,” IEEE Access 7, 763–772 (2019).
[Crossref]

H. Liu, H. Wang, and Y. Ji, “Simultaneous all-optical channel aggregation and de-aggregation for 8QAM signal in elastic optical networking,” IEEE Photonics J. 11(1), 1–8 (2019).
[Crossref]

2018 (1)

Y. F. Ji, J. W. Zhang, X. Wang, and H. Yu, “Towards converged, collaborative and co-automatic (3C) optical networks,” Sci. China Inf. Sci. 61(12), 121301 (2018).
[Crossref]

2016 (4)

Y. F. Ji, J. W. Zhang, Y. l. Zhao, X. S. Yu, J. Zhang, and X. Chen, “Prospects and research issues in multi-dimensional all optical networks,” Sci. China Inf. Sci. 59(10), 101301 (2016).
[Crossref]

Y. H. Wen, J. W. Ho, and K. M. Feng, “Phase transparent demultiplexer for QPSK signal based on nonlinear response in a double-pass architecture,” IEEE Photonics J. 8, 1–7 (2016).
[Crossref]

M. Baillot, M. Gay, C. Peucheret, J. Michel, and T. Chartier, “Phase quadrature discrimination based on three-pump four-wave mixing in nonlinear optical fibers,” Opt. Express 24(23), 26930–26941 (2016).
[Crossref]

H. Kishikawa, N. Goto, and L. R. Chen, “All-optical wavelength preserved modulation format conversion from PDM-QPSK to PDM-BPSK using FWM and interference,” J. Lightwave Technol. 34(23), 5505–5515 (2016).
[Crossref]

2015 (2)

Y. H. Wen and K. M. Feng, “A simple NRZ-OOK to PDM RZ-QPSK optical modulation format conversion by bidirectional XPM,” IEEE Photonics Technol. Lett. 27(9), 935–938 (2015).
[Crossref]

F. Parmigiani, G. Hesketh, R. Slavík, P. Horak, P. Petropoulos, and D. J. Richardson, “Polarization-Assisted Phase-Sensitive Processor,” J. Lightwave Technol. 33(6), 1166–1174 (2015).
[Crossref]

2014 (3)

2013 (1)

B. Zhang, H. Zhang, C. Yu, X. Cheng, K. Y. Yong, P. K. Kam, J. Yang, H. Zhang, Y. H. Wen, and K. M. Feng, “An all-optical modulation format conversion for 8QAM based on FWM in HNLF,” IEEE Photonics Technol. Lett. 25(4), 327–330 (2013).
[Crossref]

2012 (1)

O. Gerstel, M. Jinno, A. Lord, and S. J. B. Yoo, “Elastic optical networking: a new dawn for the optical layer?” IEEE Commun. Mag. 50(2), s12–s20 (2012).
[Crossref]

2011 (1)

2007 (1)

1999 (1)

H. C. Lim, F. Futami, and K. Kikuchi, “Polarization-independent, wavelength-shift-free optical phase conjugator using a nonlinear fiber sagnac interferometer,” IEEE Photonics Technol. Lett. 11(5), 578–580 (1999).
[Crossref]

Alishahi, F.

A. Fallahpour, M. Ziyadi, A. Mohajerin-Ariaei, Y. Cao, A. Almaiman, F. Alishahi, C. Bao, P. Liao, B. Shamee, L. Paraschis, M. Tur, C. Langrock, M. M. Fejer, J. Touch, and A. E. Willner, “Experimental demonstration of tunable optical de-aggregation of each of multiple wavelength 16-QAM channels into two 4-PAM channels,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), p. Th4I.6.

Almaiman, A.

A. Fallahpour, M. Ziyadi, A. Mohajerin-Ariaei, Y. Cao, A. Almaiman, F. Alishahi, C. Bao, P. Liao, B. Shamee, L. Paraschis, M. Tur, C. Langrock, M. M. Fejer, J. Touch, and A. E. Willner, “Experimental demonstration of tunable optical de-aggregation of each of multiple wavelength 16-QAM channels into two 4-PAM channels,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), p. Th4I.6.

Andrekson, P. A.

Astar, W.

B. M. Cannon, T. Mahmood, W. Astar, P. Boudra, T. Mohsenin, and G. M. Carter, “Polarization-insensitive phase-transmultiplexing of CSRZ-OOK and RZ-BPSK to RZ-QPSK via XPM in a PCF,” in Optical Fiber Communication Conference, (Optical Society of America, 2014), p. W2A.52.

Bai, L.

Y. F. Ji, H. X. Wang, J. B. Cui, M. T. Yu, Z. T. Yang, and L. Bai, “All-optical signal processing technologies in flexible optical networks,” Photonic Netw. Commun. 38(1), 14–36 (2019).
[Crossref]

Baillot, M.

Bao, C.

A. Fallahpour, M. Ziyadi, A. Mohajerin-Ariaei, Y. Cao, A. Almaiman, F. Alishahi, C. Bao, P. Liao, B. Shamee, L. Paraschis, M. Tur, C. Langrock, M. M. Fejer, J. Touch, and A. E. Willner, “Experimental demonstration of tunable optical de-aggregation of each of multiple wavelength 16-QAM channels into two 4-PAM channels,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), p. Th4I.6.

Bogris, A.

Boudra, P.

B. M. Cannon, T. Mahmood, W. Astar, P. Boudra, T. Mohsenin, and G. M. Carter, “Polarization-insensitive phase-transmultiplexing of CSRZ-OOK and RZ-BPSK to RZ-QPSK via XPM in a PCF,” in Optical Fiber Communication Conference, (Optical Society of America, 2014), p. W2A.52.

Cannon, B. M.

B. M. Cannon, T. Mahmood, W. Astar, P. Boudra, T. Mohsenin, and G. M. Carter, “Polarization-insensitive phase-transmultiplexing of CSRZ-OOK and RZ-BPSK to RZ-QPSK via XPM in a PCF,” in Optical Fiber Communication Conference, (Optical Society of America, 2014), p. W2A.52.

Cao, Y.

A. Fallahpour, M. Ziyadi, A. Mohajerin-Ariaei, Y. Cao, A. Almaiman, F. Alishahi, C. Bao, P. Liao, B. Shamee, L. Paraschis, M. Tur, C. Langrock, M. M. Fejer, J. Touch, and A. E. Willner, “Experimental demonstration of tunable optical de-aggregation of each of multiple wavelength 16-QAM channels into two 4-PAM channels,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), p. Th4I.6.

Carter, G. M.

B. M. Cannon, T. Mahmood, W. Astar, P. Boudra, T. Mohsenin, and G. M. Carter, “Polarization-insensitive phase-transmultiplexing of CSRZ-OOK and RZ-BPSK to RZ-QPSK via XPM in a PCF,” in Optical Fiber Communication Conference, (Optical Society of America, 2014), p. W2A.52.

Chartier, T.

Chen, L. R.

Chen, X.

Y. F. Ji, J. W. Zhang, Y. l. Zhao, X. S. Yu, J. Zhang, and X. Chen, “Prospects and research issues in multi-dimensional all optical networks,” Sci. China Inf. Sci. 59(10), 101301 (2016).
[Crossref]

Cheng, X.

B. Zhang, H. Zhang, C. Yu, X. Cheng, K. Y. Yong, P. K. Kam, J. Yang, H. Zhang, Y. H. Wen, and K. M. Feng, “An all-optical modulation format conversion for 8QAM based on FWM in HNLF,” IEEE Photonics Technol. Lett. 25(4), 327–330 (2013).
[Crossref]

Cui, J.

J. Cui, G. Lu, H. Wang, and Y. Ji, “On-chip optical vector quadrature de-multiplexer proposal for QAM de-aggregation by single bi-directional SOA-based phase-sensitive amplifier,” IEEE Access 7, 763–772 (2019).
[Crossref]

H. Liu, H. Wang, J. Cui, and Y. Ji, “Design of all-optical modulation format converter from one 8PSK to two QPSK signals based on phase sensitive amplification in elastic optical network,” IEEE Access 7, 51379–51385 (2019).
[Crossref]

Cui, J. B.

Y. F. Ji, H. X. Wang, J. B. Cui, M. T. Yu, Z. T. Yang, and L. Bai, “All-optical signal processing technologies in flexible optical networks,” Photonic Netw. Commun. 38(1), 14–36 (2019).
[Crossref]

Da Ros, F.

F. Da Ros, K. Dalgaard, Y. Fukuchi, J. Xu, M. Galili, and C. Peucheret, “Simultaneous QPSK-to- $2\times$2× BPSK wavelength and modulation format conversion in PPLN,” IEEE Photonics Technol. Lett. 26(12), 1207–1210 (2014).
[Crossref]

Dalgaard, K.

F. Da Ros, K. Dalgaard, Y. Fukuchi, J. Xu, M. Galili, and C. Peucheret, “Simultaneous QPSK-to- $2\times$2× BPSK wavelength and modulation format conversion in PPLN,” IEEE Photonics Technol. Lett. 26(12), 1207–1210 (2014).
[Crossref]

Ellis, A. D.

S. K. Ibrahim, S. Sygletos, R. Weerasuriya, and A. D. Ellis, “Novel real-time homodyne coherent receiver using a feed-forward based carrier extraction scheme for phase modulated signals,” Opt. Express 19(9), 8320–8326 (2011).
[Crossref]

R. Weerasuriya, S. Sygletos, S. K. Ibrahim, R. Phelan, J. O’Carroll, B. Kelly, J. O’Gorman, and A. D. Ellis, “Generation of frequency symmetric signals from a BPSK input for phase sensitive amplification,” in Optical Fiber Communication Conference, (Optical Society of America, 2010), p. OWT6.

Fallahpour, A.

A. Fallahpour, M. Ziyadi, A. Mohajerin-Ariaei, Y. Cao, A. Almaiman, F. Alishahi, C. Bao, P. Liao, B. Shamee, L. Paraschis, M. Tur, C. Langrock, M. M. Fejer, J. Touch, and A. E. Willner, “Experimental demonstration of tunable optical de-aggregation of each of multiple wavelength 16-QAM channels into two 4-PAM channels,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), p. Th4I.6.

Fejer, M. M.

A. Fallahpour, M. Ziyadi, A. Mohajerin-Ariaei, Y. Cao, A. Almaiman, F. Alishahi, C. Bao, P. Liao, B. Shamee, L. Paraschis, M. Tur, C. Langrock, M. M. Fejer, J. Touch, and A. E. Willner, “Experimental demonstration of tunable optical de-aggregation of each of multiple wavelength 16-QAM channels into two 4-PAM channels,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), p. Th4I.6.

Feng, K. M.

Y. H. Wen, J. W. Ho, and K. M. Feng, “Phase transparent demultiplexer for QPSK signal based on nonlinear response in a double-pass architecture,” IEEE Photonics J. 8, 1–7 (2016).
[Crossref]

Y. H. Wen and K. M. Feng, “A simple NRZ-OOK to PDM RZ-QPSK optical modulation format conversion by bidirectional XPM,” IEEE Photonics Technol. Lett. 27(9), 935–938 (2015).
[Crossref]

B. Zhang, H. Zhang, C. Yu, X. Cheng, K. Y. Yong, P. K. Kam, J. Yang, H. Zhang, Y. H. Wen, and K. M. Feng, “An all-optical modulation format conversion for 8QAM based on FWM in HNLF,” IEEE Photonics Technol. Lett. 25(4), 327–330 (2013).
[Crossref]

Feng, K.-M.

Y.-H. Wen, J.-W. Ho, and K.-M. Feng, “Simultaneous all-optical transparent phase multiplexing/de-multiplexing based on FWM in a HNLF,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), p. W4D.1.

Fukuchi, Y.

F. Da Ros, K. Dalgaard, Y. Fukuchi, J. Xu, M. Galili, and C. Peucheret, “Simultaneous QPSK-to- $2\times$2× BPSK wavelength and modulation format conversion in PPLN,” IEEE Photonics Technol. Lett. 26(12), 1207–1210 (2014).
[Crossref]

Futami, F.

H. C. Lim, F. Futami, and K. Kikuchi, “Polarization-independent, wavelength-shift-free optical phase conjugator using a nonlinear fiber sagnac interferometer,” IEEE Photonics Technol. Lett. 11(5), 578–580 (1999).
[Crossref]

Galili, M.

F. Da Ros, K. Dalgaard, Y. Fukuchi, J. Xu, M. Galili, and C. Peucheret, “Simultaneous QPSK-to- $2\times$2× BPSK wavelength and modulation format conversion in PPLN,” IEEE Photonics Technol. Lett. 26(12), 1207–1210 (2014).
[Crossref]

Gay, M.

Gerstel, O.

O. Gerstel, M. Jinno, A. Lord, and S. J. B. Yoo, “Elastic optical networking: a new dawn for the optical layer?” IEEE Commun. Mag. 50(2), s12–s20 (2012).
[Crossref]

Goto, N.

Hesketh, G.

Ho, J. W.

Y. H. Wen, J. W. Ho, and K. M. Feng, “Phase transparent demultiplexer for QPSK signal based on nonlinear response in a double-pass architecture,” IEEE Photonics J. 8, 1–7 (2016).
[Crossref]

Ho, J.-W.

Y.-H. Wen, J.-W. Ho, and K.-M. Feng, “Simultaneous all-optical transparent phase multiplexing/de-multiplexing based on FWM in a HNLF,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), p. W4D.1.

Horak, P.

Huang, H.

X. Wu, J. Wang, H. Huang, and A. E. Willner, “Experimental optical multiplexing of two 20-Gbit/s QPSK data channels from different wavelengths onto a single 40Gbit/s star 16-QAM using fiber nonlinearities,” in CLEO:2011 - Laser Applications to Photonic Applications, (Optical Society of America, 2011), p. CThH4.

Ibrahim, S. K.

S. K. Ibrahim, S. Sygletos, R. Weerasuriya, and A. D. Ellis, “Novel real-time homodyne coherent receiver using a feed-forward based carrier extraction scheme for phase modulated signals,” Opt. Express 19(9), 8320–8326 (2011).
[Crossref]

R. Weerasuriya, S. Sygletos, S. K. Ibrahim, R. Phelan, J. O’Carroll, B. Kelly, J. O’Gorman, and A. D. Ellis, “Generation of frequency symmetric signals from a BPSK input for phase sensitive amplification,” in Optical Fiber Communication Conference, (Optical Society of America, 2010), p. OWT6.

Ji, Y.

H. Liu, H. Wang, and Y. Ji, “Simultaneous all-optical channel aggregation and de-aggregation for 8QAM signal in elastic optical networking,” IEEE Photonics J. 11(1), 1–8 (2019).
[Crossref]

H. Liu, H. Wang, J. Cui, and Y. Ji, “Design of all-optical modulation format converter from one 8PSK to two QPSK signals based on phase sensitive amplification in elastic optical network,” IEEE Access 7, 51379–51385 (2019).
[Crossref]

L. Pan, H. Wang, and Y. Ji, “All-optical deaggregation from 8PSK to 3×BPSK based on FWM in HNLF,” Appl. Opt. 58(5), 1246–1252 (2019).
[Crossref]

J. Cui, G. Lu, H. Wang, and Y. Ji, “On-chip optical vector quadrature de-multiplexer proposal for QAM de-aggregation by single bi-directional SOA-based phase-sensitive amplifier,” IEEE Access 7, 763–772 (2019).
[Crossref]

Ji, Y. F.

Y. F. Ji, H. X. Wang, J. B. Cui, M. T. Yu, Z. T. Yang, and L. Bai, “All-optical signal processing technologies in flexible optical networks,” Photonic Netw. Commun. 38(1), 14–36 (2019).
[Crossref]

Y. F. Ji, J. W. Zhang, X. Wang, and H. Yu, “Towards converged, collaborative and co-automatic (3C) optical networks,” Sci. China Inf. Sci. 61(12), 121301 (2018).
[Crossref]

Y. F. Ji, J. W. Zhang, Y. l. Zhao, X. S. Yu, J. Zhang, and X. Chen, “Prospects and research issues in multi-dimensional all optical networks,” Sci. China Inf. Sci. 59(10), 101301 (2016).
[Crossref]

Jinno, M.

O. Gerstel, M. Jinno, A. Lord, and S. J. B. Yoo, “Elastic optical networking: a new dawn for the optical layer?” IEEE Commun. Mag. 50(2), s12–s20 (2012).
[Crossref]

Kam, P. K.

B. Zhang, H. Zhang, C. Yu, X. Cheng, K. Y. Yong, P. K. Kam, J. Yang, H. Zhang, Y. H. Wen, and K. M. Feng, “An all-optical modulation format conversion for 8QAM based on FWM in HNLF,” IEEE Photonics Technol. Lett. 25(4), 327–330 (2013).
[Crossref]

Karlsson, M.

Kelly, B.

R. Weerasuriya, S. Sygletos, S. K. Ibrahim, R. Phelan, J. O’Carroll, B. Kelly, J. O’Gorman, and A. D. Ellis, “Generation of frequency symmetric signals from a BPSK input for phase sensitive amplification,” in Optical Fiber Communication Conference, (Optical Society of America, 2010), p. OWT6.

Kikuchi, K.

H. C. Lim, F. Futami, and K. Kikuchi, “Polarization-independent, wavelength-shift-free optical phase conjugator using a nonlinear fiber sagnac interferometer,” IEEE Photonics Technol. Lett. 11(5), 578–580 (1999).
[Crossref]

Kishikawa, H.

Kitagawa, S.

Kumpera, A.

l. Zhao, Y.

Y. F. Ji, J. W. Zhang, Y. l. Zhao, X. S. Yu, J. Zhang, and X. Chen, “Prospects and research issues in multi-dimensional all optical networks,” Sci. China Inf. Sci. 59(10), 101301 (2016).
[Crossref]

Langrock, C.

A. Fallahpour, M. Ziyadi, A. Mohajerin-Ariaei, Y. Cao, A. Almaiman, F. Alishahi, C. Bao, P. Liao, B. Shamee, L. Paraschis, M. Tur, C. Langrock, M. M. Fejer, J. Touch, and A. E. Willner, “Experimental demonstration of tunable optical de-aggregation of each of multiple wavelength 16-QAM channels into two 4-PAM channels,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), p. Th4I.6.

Liao, P.

A. Fallahpour, M. Ziyadi, A. Mohajerin-Ariaei, Y. Cao, A. Almaiman, F. Alishahi, C. Bao, P. Liao, B. Shamee, L. Paraschis, M. Tur, C. Langrock, M. M. Fejer, J. Touch, and A. E. Willner, “Experimental demonstration of tunable optical de-aggregation of each of multiple wavelength 16-QAM channels into two 4-PAM channels,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), p. Th4I.6.

Lim, H. C.

H. C. Lim, F. Futami, and K. Kikuchi, “Polarization-independent, wavelength-shift-free optical phase conjugator using a nonlinear fiber sagnac interferometer,” IEEE Photonics Technol. Lett. 11(5), 578–580 (1999).
[Crossref]

Liu, H.

H. Liu, H. Wang, J. Cui, and Y. Ji, “Design of all-optical modulation format converter from one 8PSK to two QPSK signals based on phase sensitive amplification in elastic optical network,” IEEE Access 7, 51379–51385 (2019).
[Crossref]

H. Liu, H. Wang, and Y. Ji, “Simultaneous all-optical channel aggregation and de-aggregation for 8QAM signal in elastic optical networking,” IEEE Photonics J. 11(1), 1–8 (2019).
[Crossref]

Liu, L.

Lord, A.

O. Gerstel, M. Jinno, A. Lord, and S. J. B. Yoo, “Elastic optical networking: a new dawn for the optical layer?” IEEE Commun. Mag. 50(2), s12–s20 (2012).
[Crossref]

Lorences-Riesgo, A.

Lu, G.

J. Cui, G. Lu, H. Wang, and Y. Ji, “On-chip optical vector quadrature de-multiplexer proposal for QAM de-aggregation by single bi-directional SOA-based phase-sensitive amplifier,” IEEE Access 7, 763–772 (2019).
[Crossref]

Lundström, C.

Mahmood, T.

B. M. Cannon, T. Mahmood, W. Astar, P. Boudra, T. Mohsenin, and G. M. Carter, “Polarization-insensitive phase-transmultiplexing of CSRZ-OOK and RZ-BPSK to RZ-QPSK via XPM in a PCF,” in Optical Fiber Communication Conference, (Optical Society of America, 2014), p. W2A.52.

Malik, R.

Maruta, A.

Michel, J.

Mishina, K.

Mohajerin-Ariaei, A.

A. Fallahpour, M. Ziyadi, A. Mohajerin-Ariaei, Y. Cao, A. Almaiman, F. Alishahi, C. Bao, P. Liao, B. Shamee, L. Paraschis, M. Tur, C. Langrock, M. M. Fejer, J. Touch, and A. E. Willner, “Experimental demonstration of tunable optical de-aggregation of each of multiple wavelength 16-QAM channels into two 4-PAM channels,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), p. Th4I.6.

Mohsenin, T.

B. M. Cannon, T. Mahmood, W. Astar, P. Boudra, T. Mohsenin, and G. M. Carter, “Polarization-insensitive phase-transmultiplexing of CSRZ-OOK and RZ-BPSK to RZ-QPSK via XPM in a PCF,” in Optical Fiber Communication Conference, (Optical Society of America, 2014), p. W2A.52.

O’Carroll, J.

R. Weerasuriya, S. Sygletos, S. K. Ibrahim, R. Phelan, J. O’Carroll, B. Kelly, J. O’Gorman, and A. D. Ellis, “Generation of frequency symmetric signals from a BPSK input for phase sensitive amplification,” in Optical Fiber Communication Conference, (Optical Society of America, 2010), p. OWT6.

O’Gorman, J.

R. Weerasuriya, S. Sygletos, S. K. Ibrahim, R. Phelan, J. O’Carroll, B. Kelly, J. O’Gorman, and A. D. Ellis, “Generation of frequency symmetric signals from a BPSK input for phase sensitive amplification,” in Optical Fiber Communication Conference, (Optical Society of America, 2010), p. OWT6.

Olsson, S. L. I.

Pan, L.

Paraschis, L.

A. Fallahpour, M. Ziyadi, A. Mohajerin-Ariaei, Y. Cao, A. Almaiman, F. Alishahi, C. Bao, P. Liao, B. Shamee, L. Paraschis, M. Tur, C. Langrock, M. M. Fejer, J. Touch, and A. E. Willner, “Experimental demonstration of tunable optical de-aggregation of each of multiple wavelength 16-QAM channels into two 4-PAM channels,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), p. Th4I.6.

Parmigiani, F.

Petropoulos, P.

Peucheret, C.

M. Baillot, M. Gay, C. Peucheret, J. Michel, and T. Chartier, “Phase quadrature discrimination based on three-pump four-wave mixing in nonlinear optical fibers,” Opt. Express 24(23), 26930–26941 (2016).
[Crossref]

F. Da Ros, K. Dalgaard, Y. Fukuchi, J. Xu, M. Galili, and C. Peucheret, “Simultaneous QPSK-to- $2\times$2× BPSK wavelength and modulation format conversion in PPLN,” IEEE Photonics Technol. Lett. 26(12), 1207–1210 (2014).
[Crossref]

Phelan, R.

R. Weerasuriya, S. Sygletos, S. K. Ibrahim, R. Phelan, J. O’Carroll, B. Kelly, J. O’Gorman, and A. D. Ellis, “Generation of frequency symmetric signals from a BPSK input for phase sensitive amplification,” in Optical Fiber Communication Conference, (Optical Society of America, 2010), p. OWT6.

Radic, S.

Richardson, D. J.

Shamee, B.

A. Fallahpour, M. Ziyadi, A. Mohajerin-Ariaei, Y. Cao, A. Almaiman, F. Alishahi, C. Bao, P. Liao, B. Shamee, L. Paraschis, M. Tur, C. Langrock, M. M. Fejer, J. Touch, and A. E. Willner, “Experimental demonstration of tunable optical de-aggregation of each of multiple wavelength 16-QAM channels into two 4-PAM channels,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), p. Th4I.6.

Slavík, R.

Sygletos, S.

S. K. Ibrahim, S. Sygletos, R. Weerasuriya, and A. D. Ellis, “Novel real-time homodyne coherent receiver using a feed-forward based carrier extraction scheme for phase modulated signals,” Opt. Express 19(9), 8320–8326 (2011).
[Crossref]

R. Weerasuriya, S. Sygletos, S. K. Ibrahim, R. Phelan, J. O’Carroll, B. Kelly, J. O’Gorman, and A. D. Ellis, “Generation of frequency symmetric signals from a BPSK input for phase sensitive amplification,” in Optical Fiber Communication Conference, (Optical Society of America, 2010), p. OWT6.

Touch, J.

A. Fallahpour, M. Ziyadi, A. Mohajerin-Ariaei, Y. Cao, A. Almaiman, F. Alishahi, C. Bao, P. Liao, B. Shamee, L. Paraschis, M. Tur, C. Langrock, M. M. Fejer, J. Touch, and A. E. Willner, “Experimental demonstration of tunable optical de-aggregation of each of multiple wavelength 16-QAM channels into two 4-PAM channels,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), p. Th4I.6.

Tur, M.

A. Fallahpour, M. Ziyadi, A. Mohajerin-Ariaei, Y. Cao, A. Almaiman, F. Alishahi, C. Bao, P. Liao, B. Shamee, L. Paraschis, M. Tur, C. Langrock, M. M. Fejer, J. Touch, and A. E. Willner, “Experimental demonstration of tunable optical de-aggregation of each of multiple wavelength 16-QAM channels into two 4-PAM channels,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), p. Th4I.6.

Wang, H.

J. Cui, G. Lu, H. Wang, and Y. Ji, “On-chip optical vector quadrature de-multiplexer proposal for QAM de-aggregation by single bi-directional SOA-based phase-sensitive amplifier,” IEEE Access 7, 763–772 (2019).
[Crossref]

H. Liu, H. Wang, and Y. Ji, “Simultaneous all-optical channel aggregation and de-aggregation for 8QAM signal in elastic optical networking,” IEEE Photonics J. 11(1), 1–8 (2019).
[Crossref]

H. Liu, H. Wang, J. Cui, and Y. Ji, “Design of all-optical modulation format converter from one 8PSK to two QPSK signals based on phase sensitive amplification in elastic optical network,” IEEE Access 7, 51379–51385 (2019).
[Crossref]

L. Pan, H. Wang, and Y. Ji, “All-optical deaggregation from 8PSK to 3×BPSK based on FWM in HNLF,” Appl. Opt. 58(5), 1246–1252 (2019).
[Crossref]

Wang, H. X.

Y. F. Ji, H. X. Wang, J. B. Cui, M. T. Yu, Z. T. Yang, and L. Bai, “All-optical signal processing technologies in flexible optical networks,” Photonic Netw. Commun. 38(1), 14–36 (2019).
[Crossref]

Wang, J.

X. Wu, J. Wang, H. Huang, and A. E. Willner, “Experimental optical multiplexing of two 20-Gbit/s QPSK data channels from different wavelengths onto a single 40Gbit/s star 16-QAM using fiber nonlinearities,” in CLEO:2011 - Laser Applications to Photonic Applications, (Optical Society of America, 2011), p. CThH4.

Wang, X.

Y. F. Ji, J. W. Zhang, X. Wang, and H. Yu, “Towards converged, collaborative and co-automatic (3C) optical networks,” Sci. China Inf. Sci. 61(12), 121301 (2018).
[Crossref]

Weerasuriya, R.

S. K. Ibrahim, S. Sygletos, R. Weerasuriya, and A. D. Ellis, “Novel real-time homodyne coherent receiver using a feed-forward based carrier extraction scheme for phase modulated signals,” Opt. Express 19(9), 8320–8326 (2011).
[Crossref]

R. Weerasuriya, S. Sygletos, S. K. Ibrahim, R. Phelan, J. O’Carroll, B. Kelly, J. O’Gorman, and A. D. Ellis, “Generation of frequency symmetric signals from a BPSK input for phase sensitive amplification,” in Optical Fiber Communication Conference, (Optical Society of America, 2010), p. OWT6.

Wen, Y. H.

Y. H. Wen, J. W. Ho, and K. M. Feng, “Phase transparent demultiplexer for QPSK signal based on nonlinear response in a double-pass architecture,” IEEE Photonics J. 8, 1–7 (2016).
[Crossref]

Y. H. Wen and K. M. Feng, “A simple NRZ-OOK to PDM RZ-QPSK optical modulation format conversion by bidirectional XPM,” IEEE Photonics Technol. Lett. 27(9), 935–938 (2015).
[Crossref]

B. Zhang, H. Zhang, C. Yu, X. Cheng, K. Y. Yong, P. K. Kam, J. Yang, H. Zhang, Y. H. Wen, and K. M. Feng, “An all-optical modulation format conversion for 8QAM based on FWM in HNLF,” IEEE Photonics Technol. Lett. 25(4), 327–330 (2013).
[Crossref]

Wen, Y.-H.

Y.-H. Wen, J.-W. Ho, and K.-M. Feng, “Simultaneous all-optical transparent phase multiplexing/de-multiplexing based on FWM in a HNLF,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), p. W4D.1.

Willner, A. E.

A. Fallahpour, M. Ziyadi, A. Mohajerin-Ariaei, Y. Cao, A. Almaiman, F. Alishahi, C. Bao, P. Liao, B. Shamee, L. Paraschis, M. Tur, C. Langrock, M. M. Fejer, J. Touch, and A. E. Willner, “Experimental demonstration of tunable optical de-aggregation of each of multiple wavelength 16-QAM channels into two 4-PAM channels,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), p. Th4I.6.

X. Wu, J. Wang, H. Huang, and A. E. Willner, “Experimental optical multiplexing of two 20-Gbit/s QPSK data channels from different wavelengths onto a single 40Gbit/s star 16-QAM using fiber nonlinearities,” in CLEO:2011 - Laser Applications to Photonic Applications, (Optical Society of America, 2011), p. CThH4.

Wu, X.

X. Wu, J. Wang, H. Huang, and A. E. Willner, “Experimental optical multiplexing of two 20-Gbit/s QPSK data channels from different wavelengths onto a single 40Gbit/s star 16-QAM using fiber nonlinearities,” in CLEO:2011 - Laser Applications to Photonic Applications, (Optical Society of America, 2011), p. CThH4.

Xu, J.

F. Da Ros, K. Dalgaard, Y. Fukuchi, J. Xu, M. Galili, and C. Peucheret, “Simultaneous QPSK-to- $2\times$2× BPSK wavelength and modulation format conversion in PPLN,” IEEE Photonics Technol. Lett. 26(12), 1207–1210 (2014).
[Crossref]

Yang, J.

B. Zhang, H. Zhang, C. Yu, X. Cheng, K. Y. Yong, P. K. Kam, J. Yang, H. Zhang, Y. H. Wen, and K. M. Feng, “An all-optical modulation format conversion for 8QAM based on FWM in HNLF,” IEEE Photonics Technol. Lett. 25(4), 327–330 (2013).
[Crossref]

Yang, Z. T.

Y. F. Ji, H. X. Wang, J. B. Cui, M. T. Yu, Z. T. Yang, and L. Bai, “All-optical signal processing technologies in flexible optical networks,” Photonic Netw. Commun. 38(1), 14–36 (2019).
[Crossref]

Yong, K. Y.

B. Zhang, H. Zhang, C. Yu, X. Cheng, K. Y. Yong, P. K. Kam, J. Yang, H. Zhang, Y. H. Wen, and K. M. Feng, “An all-optical modulation format conversion for 8QAM based on FWM in HNLF,” IEEE Photonics Technol. Lett. 25(4), 327–330 (2013).
[Crossref]

Yoo, S. J. B.

O. Gerstel, M. Jinno, A. Lord, and S. J. B. Yoo, “Elastic optical networking: a new dawn for the optical layer?” IEEE Commun. Mag. 50(2), s12–s20 (2012).
[Crossref]

Yu, C.

B. Zhang, H. Zhang, C. Yu, X. Cheng, K. Y. Yong, P. K. Kam, J. Yang, H. Zhang, Y. H. Wen, and K. M. Feng, “An all-optical modulation format conversion for 8QAM based on FWM in HNLF,” IEEE Photonics Technol. Lett. 25(4), 327–330 (2013).
[Crossref]

Yu, H.

Y. F. Ji, J. W. Zhang, X. Wang, and H. Yu, “Towards converged, collaborative and co-automatic (3C) optical networks,” Sci. China Inf. Sci. 61(12), 121301 (2018).
[Crossref]

Yu, M. T.

Y. F. Ji, H. X. Wang, J. B. Cui, M. T. Yu, Z. T. Yang, and L. Bai, “All-optical signal processing technologies in flexible optical networks,” Photonic Netw. Commun. 38(1), 14–36 (2019).
[Crossref]

Yu, X. S.

Y. F. Ji, J. W. Zhang, Y. l. Zhao, X. S. Yu, J. Zhang, and X. Chen, “Prospects and research issues in multi-dimensional all optical networks,” Sci. China Inf. Sci. 59(10), 101301 (2016).
[Crossref]

Zhang, B.

B. Zhang, H. Zhang, C. Yu, X. Cheng, K. Y. Yong, P. K. Kam, J. Yang, H. Zhang, Y. H. Wen, and K. M. Feng, “An all-optical modulation format conversion for 8QAM based on FWM in HNLF,” IEEE Photonics Technol. Lett. 25(4), 327–330 (2013).
[Crossref]

Zhang, H.

B. Zhang, H. Zhang, C. Yu, X. Cheng, K. Y. Yong, P. K. Kam, J. Yang, H. Zhang, Y. H. Wen, and K. M. Feng, “An all-optical modulation format conversion for 8QAM based on FWM in HNLF,” IEEE Photonics Technol. Lett. 25(4), 327–330 (2013).
[Crossref]

B. Zhang, H. Zhang, C. Yu, X. Cheng, K. Y. Yong, P. K. Kam, J. Yang, H. Zhang, Y. H. Wen, and K. M. Feng, “An all-optical modulation format conversion for 8QAM based on FWM in HNLF,” IEEE Photonics Technol. Lett. 25(4), 327–330 (2013).
[Crossref]

Zhang, J.

Y. F. Ji, J. W. Zhang, Y. l. Zhao, X. S. Yu, J. Zhang, and X. Chen, “Prospects and research issues in multi-dimensional all optical networks,” Sci. China Inf. Sci. 59(10), 101301 (2016).
[Crossref]

Zhang, J. W.

Y. F. Ji, J. W. Zhang, X. Wang, and H. Yu, “Towards converged, collaborative and co-automatic (3C) optical networks,” Sci. China Inf. Sci. 61(12), 121301 (2018).
[Crossref]

Y. F. Ji, J. W. Zhang, Y. l. Zhao, X. S. Yu, J. Zhang, and X. Chen, “Prospects and research issues in multi-dimensional all optical networks,” Sci. China Inf. Sci. 59(10), 101301 (2016).
[Crossref]

Ziyadi, M.

A. Fallahpour, M. Ziyadi, A. Mohajerin-Ariaei, Y. Cao, A. Almaiman, F. Alishahi, C. Bao, P. Liao, B. Shamee, L. Paraschis, M. Tur, C. Langrock, M. M. Fejer, J. Touch, and A. E. Willner, “Experimental demonstration of tunable optical de-aggregation of each of multiple wavelength 16-QAM channels into two 4-PAM channels,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), p. Th4I.6.

Appl. Opt. (1)

IEEE Access (2)

H. Liu, H. Wang, J. Cui, and Y. Ji, “Design of all-optical modulation format converter from one 8PSK to two QPSK signals based on phase sensitive amplification in elastic optical network,” IEEE Access 7, 51379–51385 (2019).
[Crossref]

J. Cui, G. Lu, H. Wang, and Y. Ji, “On-chip optical vector quadrature de-multiplexer proposal for QAM de-aggregation by single bi-directional SOA-based phase-sensitive amplifier,” IEEE Access 7, 763–772 (2019).
[Crossref]

IEEE Commun. Mag. (1)

O. Gerstel, M. Jinno, A. Lord, and S. J. B. Yoo, “Elastic optical networking: a new dawn for the optical layer?” IEEE Commun. Mag. 50(2), s12–s20 (2012).
[Crossref]

IEEE Photonics J. (2)

Y. H. Wen, J. W. Ho, and K. M. Feng, “Phase transparent demultiplexer for QPSK signal based on nonlinear response in a double-pass architecture,” IEEE Photonics J. 8, 1–7 (2016).
[Crossref]

H. Liu, H. Wang, and Y. Ji, “Simultaneous all-optical channel aggregation and de-aggregation for 8QAM signal in elastic optical networking,” IEEE Photonics J. 11(1), 1–8 (2019).
[Crossref]

IEEE Photonics Technol. Lett. (4)

H. C. Lim, F. Futami, and K. Kikuchi, “Polarization-independent, wavelength-shift-free optical phase conjugator using a nonlinear fiber sagnac interferometer,” IEEE Photonics Technol. Lett. 11(5), 578–580 (1999).
[Crossref]

F. Da Ros, K. Dalgaard, Y. Fukuchi, J. Xu, M. Galili, and C. Peucheret, “Simultaneous QPSK-to- $2\times$2× BPSK wavelength and modulation format conversion in PPLN,” IEEE Photonics Technol. Lett. 26(12), 1207–1210 (2014).
[Crossref]

B. Zhang, H. Zhang, C. Yu, X. Cheng, K. Y. Yong, P. K. Kam, J. Yang, H. Zhang, Y. H. Wen, and K. M. Feng, “An all-optical modulation format conversion for 8QAM based on FWM in HNLF,” IEEE Photonics Technol. Lett. 25(4), 327–330 (2013).
[Crossref]

Y. H. Wen and K. M. Feng, “A simple NRZ-OOK to PDM RZ-QPSK optical modulation format conversion by bidirectional XPM,” IEEE Photonics Technol. Lett. 27(9), 935–938 (2015).
[Crossref]

J. Lightwave Technol. (2)

Opt. Express (4)

Opt. Lett. (1)

Photonic Netw. Commun. (1)

Y. F. Ji, H. X. Wang, J. B. Cui, M. T. Yu, Z. T. Yang, and L. Bai, “All-optical signal processing technologies in flexible optical networks,” Photonic Netw. Commun. 38(1), 14–36 (2019).
[Crossref]

Sci. China Inf. Sci. (2)

Y. F. Ji, J. W. Zhang, Y. l. Zhao, X. S. Yu, J. Zhang, and X. Chen, “Prospects and research issues in multi-dimensional all optical networks,” Sci. China Inf. Sci. 59(10), 101301 (2016).
[Crossref]

Y. F. Ji, J. W. Zhang, X. Wang, and H. Yu, “Towards converged, collaborative and co-automatic (3C) optical networks,” Sci. China Inf. Sci. 61(12), 121301 (2018).
[Crossref]

Other (5)

X. Wu, J. Wang, H. Huang, and A. E. Willner, “Experimental optical multiplexing of two 20-Gbit/s QPSK data channels from different wavelengths onto a single 40Gbit/s star 16-QAM using fiber nonlinearities,” in CLEO:2011 - Laser Applications to Photonic Applications, (Optical Society of America, 2011), p. CThH4.

B. M. Cannon, T. Mahmood, W. Astar, P. Boudra, T. Mohsenin, and G. M. Carter, “Polarization-insensitive phase-transmultiplexing of CSRZ-OOK and RZ-BPSK to RZ-QPSK via XPM in a PCF,” in Optical Fiber Communication Conference, (Optical Society of America, 2014), p. W2A.52.

A. Fallahpour, M. Ziyadi, A. Mohajerin-Ariaei, Y. Cao, A. Almaiman, F. Alishahi, C. Bao, P. Liao, B. Shamee, L. Paraschis, M. Tur, C. Langrock, M. M. Fejer, J. Touch, and A. E. Willner, “Experimental demonstration of tunable optical de-aggregation of each of multiple wavelength 16-QAM channels into two 4-PAM channels,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), p. Th4I.6.

Y.-H. Wen, J.-W. Ho, and K.-M. Feng, “Simultaneous all-optical transparent phase multiplexing/de-multiplexing based on FWM in a HNLF,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), p. W4D.1.

R. Weerasuriya, S. Sygletos, S. K. Ibrahim, R. Phelan, J. O’Carroll, B. Kelly, J. O’Gorman, and A. D. Ellis, “Generation of frequency symmetric signals from a BPSK input for phase sensitive amplification,” in Optical Fiber Communication Conference, (Optical Society of America, 2010), p. OWT6.

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Figures (11)

Fig. 1.
Fig. 1. Scheme of optical channel aggregator with constellation diagrams (a) OOK b) BPSK (M=2) c) QPSK (M=4), (d) aggregated QPSK (M=2) or (e) aggregated 8PSK (M=4).
Fig. 2.
Fig. 2. (a) Theoretical value and actual measured value of the phase shift $\Delta \varphi$ on MPSK varies with the OOK power; (b) The amplitude jitter of Q/8PSK varies with the corresponding B/QPSK power under the fixed OOK power of 31mW and 15mW respectively.
Fig. 3.
Fig. 3. Constellation diagrams of (a) aggregated QPSK signal (M=2), (b) recovered BPSK and (c) ’OOK’ signals; (d) aggregated 8PSK signal (M=4), (e) recovered QPSK and (f) ’OOK’ signal.
Fig. 4.
Fig. 4. (a) Scheme of optical channel de-aggregator from aggregated 2MPSK signal into MPSK and OOK signals; (b) and (c) are the corresponding schematic signal spectra before and after the cascaded FWM process in the HNLF at port C and port D respectively
Fig. 5.
Fig. 5. Schematic diagram for m value by phase squeezing analysis of optical vectors.
Fig. 6.
Fig. 6. (a) Phase-to-phase and (b) phase-to-amplitude gain transfer functions for QPSK (M=2) de-aggregation to BPSK and ’OOK’ respectively;(c) Phase-to-phase and (d) phase-to-amplitude gain transfer functions for 8PSK (M=4) de-aggregation to QPSK and ’OOK’ respectively.
Fig. 7.
Fig. 7. (a) Black box schematic of phase locked Pump2 extraction device; (b) Optical spectrum of input 2MPSK signal (M=2); (c) Measured self-heterodyned linewidth for output P2.
Fig. 8.
Fig. 8. (a) The whole setup for optical channel aggregator and de-aggregator for OOK and MPSK signals and (b-e) the corresponding optical spectra of aggregated QPSK (M=2) and 8PSK (M=4) as examples before and after the HNLF2 respectively.
Fig. 9.
Fig. 9. Input-output constellations and waveforms for M=2 and M=4 cases.
Fig. 10.
Fig. 10. (a) The PN of the aggregated QPSK (M=2) and recovered BPSK signals and the ASD of the aggregated QPSK and recovered OOK signal with the varying OSNR of the QPSK signal; (b) The PN of the aggregated 8PSK (M=4) and recovered QPSK signals and the ASD of the aggregated 8PSK and recovered OOK signal with the varying OSNR of the 8PSK signal.
Fig. 11.
Fig. 11. BER curves versus varying OSNR of (a) the aggregated QPSK (M=2) and (b) the aggregated 8PSK (M=4) transmitted in the link. R-B/QPSK: Recovered B/QPSK, R-OOK: Recovered OOK, A-Q/8PSK: aggregated Q/8PSK, FEC thr: forward error correction threshold.

Tables (2)

Tables Icon

Table 1. The optical mapping and logic pattern among the signals in aggregation.

Tables Icon

Table 2. The optical mapping and logic pattern among the signals in de-aggregation.

Equations (12)

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

A 2MPSK = | A MPSK | exp [ j ( φ M P S K + 2 γ L e f f P O O K ) ]
φ 2 M P S K = φ M P S K + 2 γ L e f f P O O K = φ M P S K + Δ φ ,
[ E A1 E B1 ] = [ A P1 exp ( j φ P 1 ) + A S exp ( j φ S ) A P 2 exp ( j φ P 2 ) ] .
φ H = ( M 1 ) φ S ( M 2 ) φ P1 φ i = ( M 1 ) φ P 1 ( M 1 ) φ S + φ P 2 .
[ E A2 E B2 ] = [ A P1 exp ( j φ P 1 ) + A S exp ( j φ S ) A P 2 exp ( j φ P 2 ) + m A S exp ( j φ i ) ] ,
[ E G E H ] = 1 2 [ 1 j 1 1 ] × [ E E E F ] = 1 2 [ 1 j 1 1 ] × [ A S exp ( j φ S ) m A S exp ( j φ i ) ] = 1 2 A S [ exp ( j φ S ) + m exp ( j ( φ i + π / 2 ) ) exp ( j φ S ) + m exp ( j ( φ i + π ) ) ] ,
( M 1 ) φ P1 + φ P2  M φ S0 = 0 ,
[ E G E H ] = 1 2 A S exp ( j φ S 0 ) [ exp ( j φ m ) + m exp ( j ( ( M 1 ) φ m + π / 2 ) ) exp ( j φ m ) + m exp ( j ( ( M 1 ) φ m + π ) ) ] .
m sin 1 = 1 sin 3 ,
[ E G E H ] = 1 2 A S exp ( j φ S 0 ) [ exp ( j φ m ) + exp ( j ( φ m + π / 2 ) ) exp ( j φ m ) + exp ( j ( φ m + π ) ) ] .
[ E G E H ] = 1 2 A S exp ( j φ S 0 ) [ exp ( j φ m ) + 0.414 exp ( j ( 3 φ m + π / 2 ) ) exp ( j φ m ) + 0.414 exp ( j ( 3 φ m + π ) ) ] .
φ MH = M φ S ( M 1 ) φ P 1 = φ B P S K + M φ S 0 ( M 1 ) φ P 1 ,

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