Abstract

We theoretically and experimentally study the principle of phase-sensitive frequency conversion in a highly-nonlinear fiber using three pump waves. This mechanism, originally demonstrated with four continuous-wave pumps and a signal wave, is based on four-wave mixing and enables to convert the two quadrature components of the signal to different frequencies. In this work, we derive a set of two simple equations to describe this mechanism and find analytic solutions. We show that only three pumps are required, instead of four as originally proposed. We give simple relations to determine the initial conditions for the power levels and the phases of the pumps. To validate this approach, we perform an experimental demonstration of the three-pump scheme and find excellent agreement with the theory.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
QPSK-to-2×BPSK wavelength and modulation format conversion through phase-sensitive four-wave mixing in a highly nonlinear optical fiber

Francesco Da Ros, Kjeld Dalgaard, Lei Lei, Jing Xu, and Christophe Peucheret
Opt. Express 21(23) 28743-28750 (2013)

Raman enhanced polarization-insensitive wavelength conversion based on two-pump four-wave mixing

Xiaojie Guo and Chester Shu
Opt. Express 24(25) 28648-28658 (2016)

References

  • View by:
  • |
  • |
  • |

  1. Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
    [Crossref]
  2. R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
    [Crossref]
  3. K. Croussore and G. Li, “Phase-regenerative wavelength conversion for BPSK and DPSK signals,” IEEE Photon. Technol. Lett. 21, 70–72 (2009).
    [Crossref]
  4. R. P. Webb, J. M. Dailey, R. J. Manning, and A. D. Ellis, “Phase discrimination and simultaneous frequency conversion of the orthogonal components of an optical signal by four-wave mixing in an SOA,” Opt. Express 19, 20015–20022 (2011).
    [Crossref]
  5. F. Da Ros, K. Dalgaard, L. Lei, J. Xu, and C. Peucheret, “QPSK-to-2xBPSK wavelength and modulation format conversion through phase-sensitive four-wave mixing in a highly nonlinear optical fiber,” Opt. Express 21, 28743–28750 (2013).
    [Crossref]
  6. F. Da Ros, K. Dalgaard, Y. Fukuchi, J. Xu, M. Galili, and C. Peucheret, “Simultaneous QPSK-to-2xBPSK wavelength and modulation format conversion in PPLN,” IEEE Photon. Technol. Lett. 26, 1207–1210 (2014).
    [Crossref]
  7. X. Fu and C. Shu, “Phase-sensitive four-wave mixing interferometer,” Opt. Lett. 39, 4427–4430 (2014).
    [Crossref]
  8. M. Baillot, T. Chartier, and M. Joindot, “Multiple four-wave mixing in optical fibres,” in the European Conference on Optical Communication (ECOC) (2014).
  9. R. P. Webb, M. Power, and R. J. Manning, “Phase-sensitive frequency conversion of quadrature modulated signals,” Opt. Express 21, 12713–12727 (2013).
    [Crossref]

2014 (2)

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

X. Fu and C. Shu, “Phase-sensitive four-wave mixing interferometer,” Opt. Lett. 39, 4427–4430 (2014).
[Crossref]

2013 (2)

2011 (2)

R. P. Webb, J. M. Dailey, R. J. Manning, and A. D. Ellis, “Phase discrimination and simultaneous frequency conversion of the orthogonal components of an optical signal by four-wave mixing in an SOA,” Opt. Express 19, 20015–20022 (2011).
[Crossref]

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

2010 (1)

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

2009 (1)

K. Croussore and G. Li, “Phase-regenerative wavelength conversion for BPSK and DPSK signals,” IEEE Photon. Technol. Lett. 21, 70–72 (2009).
[Crossref]

Andrekson, P. A.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Baillot, M.

M. Baillot, T. Chartier, and M. Joindot, “Multiple four-wave mixing in optical fibres,” in the European Conference on Optical Communication (ECOC) (2014).

Blessing, D. J.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

Bogris, A.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Chartier, T.

M. Baillot, T. Chartier, and M. Joindot, “Multiple four-wave mixing in optical fibres,” in the European Conference on Optical Communication (ECOC) (2014).

Croussore, K.

K. Croussore and G. Li, “Phase-regenerative wavelength conversion for BPSK and DPSK signals,” IEEE Photon. Technol. Lett. 21, 70–72 (2009).
[Crossref]

Da Ros, F.

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

F. Da Ros, K. Dalgaard, L. Lei, J. Xu, and C. Peucheret, “QPSK-to-2xBPSK wavelength and modulation format conversion through phase-sensitive four-wave mixing in a highly nonlinear optical fiber,” Opt. Express 21, 28743–28750 (2013).
[Crossref]

Dailey, J. M.

Dalgaard, K.

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

F. Da Ros, K. Dalgaard, L. Lei, J. Xu, and C. Peucheret, “QPSK-to-2xBPSK wavelength and modulation format conversion through phase-sensitive four-wave mixing in a highly nonlinear optical fiber,” Opt. Express 21, 28743–28750 (2013).
[Crossref]

Dasgupta, S.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Ellis, A. D.

R. P. Webb, J. M. Dailey, R. J. Manning, and A. D. Ellis, “Phase discrimination and simultaneous frequency conversion of the orthogonal components of an optical signal by four-wave mixing in an SOA,” Opt. Express 19, 20015–20022 (2011).
[Crossref]

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Fu, X.

Fukuchi, Y.

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

Galili, M.

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

Grüner-Nielsen, L.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Herstrøm, S.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Jakobsen, D.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Joindot, M.

M. Baillot, T. Chartier, and M. Joindot, “Multiple four-wave mixing in optical fibres,” in the European Conference on Optical Communication (ECOC) (2014).

Kakande, J.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Karlsson, M.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

Lei, L.

Li, G.

K. Croussore and G. Li, “Phase-regenerative wavelength conversion for BPSK and DPSK signals,” IEEE Photon. Technol. Lett. 21, 70–72 (2009).
[Crossref]

Lundström, C.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Manning, R. J.

McKinstrie, C. J.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

O’Gorman, J.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Parmigiani, F.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Petropoulos, P.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Peucheret, C.

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

F. Da Ros, K. Dalgaard, L. Lei, J. Xu, and C. Peucheret, “QPSK-to-2xBPSK wavelength and modulation format conversion through phase-sensitive four-wave mixing in a highly nonlinear optical fiber,” Opt. Express 21, 28743–28750 (2013).
[Crossref]

Phelan, R.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Power, M.

Puttnam, B. J.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

Richardson, D. J.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Shu, C.

Sjödin, M.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Slavík, R.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Sygletos, S.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Syvridis, D.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Tipsuwannakul, E.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

Toda, H.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

Tong, Z.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

Webb, R. P.

Weerasuriya, R.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Xu, J.

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

F. Da Ros, K. Dalgaard, L. Lei, J. Xu, and C. Peucheret, “QPSK-to-2xBPSK wavelength and modulation format conversion through phase-sensitive four-wave mixing in a highly nonlinear optical fiber,” Opt. Express 21, 28743–28750 (2013).
[Crossref]

IEEE Photon. Technol. Lett. (2)

K. Croussore and G. Li, “Phase-regenerative wavelength conversion for BPSK and DPSK signals,” IEEE Photon. Technol. Lett. 21, 70–72 (2009).
[Crossref]

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

Nat. Photonics (2)

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Other (1)

M. Baillot, T. Chartier, and M. Joindot, “Multiple four-wave mixing in optical fibres,” in the European Conference on Optical Communication (ECOC) (2014).

Cited By

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

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1 Principle of phase-sensitive FWM frequency conversion.
Fig. 2
Fig. 2 Different terms of Eqs. (10) and (11) represented as phasors in the complex plane for the initial conditions ϕ 1 = ϕ 6 0 = ϕ 7 = 0 and ϕ3 = π.
Fig. 3
Fig. 3 Experimental setup of a phase-sensitive frequency converter.
Fig. 4
Fig. 4 Optical spectra at the output of the HNLF for (a) δϕ6 = 0 and (b) δϕ6 = π/2.
Fig. 5
Fig. 5 Evolution of the powers P2 and P4 of idlers I2 and I4 as a function of ϕ6.

Tables (2)

Tables Icon

Table 1 Possible values of the phases of the waves according to Eqs. (15) and (16).

Tables Icon

Table 2 Power levels and phases of the three pumps and the signal at the input of the HNLF.

Equations (49)

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

d A n d z = α 2 A n + i γ ( | A n | 2 + 2 q = 1 ( n ) N | A n | 2 ) A n + i γ p = 1 N m = 1 ( n , p ) N d n + p m A n + p m A m A p * e i Δ β n + p m , m , p , n z ,
d n + p m = { 1 if n + p m = m , 2 if n + p m m .
Δ β n + p m , m , p , n = Δ ω 2 β 2 ( n m ) ( p m ) + 1 2 Δ ω 3 β 3 ( n m ) ( p m ) ( n + p N 1 ) + 1 24 Δ ω 4 β 4 ( n m ) ( p m ) [ 3 ( n + p N 1 ) 2 + ( n m ) 2 + ( p m ) 2 ] ,
d A 2 d z = α 2 A 2 + i γ ( | A 2 | 2 + 2 | A 1 | 2 + 2 | A 3 | 2 + 2 | A 4 | 2 + 2 | A 5 | 2 + 2 | A 6 | 2 + 2 | A 7 | 2 ) A 2 + i γ ( A 3 2 A 4 * e i Δ β 3 z + A 4 2 A 6 * e i Δ β 13 z + 2 A 1 A 3 A 2 * e i Δ β 5 z + 2 A 3 A 4 A 5 * e i Δ β 7 z + 2 A 1 A 4 A 3 * e i Δ β 9 z + 2 A 3 A 5 A 6 * e i Δ β 10 z + 2 A 1 A 5 A 4 * e i Δ β 12 z + 2 A 3 A 6 A 7 * e i Δ β 14 z + 2 A 1 A 6 A 5 * e i Δ β 15 z + 2 A 1 A 7 A 6 * e i Δ β 18 z + 2 A 4 A 5 A 7 * e i Δ β 19 z ) ,
d A 4 d z = α 2 A 4 + i γ ( | A 4 | 2 + 2 | A 1 | 2 + 2 | A 2 | 2 + 2 | A 3 | 2 + 2 | A 5 | 2 + 2 | A 6 | 2 + 2 | A 7 | 2 ) A 4 + i γ ( A 5 2 A 6 * e i Δ β 2 z + A 3 2 A 2 * e i Δ β 3 z + 2 A 3 A 5 A 4 * e i Δ β 1 z + 2 A 3 A 6 A 5 * e i Δ β 6 z + 2 A 2 A 5 A 3 * e i Δ β 7 z + 2 A 5 A 6 A 7 * e i Δ β 8 z + 2 A 2 A 3 A 1 * e i Δ β 9 z + 2 A 3 A 7 A 6 * e i Δ β 11 z + 2 A 1 A 5 A 2 * e i Δ β 12 z + 2 A 2 A 6 A 4 * e i Δ β 13 z + 2 A 2 A 7 A 5 * e i Δ β 19 z + 2 A 1 A 6 A 3 * e i Δ β 20 z + 2 A 1 A 7 A 4 * e i Δ β 22 z ) ,
d A 2 d z = i γ ( 2 A 3 A 5 A 6 * e i Δ β 10 z + 2 A 3 A 6 A 7 * e i Δ β 14 z + 2 A 1 A 6 A 5 * e i Δ β 15 z + 2 A 1 A 7 A 6 * e i Δ β 18 z ) ,
d A 4 d z = i γ ( A 5 2 A 6 * e i Δ β 2 z + 2 A 3 A 6 A 5 * e i Δ β 6 z + 2 A 5 A 6 A 7 * e i Δ β 8 z + 2 A 3 A 7 A 6 * e i Δ β 11 z + 2 A 1 A 6 A 3 * e i Δ β 20 z ) .
d A 2 d z = i γ ( 2 A 3 A 5 A 6 * + 2 A 3 A 6 A 7 * + 2 A 1 A 6 A 5 * + 2 A 1 A 7 A 6 * ) ,
d A 4 d z = i γ ( A 5 2 A 6 * + 2 A 3 A 6 A 5 * + 2 A 5 A 6 A 7 * + 2 A 3 A 7 A 6 * + 2 A 1 A 6 A 3 * ) .
d A 2 d z = 2 i γ ( A 1 A 7 A 6 * + A 3 A 6 A 7 * ) ,
d A 4 d z = 2 i γ ( A 3 A 7 A 6 * + A 1 A 6 A 3 * ) .
P 1 = P 3 = P 7 ,
ϕ 1 + ϕ 7 ϕ 6 0 = ϕ 3 + ϕ 6 0 ϕ 7 + ( 2 k + 1 ) π ,
ϕ 3 + ϕ 7 ϕ 6 0 = ϕ 1 + ϕ 6 0 ϕ 3 + 2 k π ,
ϕ 1 = 6 ϕ 6 0 5 ϕ 7 + 2 k π ,
ϕ 3 = 4 ϕ 6 0 + 3 ϕ 7 + ( 2 k + 1 ) π .
A 2 ( L ) = 4 γ P 6 P 0 L e i ( 5 ϕ 6 0 4 ϕ 7 ) sin δ ϕ 6 ,
A 4 ( L ) = 4 i γ P 6 P 0 L e i ( 3 ϕ 6 0 2 ϕ 7 ) cos δ ϕ 6 ,
P 2 ( L ) = | A 2 ( L ) | 2 = 16 P 6 γ 2 P 0 2 L 2 sin 2 δ ϕ 6 ,
P 4 ( L ) = | A 4 ( L ) | 2 = 16 P 6 γ 2 P 0 2 L 2 cos 2 δ ϕ 6 .
d A 1 d z = α 2 A 1 + i γ ( | A 1 | 2 + 2 | A 2 | 2 + 2 | A 3 | 2 + 2 | A 4 | 2 + 2 | A 5 | 2 + 2 | A 6 | 2 + 2 | A 7 | 2 ) A 1 + i γ ( A 2 2 A 3 * e i Δ β 5 z + A 3 2 A 5 * e i Δ β 17 z + A 4 2 A 7 * e i Δ β 22 z + 2 A 2 A 3 A 4 * e i Δ β 9 z + 2 A 2 A 4 A 5 * e i Δ β 12 z + 2 A 2 A 5 A 6 * e i Δ β 15 z + 2 A 2 A 6 A 7 * e i Δ β 18 z + 2 A 3 A 4 A 6 * e i Δ β 20 z + 2 A 3 A 5 A 7 * e i Δ β 21 z ) ,
d A 2 d z = α 2 A 2 + i γ ( | A 2 | 2 + 2 | A 1 | 2 + 2 | A 3 | 2 + 2 | A 4 | 2 + 2 | A 5 | 2 + 2 | A 6 | 2 + 2 | A 7 | 2 ) A 2 + i γ ( A 3 2 A 4 * e i Δ β 3 z + A 4 2 A 6 * e i Δ β 13 z + 2 A 1 A 3 A 2 * e i Δ β 5 z + 2 A 3 A 4 A 5 * e i Δ β 7 z + 2 A 1 A 4 A 3 * e i Δ β 9 z + 2 A 3 A 5 A 6 * e i Δ β 10 z + 2 A 1 A 5 A 4 * e i Δ β 12 z + 2 A 3 A 6 A 7 * e i Δ β 14 z + 2 A 1 A 6 A 5 * e i Δ β 15 z + 2 A 1 A 7 A 6 * e i Δ β 14 z + 2 A 4 A 5 A 7 * e i Δ β 19 z ) ,
d A 3 d z = α 2 A 3 + i γ ( | A 3 | 2 + 2 | A 1 | 2 + 2 | A 2 | 2 + 2 | A 4 | 2 + 2 | A 5 | 2 + 2 | A 6 | 2 + 2 | A 7 | 2 ) A 3 + i γ ( A 4 2 A 5 * e i Δ β 1 z + A 2 2 A 1 * e i Δ β 5 z + A 5 2 A 7 * e i Δ β 16 z + 2 A 2 A 4 A 3 * e i Δ β 3 z + 2 A 4 A 5 A 6 * e i Δ β 6 z + 2 A 2 A 5 A 4 * e i Δ β 7 z + 2 A 1 A 4 A 2 * e i Δ β 9 z + 2 A 2 A 6 A 5 * e i Δ β 10 z + 2 A 4 A 6 A 7 * e i Δ β 11 z + 2 A 2 A 7 A 6 * e i Δ β 14 z + 2 A 1 A 5 A 3 * e i Δ β 17 z + 2 A 1 A 6 A 4 * e i Δ β 20 z + 2 A 1 A 7 A 5 * e i Δ β 21 z ) ,
d A 4 d z = α 2 A 4 + i γ ( | A 4 | 2 + 2 | A 1 | 2 + 2 | A 2 | 2 + 2 | A 3 | 2 + 2 | A 5 | 2 + 2 | A 6 | 2 + 2 | A 7 | 2 ) A 4 + i γ ( A 5 2 A 6 * e i Δ β 2 z + A 3 2 A 2 * e i Δ β 3 z + 2 A 3 A 5 A 4 * e i Δ β 1 z + 2 A 3 A 6 A 5 * e i Δ β 6 z + 2 A 2 A 5 A 3 * e i Δ β 7 z + 2 A 5 A 6 A 7 * e i Δ β 8 z + 2 A 2 A 3 A 1 * e i Δ β 9 z + 2 A 3 A 7 A 6 * e i Δ β 11 z + 2 A 1 A 5 A 2 * e i Δ β 12 z + 2 A 2 A 6 A 4 * e i Δ β 13 z + 2 A 2 A 7 A 5 * e i Δ β 19 z + 2 A 1 A 6 A 3 * e i Δ β 20 z + 2 A 1 A 7 A 4 * e i Δ β 22 z ) ,
d A 5 d z = α 2 A 5 + i γ ( | A 5 | 2 + 2 | A 1 | 2 + 2 | A 2 | 2 + 2 | A 3 | 2 + 2 | A 4 | 2 + 2 | A 6 | 2 + 2 | A 7 | 2 ) A 5 + i γ ( A 4 2 A 3 * e i Δ β 1 z + A 6 2 A 7 * e i Δ β 4 z + A 3 2 A 1 * e i Δ β 17 z + 2 A 4 A 6 A 5 * e i Δ β 2 z + 2 A 3 A 6 A 4 * e i Δ β 6 z + 2 A 3 A 4 A 2 * e i Δ β 7 z + 2 A 4 A 7 A 6 * e i Δ β 8 z + 2 A 2 A 6 A 3 * e i Δ β 10 z + 2 A 2 A 4 A 1 * e i Δ β 12 z + 2 A 1 A 6 A 2 * e i Δ β 15 z + 2 A 3 A 7 A 5 * e i Δ β 16 z + 2 A 2 A 7 A 4 * e i Δ β 19 z + 2 A 1 A 7 A 3 * e i Δ β 21 z ) ,
d A 6 d z = α 2 A 6 + i γ ( | A 6 | 2 + 2 | A 1 | 2 + 2 | A 2 | 2 + 2 | A 3 | 2 + 2 | A 4 | 2 + 2 | A 5 | 2 + 2 | A 7 | 2 ) A 6 + i γ ( A 5 2 A 4 * e i Δ β 2 z + A 4 2 A 2 * e i Δ β 13 z + 2 A 2 A 5 A 1 * e i Δ β 15 z + 2 A 5 A 7 A 6 * e i Δ β 4 z + 2 A 4 A 5 A 3 * e i Δ β 6 z + 2 A 4 A 7 A 5 * e i Δ β 8 z + 2 A 3 A 5 A 2 * e i Δ β 10 z + 2 A 3 A 7 A 4 * e i Δ β 11 z + 2 A 2 A 7 A 3 * e i Δ β 14 z + 2 A 1 A 7 A 2 * e i Δ β 18 z + 2 A 3 A 4 A 1 * e i Δ β 20 z ) ,
d A 7 d z = α 2 A 7 + i γ ( | A 7 | 2 + 2 | A 1 | 2 + 2 | A 2 | 2 + 2 | A 3 | 2 + 2 | A 4 | 2 + 2 | A 5 | 2 + 2 | A 6 | 2 ) A 7 + i γ ( A 6 2 A 5 * e i Δ β 4 z + A 5 2 A 3 * e i Δ β 16 z + A 4 2 A 1 * e i Δ β 22 z + 2 A 5 A 6 A 4 * e i Δ β 4 z + 2 A 4 A 6 A 3 * e i Δ β 11 z + 2 A 3 A 6 A 2 * e i Δ β 14 z + 2 A 2 A 6 A 1 * e i Δ β 18 z + 2 A 4 A 5 A 2 * e i Δ β 19 z + 2 A 3 A 5 A 1 * e i Δ β 21 z ) ,
Δ β 1 = Δ ω 2 β 2 + 2 24 Δ ω 4 β 4 ,
Δ β 2 = Δ ω 2 β 2 + Δ ω 3 β 3 14 24 Δ ω 4 β 4 ,
Δ β 3 = Δ ω 2 β 2 Δ ω 3 β 3 14 24 Δ ω 4 β 4 ,
Δ β 4 = Δ ω 2 β 2 + 4 2 Δ ω 4 β 3 + 50 24 Δ ω 4 β 4 ,
Δ β 5 = Δ ω 2 β 2 4 2 Δ ω 4 β 3 + 50 24 Δ ω 4 β 4 ,
Δ β 6 = 2 Δ ω 2 β 2 + Δ ω 3 β 3 + 16 24 Δ ω 4 β 4 ,
Δ β 7 = 2 Δ ω 2 β 2 Δ ω 3 β 3 + 16 24 Δ ω 4 β 4 ,
Δ β 8 = 2 Δ ω 2 β 2 + 6 2 Δ ω 3 β 3 + 16 24 Δ ω 4 β 4 ,
Δ β 9 = 2 Δ ω 2 β 2 6 2 Δ ω 3 β 3 + 64 24 Δ ω 4 β 4 ,
Δ β 10 = 3 Δ ω 2 β 2 + 30 24 Δ ω 4 β 4 ,
Δ β 11 = 3 Δ ω 2 β 2 + 6 2 Δ ω 3 β 3 + 66 24 Δ ω 4 β 4 ,
Δ β 12 = 3 Δ ω 2 β 2 6 2 Δ ω 3 β 3 + 66 24 Δ ω 4 β 4 ,
Δ β 13 = 4 Δ ω 2 β 2 + 32 24 Δ ω 4 β 4 ,
Δ β 14 = 4 Δ ω 2 β 2 + 4 2 Δ ω 3 β 3 + 80 24 Δ ω 4 β 4 ,
Δ β 15 = 4 Δ ω 2 β 2 4 2 Δ ω 3 β 3 + 80 24 Δ ω 4 β 4 ,
Δ β 16 = 4 Δ ω 2 β 2 + 8 2 Δ ω 3 β 3 + 80 24 Δ ω 4 β 4 ,
Δ β 17 = 4 Δ ω 2 β 2 8 2 Δ ω 3 β 3 + 80 24 Δ ω 4 β 4 ,
Δ β 18 = 5 Δ ω 2 β 2 + 130 24 Δ ω 4 β 4 ,
Δ β 19 = 6 Δ ω 2 β 2 + 6 2 Δ ω 3 β 3 + 96 24 Δ ω 4 β 4 ,
Δ β 20 = 6 Δ ω 2 β 2 6 2 Δ ω 3 β 3 + 96 24 Δ ω 4 β 4 ,
Δ β 21 = 8 Δ ω 2 β 2 + 160 24 Δ ω 4 β 4 ,
Δ β 22 = 9 Δ ω 2 β 2 + 162 24 Δ ω 4 β 4 .

Metrics