Abstract

In this paper we theoretically derive for the first time a matrix formalism for a coupled dual-core fiber optical parametric amplifier (FOPA). One of the most advantageous properties of this degenerate pump FOPA is the spectrally flat gain obtained when certain design parameters are met. This flat gain is obtained either in phase-sensitive (PS) or phase-insensitive (PI) operation of the dual-core FOPA. Properties such as maximum and minimum PS gain, along with maximum bandwidth and difference between maximum PS and PI gain are also investigated.

© 2017 Optical Society of America

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References

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  1. Z. Tong, C. Lundström, P. A. Andrekson, M. Karlsson, and A. Bogris, “Ultralow noise, broadband Phase-Sensitive optical amplifiers, and their applications,” IEEE J. Sel. Top. Quantum Electron. 18(2), 1016–1032 (2012).
    [Crossref]
  2. J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
    [Crossref]
  3. M. E. Marhic, P. A. Andrekson, P. Petropoulos, S. Radic, C. Peucheret, and M. Jazayerifar, “Fiber optical parametric amplifiers in optical communication systems,” Laser Photon. Rev. 9(1), 50–74 (2015).
    [Crossref] [PubMed]
  4. P. H. Tatsing, A. Mohamadou, C. Bouri, C. G. L. Tiofack, and T. C. Kofane, “Modulation instability in nonlinear positive–negative index couplers with saturable nonlinearity,” J. Opt. Soc. Am. B 29(12), 3218–3225 (2012).
    [Crossref]
  5. S. Trillo, S. Wabnitz, G. I. Stegeman, and E. M. Wright, “Parametric amplification and modulational instabilities in dispersive nonlinear directional couplers with relaxing nonlinearity,” J. Opt. Soc. Am. B 6(5), 889–900 (1989).
    [Crossref]
  6. R. Ganapathy, B. A. Malomed, and K. Porsezian, “Modulational instability and generation of pulse trains in asymmetric dual-core nonlinear optical fibers,” Phys. Lett. A 354(5–6), 366–372 (2006).
    [Crossref]
  7. X. He, T. Tang, and W. Liu, “Modulation instabilities in two-core nonlinear fiber coupler,” in Sixth International Conference on Electronics and Information Engineering (International Society for Optics and Photonics, 2015) pp. 979410.
  8. K. Nithyanandan, R. Vasantha Jayakantha Raja, and K. Porsezian, “Modulational instability in a twin-core fiber with the effect of saturable nonlinear response and coupling coefficient dispersion,” Phys. Rev. A,  87(4), 043805 (2013).
    [Crossref]
  9. J. H. Li, K. S. Chiang, and K. W. Chow, “Modulation instabilities in two-core optical fibers,” J. Opt. Soc. Am. B 28(7), 1693–1701 (2011).
    [Crossref]
  10. J. H. Li, K. S. Chiang, B. A. Malomed, and K. W. Chow, “Modulation instabilities in birefringent Two-Core optical fibers,” in Communications and Photonics Conference Asia (IEEE, 2012).
    [Crossref]
  11. J. Janszky, C. Sibilia, M. Bertolotti, P. Adam, and A. Petak, “Properties of a directional coupler with parametric amplification,” Quantum Semiclass. Opt. J. Eur. Opt. Soc. B 7(4), 509 (1995).
    [Crossref]
  12. A. Mecozzi, “Parametric amplification and squeezed-light generation in a nonlinear directional coupler,” Opt. Lett. 13(10), 925–927 (1988).
    [Crossref] [PubMed]
  13. G. P. Agrawal, S. Mumtaz, and R.-J. Essiambre, “Nonlinear performance of SDM systems designed with multimode or multicore fibers,” in Optical Fiber Communication Conference (Optical Society of America, 2013) p. OM3I.6.
  14. S. Mumtaz, R. J. Essiambre, and G. P. Agrawal, “Nonlinear propagation in multimode and multicore fibers: Generalization of the Manakov Equations,” J. Lightwave Technol. 31(3), 398–406 (2013).
    [Crossref]
  15. M. Karlsson, “Transmission systems with low noise Phase-Sensitive parametric amplifiers,” J. Lightwave Technol. 34(5), 1411–1423 (2016).
    [Crossref]
  16. C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum Electron. 8(3), 538–547 (2002).
    [Crossref]
  17. C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Correction to “Parametric amplifiers driven by two pump waves”,” IEEE J. Sel. Top. Quantum Electron. 8(4), 956 (2002).
  18. G. Agrawal, “Chapter 10 - four-wave mixing,” in Nonlinear Fiber Optics, 5th ed. (Academic Press, 2013) pp. 397–456.
    [Crossref]
  19. T. Richter, B. Corcoran, S. L. Olsson, C. Lundström, M. Karlsson, C. Schubert, and P. A. Andrekson, “Experimental characterization of a Phase-Sensitive Four-Mode Fiber-Optic parametric amplifier,” in European Conference and Exhibition on Optical Communication (Optical Society of America, 2012) p. Th.1.F.1.
    [Crossref]

2016 (1)

2015 (1)

M. E. Marhic, P. A. Andrekson, P. Petropoulos, S. Radic, C. Peucheret, and M. Jazayerifar, “Fiber optical parametric amplifiers in optical communication systems,” Laser Photon. Rev. 9(1), 50–74 (2015).
[Crossref] [PubMed]

2013 (2)

K. Nithyanandan, R. Vasantha Jayakantha Raja, and K. Porsezian, “Modulational instability in a twin-core fiber with the effect of saturable nonlinear response and coupling coefficient dispersion,” Phys. Rev. A,  87(4), 043805 (2013).
[Crossref]

S. Mumtaz, R. J. Essiambre, and G. P. Agrawal, “Nonlinear propagation in multimode and multicore fibers: Generalization of the Manakov Equations,” J. Lightwave Technol. 31(3), 398–406 (2013).
[Crossref]

2012 (2)

P. H. Tatsing, A. Mohamadou, C. Bouri, C. G. L. Tiofack, and T. C. Kofane, “Modulation instability in nonlinear positive–negative index couplers with saturable nonlinearity,” J. Opt. Soc. Am. B 29(12), 3218–3225 (2012).
[Crossref]

Z. Tong, C. Lundström, P. A. Andrekson, M. Karlsson, and A. Bogris, “Ultralow noise, broadband Phase-Sensitive optical amplifiers, and their applications,” IEEE J. Sel. Top. Quantum Electron. 18(2), 1016–1032 (2012).
[Crossref]

2011 (1)

2006 (1)

R. Ganapathy, B. A. Malomed, and K. Porsezian, “Modulational instability and generation of pulse trains in asymmetric dual-core nonlinear optical fibers,” Phys. Lett. A 354(5–6), 366–372 (2006).
[Crossref]

2002 (3)

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum Electron. 8(3), 538–547 (2002).
[Crossref]

C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Correction to “Parametric amplifiers driven by two pump waves”,” IEEE J. Sel. Top. Quantum Electron. 8(4), 956 (2002).

1995 (1)

J. Janszky, C. Sibilia, M. Bertolotti, P. Adam, and A. Petak, “Properties of a directional coupler with parametric amplification,” Quantum Semiclass. Opt. J. Eur. Opt. Soc. B 7(4), 509 (1995).
[Crossref]

1989 (1)

1988 (1)

Adam, P.

J. Janszky, C. Sibilia, M. Bertolotti, P. Adam, and A. Petak, “Properties of a directional coupler with parametric amplification,” Quantum Semiclass. Opt. J. Eur. Opt. Soc. B 7(4), 509 (1995).
[Crossref]

Agrawal, G.

G. Agrawal, “Chapter 10 - four-wave mixing,” in Nonlinear Fiber Optics, 5th ed. (Academic Press, 2013) pp. 397–456.
[Crossref]

Agrawal, G. P.

S. Mumtaz, R. J. Essiambre, and G. P. Agrawal, “Nonlinear propagation in multimode and multicore fibers: Generalization of the Manakov Equations,” J. Lightwave Technol. 31(3), 398–406 (2013).
[Crossref]

G. P. Agrawal, S. Mumtaz, and R.-J. Essiambre, “Nonlinear performance of SDM systems designed with multimode or multicore fibers,” in Optical Fiber Communication Conference (Optical Society of America, 2013) p. OM3I.6.

Andrekson, P. A.

M. E. Marhic, P. A. Andrekson, P. Petropoulos, S. Radic, C. Peucheret, and M. Jazayerifar, “Fiber optical parametric amplifiers in optical communication systems,” Laser Photon. Rev. 9(1), 50–74 (2015).
[Crossref] [PubMed]

Z. Tong, C. Lundström, P. A. Andrekson, M. Karlsson, and A. Bogris, “Ultralow noise, broadband Phase-Sensitive optical amplifiers, and their applications,” IEEE J. Sel. Top. Quantum Electron. 18(2), 1016–1032 (2012).
[Crossref]

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

T. Richter, B. Corcoran, S. L. Olsson, C. Lundström, M. Karlsson, C. Schubert, and P. A. Andrekson, “Experimental characterization of a Phase-Sensitive Four-Mode Fiber-Optic parametric amplifier,” in European Conference and Exhibition on Optical Communication (Optical Society of America, 2012) p. Th.1.F.1.
[Crossref]

Bertolotti, M.

J. Janszky, C. Sibilia, M. Bertolotti, P. Adam, and A. Petak, “Properties of a directional coupler with parametric amplification,” Quantum Semiclass. Opt. J. Eur. Opt. Soc. B 7(4), 509 (1995).
[Crossref]

Bogris, A.

Z. Tong, C. Lundström, P. A. Andrekson, M. Karlsson, and A. Bogris, “Ultralow noise, broadband Phase-Sensitive optical amplifiers, and their applications,” IEEE J. Sel. Top. Quantum Electron. 18(2), 1016–1032 (2012).
[Crossref]

Bouri, C.

Chiang, K. S.

J. H. Li, K. S. Chiang, and K. W. Chow, “Modulation instabilities in two-core optical fibers,” J. Opt. Soc. Am. B 28(7), 1693–1701 (2011).
[Crossref]

J. H. Li, K. S. Chiang, B. A. Malomed, and K. W. Chow, “Modulation instabilities in birefringent Two-Core optical fibers,” in Communications and Photonics Conference Asia (IEEE, 2012).
[Crossref]

Chow, K. W.

J. H. Li, K. S. Chiang, and K. W. Chow, “Modulation instabilities in two-core optical fibers,” J. Opt. Soc. Am. B 28(7), 1693–1701 (2011).
[Crossref]

J. H. Li, K. S. Chiang, B. A. Malomed, and K. W. Chow, “Modulation instabilities in birefringent Two-Core optical fibers,” in Communications and Photonics Conference Asia (IEEE, 2012).
[Crossref]

Chraplyvy, A. R.

C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Correction to “Parametric amplifiers driven by two pump waves”,” IEEE J. Sel. Top. Quantum Electron. 8(4), 956 (2002).

C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum Electron. 8(3), 538–547 (2002).
[Crossref]

Corcoran, B.

T. Richter, B. Corcoran, S. L. Olsson, C. Lundström, M. Karlsson, C. Schubert, and P. A. Andrekson, “Experimental characterization of a Phase-Sensitive Four-Mode Fiber-Optic parametric amplifier,” in European Conference and Exhibition on Optical Communication (Optical Society of America, 2012) p. Th.1.F.1.
[Crossref]

Essiambre, R. J.

Essiambre, R.-J.

G. P. Agrawal, S. Mumtaz, and R.-J. Essiambre, “Nonlinear performance of SDM systems designed with multimode or multicore fibers,” in Optical Fiber Communication Conference (Optical Society of America, 2013) p. OM3I.6.

Ganapathy, R.

R. Ganapathy, B. A. Malomed, and K. Porsezian, “Modulational instability and generation of pulse trains in asymmetric dual-core nonlinear optical fibers,” Phys. Lett. A 354(5–6), 366–372 (2006).
[Crossref]

Hansryd, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

He, X.

X. He, T. Tang, and W. Liu, “Modulation instabilities in two-core nonlinear fiber coupler,” in Sixth International Conference on Electronics and Information Engineering (International Society for Optics and Photonics, 2015) pp. 979410.

Hedekvist, P. O.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Janszky, J.

J. Janszky, C. Sibilia, M. Bertolotti, P. Adam, and A. Petak, “Properties of a directional coupler with parametric amplification,” Quantum Semiclass. Opt. J. Eur. Opt. Soc. B 7(4), 509 (1995).
[Crossref]

Jazayerifar, M.

M. E. Marhic, P. A. Andrekson, P. Petropoulos, S. Radic, C. Peucheret, and M. Jazayerifar, “Fiber optical parametric amplifiers in optical communication systems,” Laser Photon. Rev. 9(1), 50–74 (2015).
[Crossref] [PubMed]

Karlsson, M.

M. Karlsson, “Transmission systems with low noise Phase-Sensitive parametric amplifiers,” J. Lightwave Technol. 34(5), 1411–1423 (2016).
[Crossref]

Z. Tong, C. Lundström, P. A. Andrekson, M. Karlsson, and A. Bogris, “Ultralow noise, broadband Phase-Sensitive optical amplifiers, and their applications,” IEEE J. Sel. Top. Quantum Electron. 18(2), 1016–1032 (2012).
[Crossref]

T. Richter, B. Corcoran, S. L. Olsson, C. Lundström, M. Karlsson, C. Schubert, and P. A. Andrekson, “Experimental characterization of a Phase-Sensitive Four-Mode Fiber-Optic parametric amplifier,” in European Conference and Exhibition on Optical Communication (Optical Society of America, 2012) p. Th.1.F.1.
[Crossref]

Kofane, T. C.

Li, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Li, J. H.

J. H. Li, K. S. Chiang, and K. W. Chow, “Modulation instabilities in two-core optical fibers,” J. Opt. Soc. Am. B 28(7), 1693–1701 (2011).
[Crossref]

J. H. Li, K. S. Chiang, B. A. Malomed, and K. W. Chow, “Modulation instabilities in birefringent Two-Core optical fibers,” in Communications and Photonics Conference Asia (IEEE, 2012).
[Crossref]

Liu, W.

X. He, T. Tang, and W. Liu, “Modulation instabilities in two-core nonlinear fiber coupler,” in Sixth International Conference on Electronics and Information Engineering (International Society for Optics and Photonics, 2015) pp. 979410.

Lundström, C.

Z. Tong, C. Lundström, P. A. Andrekson, M. Karlsson, and A. Bogris, “Ultralow noise, broadband Phase-Sensitive optical amplifiers, and their applications,” IEEE J. Sel. Top. Quantum Electron. 18(2), 1016–1032 (2012).
[Crossref]

T. Richter, B. Corcoran, S. L. Olsson, C. Lundström, M. Karlsson, C. Schubert, and P. A. Andrekson, “Experimental characterization of a Phase-Sensitive Four-Mode Fiber-Optic parametric amplifier,” in European Conference and Exhibition on Optical Communication (Optical Society of America, 2012) p. Th.1.F.1.
[Crossref]

Malomed, B. A.

R. Ganapathy, B. A. Malomed, and K. Porsezian, “Modulational instability and generation of pulse trains in asymmetric dual-core nonlinear optical fibers,” Phys. Lett. A 354(5–6), 366–372 (2006).
[Crossref]

J. H. Li, K. S. Chiang, B. A. Malomed, and K. W. Chow, “Modulation instabilities in birefringent Two-Core optical fibers,” in Communications and Photonics Conference Asia (IEEE, 2012).
[Crossref]

Marhic, M. E.

M. E. Marhic, P. A. Andrekson, P. Petropoulos, S. Radic, C. Peucheret, and M. Jazayerifar, “Fiber optical parametric amplifiers in optical communication systems,” Laser Photon. Rev. 9(1), 50–74 (2015).
[Crossref] [PubMed]

McKinstrie, C. J.

C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum Electron. 8(3), 538–547 (2002).
[Crossref]

C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Correction to “Parametric amplifiers driven by two pump waves”,” IEEE J. Sel. Top. Quantum Electron. 8(4), 956 (2002).

Mecozzi, A.

Mohamadou, A.

Mumtaz, S.

S. Mumtaz, R. J. Essiambre, and G. P. Agrawal, “Nonlinear propagation in multimode and multicore fibers: Generalization of the Manakov Equations,” J. Lightwave Technol. 31(3), 398–406 (2013).
[Crossref]

G. P. Agrawal, S. Mumtaz, and R.-J. Essiambre, “Nonlinear performance of SDM systems designed with multimode or multicore fibers,” in Optical Fiber Communication Conference (Optical Society of America, 2013) p. OM3I.6.

Nithyanandan, K.

K. Nithyanandan, R. Vasantha Jayakantha Raja, and K. Porsezian, “Modulational instability in a twin-core fiber with the effect of saturable nonlinear response and coupling coefficient dispersion,” Phys. Rev. A,  87(4), 043805 (2013).
[Crossref]

Olsson, S. L.

T. Richter, B. Corcoran, S. L. Olsson, C. Lundström, M. Karlsson, C. Schubert, and P. A. Andrekson, “Experimental characterization of a Phase-Sensitive Four-Mode Fiber-Optic parametric amplifier,” in European Conference and Exhibition on Optical Communication (Optical Society of America, 2012) p. Th.1.F.1.
[Crossref]

Petak, A.

J. Janszky, C. Sibilia, M. Bertolotti, P. Adam, and A. Petak, “Properties of a directional coupler with parametric amplification,” Quantum Semiclass. Opt. J. Eur. Opt. Soc. B 7(4), 509 (1995).
[Crossref]

Petropoulos, P.

M. E. Marhic, P. A. Andrekson, P. Petropoulos, S. Radic, C. Peucheret, and M. Jazayerifar, “Fiber optical parametric amplifiers in optical communication systems,” Laser Photon. Rev. 9(1), 50–74 (2015).
[Crossref] [PubMed]

Peucheret, C.

M. E. Marhic, P. A. Andrekson, P. Petropoulos, S. Radic, C. Peucheret, and M. Jazayerifar, “Fiber optical parametric amplifiers in optical communication systems,” Laser Photon. Rev. 9(1), 50–74 (2015).
[Crossref] [PubMed]

Porsezian, K.

K. Nithyanandan, R. Vasantha Jayakantha Raja, and K. Porsezian, “Modulational instability in a twin-core fiber with the effect of saturable nonlinear response and coupling coefficient dispersion,” Phys. Rev. A,  87(4), 043805 (2013).
[Crossref]

R. Ganapathy, B. A. Malomed, and K. Porsezian, “Modulational instability and generation of pulse trains in asymmetric dual-core nonlinear optical fibers,” Phys. Lett. A 354(5–6), 366–372 (2006).
[Crossref]

Radic, S.

M. E. Marhic, P. A. Andrekson, P. Petropoulos, S. Radic, C. Peucheret, and M. Jazayerifar, “Fiber optical parametric amplifiers in optical communication systems,” Laser Photon. Rev. 9(1), 50–74 (2015).
[Crossref] [PubMed]

C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Correction to “Parametric amplifiers driven by two pump waves”,” IEEE J. Sel. Top. Quantum Electron. 8(4), 956 (2002).

C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum Electron. 8(3), 538–547 (2002).
[Crossref]

Richter, T.

T. Richter, B. Corcoran, S. L. Olsson, C. Lundström, M. Karlsson, C. Schubert, and P. A. Andrekson, “Experimental characterization of a Phase-Sensitive Four-Mode Fiber-Optic parametric amplifier,” in European Conference and Exhibition on Optical Communication (Optical Society of America, 2012) p. Th.1.F.1.
[Crossref]

Schubert, C.

T. Richter, B. Corcoran, S. L. Olsson, C. Lundström, M. Karlsson, C. Schubert, and P. A. Andrekson, “Experimental characterization of a Phase-Sensitive Four-Mode Fiber-Optic parametric amplifier,” in European Conference and Exhibition on Optical Communication (Optical Society of America, 2012) p. Th.1.F.1.
[Crossref]

Sibilia, C.

J. Janszky, C. Sibilia, M. Bertolotti, P. Adam, and A. Petak, “Properties of a directional coupler with parametric amplification,” Quantum Semiclass. Opt. J. Eur. Opt. Soc. B 7(4), 509 (1995).
[Crossref]

Stegeman, G. I.

Tang, T.

X. He, T. Tang, and W. Liu, “Modulation instabilities in two-core nonlinear fiber coupler,” in Sixth International Conference on Electronics and Information Engineering (International Society for Optics and Photonics, 2015) pp. 979410.

Tatsing, P. H.

Tiofack, C. G. L.

Tong, Z.

Z. Tong, C. Lundström, P. A. Andrekson, M. Karlsson, and A. Bogris, “Ultralow noise, broadband Phase-Sensitive optical amplifiers, and their applications,” IEEE J. Sel. Top. Quantum Electron. 18(2), 1016–1032 (2012).
[Crossref]

Trillo, S.

Vasantha Jayakantha Raja, R.

K. Nithyanandan, R. Vasantha Jayakantha Raja, and K. Porsezian, “Modulational instability in a twin-core fiber with the effect of saturable nonlinear response and coupling coefficient dispersion,” Phys. Rev. A,  87(4), 043805 (2013).
[Crossref]

Wabnitz, S.

Westlund, M.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Wright, E. M.

IEEE J. Sel. Top. Quantum Electron. (4)

Z. Tong, C. Lundström, P. A. Andrekson, M. Karlsson, and A. Bogris, “Ultralow noise, broadband Phase-Sensitive optical amplifiers, and their applications,” IEEE J. Sel. Top. Quantum Electron. 18(2), 1016–1032 (2012).
[Crossref]

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum Electron. 8(3), 538–547 (2002).
[Crossref]

C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Correction to “Parametric amplifiers driven by two pump waves”,” IEEE J. Sel. Top. Quantum Electron. 8(4), 956 (2002).

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (3)

Laser Photon. Rev. (1)

M. E. Marhic, P. A. Andrekson, P. Petropoulos, S. Radic, C. Peucheret, and M. Jazayerifar, “Fiber optical parametric amplifiers in optical communication systems,” Laser Photon. Rev. 9(1), 50–74 (2015).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Lett. A (1)

R. Ganapathy, B. A. Malomed, and K. Porsezian, “Modulational instability and generation of pulse trains in asymmetric dual-core nonlinear optical fibers,” Phys. Lett. A 354(5–6), 366–372 (2006).
[Crossref]

Phys. Rev. A (1)

K. Nithyanandan, R. Vasantha Jayakantha Raja, and K. Porsezian, “Modulational instability in a twin-core fiber with the effect of saturable nonlinear response and coupling coefficient dispersion,” Phys. Rev. A,  87(4), 043805 (2013).
[Crossref]

Quantum Semiclass. Opt. J. Eur. Opt. Soc. B (1)

J. Janszky, C. Sibilia, M. Bertolotti, P. Adam, and A. Petak, “Properties of a directional coupler with parametric amplification,” Quantum Semiclass. Opt. J. Eur. Opt. Soc. B 7(4), 509 (1995).
[Crossref]

Other (5)

G. P. Agrawal, S. Mumtaz, and R.-J. Essiambre, “Nonlinear performance of SDM systems designed with multimode or multicore fibers,” in Optical Fiber Communication Conference (Optical Society of America, 2013) p. OM3I.6.

G. Agrawal, “Chapter 10 - four-wave mixing,” in Nonlinear Fiber Optics, 5th ed. (Academic Press, 2013) pp. 397–456.
[Crossref]

T. Richter, B. Corcoran, S. L. Olsson, C. Lundström, M. Karlsson, C. Schubert, and P. A. Andrekson, “Experimental characterization of a Phase-Sensitive Four-Mode Fiber-Optic parametric amplifier,” in European Conference and Exhibition on Optical Communication (Optical Society of America, 2012) p. Th.1.F.1.
[Crossref]

X. He, T. Tang, and W. Liu, “Modulation instabilities in two-core nonlinear fiber coupler,” in Sixth International Conference on Electronics and Information Engineering (International Society for Optics and Photonics, 2015) pp. 979410.

J. H. Li, K. S. Chiang, B. A. Malomed, and K. W. Chow, “Modulation instabilities in birefringent Two-Core optical fibers,” in Communications and Photonics Conference Asia (IEEE, 2012).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Schematic of the model used in numerical computations. λs-wavelength of the signal, λp-wavelength of the pump, λi-wavelength of the idler.
Fig. 2
Fig. 2 Parametric gain coefficient g as a function of Δβ.
Fig. 3
Fig. 3 Gain G1 versus a) λs and b) ϕ. fp-frequency of the pump and f0-zero dispersion frequency.
Fig. 4
Fig. 4 GER as a function of the coupling coefficient C with Δβ = 0.

Tables (1)

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Table 1 Setup Parameters

Equations (41)

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i d E 1 d z + γ | E 1 | 2 E 1 + C E 2 = 0
i d E 2 d z + γ | E 2 | 2 E 2 + C E 1 = 0
E 1 = u p 1 exp ( i ( ω p 1 t β p 1 z ) ) + u s 1 exp ( i ( ω s 1 t β s 1 z ) ) + u i 1 exp ( i ( ω i 1 t β i 1 z ) )
E 2 = u p 2 exp ( i ( ω p 2 t β p 2 z ) ) + u s 2 exp ( i ( ω s 2 t β s 2 z ) ) + u i 2 exp ( i ( ω i 2 t β i 2 z ) )
d u p 1 d z = i u p 1 ( β p 1 + γ ( 2 P 1 | u p 1 | 2 ) ) + i γ 2 u p 1 * u s 1 u i 1 + i C u p 2
d u s 1 d z = i u s 1 ( β s 1 + γ ( 2 P 1 | u s 1 | 2 ) ) + i γ u p 1 2 u i 1 * + i C u s 2
d u i 1 d z = i u i 1 ( β i 1 + γ ( 2 P 1 | u i 1 | 2 ) ) + i γ u p 1 2 u s 1 * + i C u i 2
d u p 2 d z = i u p 2 ( β p 2 + γ ( 2 P 2 | u p 2 | 2 ) ) + i γ 2 u p 2 * u s 2 u i 2 + i C u p 1
d u s 1 d z = i u s 2 ( β s 2 + γ ( 2 P 2 | u s 2 | 2 ) ) + i γ u p 2 * u i 2 * + i C u s 1
d u i 2 d z = i u i 2 ( β i 2 + γ ( 2 P 2 | u i 2 | 2 ) ) + i γ u p 2 * u s 2 * + i C u i 1
P 1 = | u p 1 | 2 + | u s 1 | 2 + | u i 1 | 2
P 2 = | u p 2 | 2 + | u s 2 | 2 + | u i 2 | 2
R = | u s | 2 | u i | 2 = | u s 1 | 2 + | u s 2 | 2 | u i 1 | 2 | u i 2 | 2
β p 1 = β p 2
β s 1 = β s 2
β i 1 = β i 2
d d z E ( z ) = i M E ( z )
M = ( K 0 P p γ 2 C 0 P p γ 2 K 0 0 C C 0 K 0 P p γ 2 0 C P p γ 2 K 0 )
K 0 = k C
E ( z ) = ( e s 1 ( z ) e i 1 * ( z ) e s 2 ( z ) e i 2 * ( z ) ) .
E ( 0 ) = ( e s 10 e i 10 * e s 20 e i 20 * )
E ( z ) = K ( z ) E ( 0 )
( A B D E B F E G D E A B E G B F ) ,
g 1 = P p 2 γ 2 4 ( K 0 + C ) 2 = P p 2 γ 2 4 k 2
g 2 = P p 2 γ 2 4 ( K 0 C ) 2 = P p 2 γ 2 4 ( k 2 C ) 2
A = cosh ( g 1 z 2 ) 2 + cosh ( g 2 z 2 ) 2 + + ( K 0 C ) sinh ( g 2 z 2 ) i g 2 + ( K 0 + C ) sinh ( g 1 z 2 ) i g 1
B = P p γ sinh ( g 1 z 2 ) i 2 g 1 + P p γ sinh ( g 2 z 2 ) i 2 g 2
D = cosh 2 ( g 1 z 4 ) cosh 2 ( g 2 z 4 ) + + ( K 0 + C ) sinh ( g 1 z 2 ) i g 1 ( K 0 C ) sinh ( g 2 z 2 ) i g 2
E = P p γ sinh ( g 1 z 2 ) i 2 g 1 P p γ sinh ( g 2 z 2 ) i 2 g 2
F = cosh ( g 1 z 2 ) 2 + cosh ( g 2 z 2 ) 2 ( K 0 + C ) sinh ( g 1 z 2 ) i g 1 ( K 0 C ) sinh ( g 2 z 2 ) i g 2
G = cosh ( g 1 z 4 ) cosh 2 ( g 2 z 4 ) ( K 0 + C ) sinh ( g 1 z 2 ) i g 1 + ( K 0 C ) sinh ( g 2 z 2 ) i g 2 .
d d z ( e s 1 ( z ) e i 1 * ( z ) e s 2 ( z ) e i 2 * ( z ) ) = ( K 0 P p γ 2 C 0 P p γ 2 K 0 0 C C 0 K 0 P p γ 2 0 C P p γ 2 K 0 ) ( e s 1 ( z ) e i 1 * ( z ) e s 2 ( z ) e i 2 * ( z ) )
d d z ( e s 1 ( z ) e s 2 ( z ) e i 1 * ( z ) e i 2 * ( z ) ) = ( K 0 C P p γ 2 0 C K 0 0 P p γ 2 P p γ 2 0 K 0 C 0 P p γ 2 C K 0 ) ( e s 1 ( z ) e s 2 ( z ) e i 1 * ( z ) e i 2 * ( z ) )
d d z ( e o ( z ) e e * ( z ) ) = ( τ δ δ τ ) ( e o ( z ) e e * ( z ) )
σ 1 = ( 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 )
G 1 , 2 = | u s 1 , 2 ( L ) | 2 P s 0
E ( 0 ) = e s 10 ( 1 0 0 0 ) .
E ( 0 ) = e s 10 ( 1 0 exp ( i ϕ ) 0 ) .
GER = max π ϕ π G 1 min π ϕ π G 1
G 1 , 2 PS , min = | A B + D E | 2 = = 1 P p γ sin ( z C 2 + P p γ C ) 2 ( C + P p γ ) .
G 1 , 2 PS , max G 1 PI , max = cosh ( P p γ z ) P p 2 γ 2 z 2 16 + cosh ( P p γ z 4 ) 4 cosh ( P p γ z ) cosh ( P p γ z 4 ) 4 8 ,

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