Abstract

Implications of spontaneous and stimulated Raman scattering (SSRS) and phase noise on the spatial evolution of multiple-order sidebands arising from four-wave mixing (FWM) along the length of an optical fiber are investigated. A modified split-step Fourier method is used to solve the governing coupled nonlinear Schrödinger equations. The phase noise overcomes the depletive nature of SSRS and stabilizes the FWM sidebands, in good agreement with experimental results.

© 2014 Optical Society of America

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  1. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).
  2. P. P. Mitra and J. B. Stark, Nature 411, 1027 (2001).
    [CrossRef]
  3. J. R. Thompson and R. Roy, Phys. Rev. A 43, 4987 (1991).
    [CrossRef]
  4. J. R. Thompson and R. Roy, Opt. Lett. 16, 557 (1991).
    [CrossRef]
  5. J. R. Thompson and R. Roy, Phys. Rev. A 44, 7605 (1991).
    [CrossRef]
  6. S. Trillo, S. Wabnitz, and T. A. B. Kennedy, Phys. Rev. A 50, 1732 (1994).
    [CrossRef]
  7. J. Fatome, C. Finot, A. Armaroli, and S. Trillo, Opt. Lett. 38, 181 (2013).
    [CrossRef]
  8. D. L. Hart, A. F. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
    [CrossRef]
  9. D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
    [CrossRef]
  10. B. Khubchandani, P. N. Guzdar, and R. Roy, Phys. Rev. E 66, 066609 (2002).
    [CrossRef]
  11. C. Headley and G. P. Agrawal, IEEE J. Quantum Electron. QE-31, 2058 (1995).
    [CrossRef]
  12. C. Headley and G. P. Agrawal, J. Opt. Soc. Am. B 13, 2170 (1996).
    [CrossRef]
  13. J. Chang, D. Baiocchi, J. Vas, and J. R. Thompson, Opt. Commun. 139, 227 (1997).
    [CrossRef]
  14. E. Landahl, D. Baiocchi, and J. R. Thompson, Opt. Commun. 150, 339 (1998).
    [CrossRef]
  15. L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, Opt. Commun. 193, 289 (2001).
    [CrossRef]
  16. L. Garcia, J. Jenkins, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, J. Opt. Soc. Am. B 19, 2727 (2002).
    [CrossRef]
  17. E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, IEEE J. Quantum Electron. 26, 1815 (1990).
    [CrossRef]
  18. F. Vanholsbeeck, P. Emplit, and S. Coen, Opt. Lett. 28, 1960 (2003).
    [CrossRef]
  19. J. E. Sharping, M. Fiorentino, and P. Kumar, Opt. Lett. 26, 367 (2001).
    [CrossRef]
  20. H. Takesue and K. Inoue, Phys. Rev. A 70, 031802(R) (2004).
    [CrossRef]
  21. Q. Lin, F. Yaman, and G. P. Agrawal, Opt. Lett. 31, 1286 (2006).
    [CrossRef]
  22. Q. Lin, F. Yaman, and G. P. Agrawal, Phys. Rev. A 75, 023803 (2007).
    [CrossRef]
  23. N. A. Silva, N. J. Muga, and A. N. Pinto, J. Lightwave Technol. 27, 4979 (2009).
    [CrossRef]
  24. N. A. Silva, N. J. Muga, and A. N. Pinto, Opt. Commun. 284, 3408 (2011).
    [CrossRef]
  25. X. Liu, X. Zhou, and C. Lu, Phys. Rev. A 72, 013811 (2005).
    [CrossRef]
  26. X. Liu, X. Zhou, and C. Lu, Opt. Lett. 30, 2257 (2005).
    [CrossRef]
  27. X.-M. Liu, Phys. Rev. A 77, 043818 (2008).
    [CrossRef]

2013 (1)

2011 (1)

N. A. Silva, N. J. Muga, and A. N. Pinto, Opt. Commun. 284, 3408 (2011).
[CrossRef]

2009 (1)

2008 (1)

X.-M. Liu, Phys. Rev. A 77, 043818 (2008).
[CrossRef]

2007 (1)

Q. Lin, F. Yaman, and G. P. Agrawal, Phys. Rev. A 75, 023803 (2007).
[CrossRef]

2006 (1)

2005 (2)

X. Liu, X. Zhou, and C. Lu, Opt. Lett. 30, 2257 (2005).
[CrossRef]

X. Liu, X. Zhou, and C. Lu, Phys. Rev. A 72, 013811 (2005).
[CrossRef]

2004 (1)

H. Takesue and K. Inoue, Phys. Rev. A 70, 031802(R) (2004).
[CrossRef]

2003 (1)

2002 (2)

2001 (3)

P. P. Mitra and J. B. Stark, Nature 411, 1027 (2001).
[CrossRef]

L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, Opt. Commun. 193, 289 (2001).
[CrossRef]

J. E. Sharping, M. Fiorentino, and P. Kumar, Opt. Lett. 26, 367 (2001).
[CrossRef]

1998 (2)

E. Landahl, D. Baiocchi, and J. R. Thompson, Opt. Commun. 150, 339 (1998).
[CrossRef]

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

1997 (1)

J. Chang, D. Baiocchi, J. Vas, and J. R. Thompson, Opt. Commun. 139, 227 (1997).
[CrossRef]

1996 (1)

1995 (1)

C. Headley and G. P. Agrawal, IEEE J. Quantum Electron. QE-31, 2058 (1995).
[CrossRef]

1994 (2)

S. Trillo, S. Wabnitz, and T. A. B. Kennedy, Phys. Rev. A 50, 1732 (1994).
[CrossRef]

D. L. Hart, A. F. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef]

1991 (3)

J. R. Thompson and R. Roy, Phys. Rev. A 43, 4987 (1991).
[CrossRef]

J. R. Thompson and R. Roy, Phys. Rev. A 44, 7605 (1991).
[CrossRef]

J. R. Thompson and R. Roy, Opt. Lett. 16, 557 (1991).
[CrossRef]

1990 (1)

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, IEEE J. Quantum Electron. 26, 1815 (1990).
[CrossRef]

Agrawal, G. P.

Q. Lin, F. Yaman, and G. P. Agrawal, Phys. Rev. A 75, 023803 (2007).
[CrossRef]

Q. Lin, F. Yaman, and G. P. Agrawal, Opt. Lett. 31, 1286 (2006).
[CrossRef]

C. Headley and G. P. Agrawal, J. Opt. Soc. Am. B 13, 2170 (1996).
[CrossRef]

C. Headley and G. P. Agrawal, IEEE J. Quantum Electron. QE-31, 2058 (1995).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

Armaroli, A.

Baiocchi, D.

E. Landahl, D. Baiocchi, and J. R. Thompson, Opt. Commun. 150, 339 (1998).
[CrossRef]

J. Chang, D. Baiocchi, J. Vas, and J. R. Thompson, Opt. Commun. 139, 227 (1997).
[CrossRef]

Beletic, J. W.

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

Chang, J.

J. Chang, D. Baiocchi, J. Vas, and J. R. Thompson, Opt. Commun. 139, 227 (1997).
[CrossRef]

Coen, S.

Dianov, E. M.

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, IEEE J. Quantum Electron. 26, 1815 (1990).
[CrossRef]

Emplit, P.

Fatome, J.

Finot, C.

Fiorentino, M.

Garcia, L.

L. Garcia, J. Jenkins, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, J. Opt. Soc. Am. B 19, 2727 (2002).
[CrossRef]

L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, Opt. Commun. 193, 289 (2001).
[CrossRef]

Goedde, C. G.

L. Garcia, J. Jenkins, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, J. Opt. Soc. Am. B 19, 2727 (2002).
[CrossRef]

L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, Opt. Commun. 193, 289 (2001).
[CrossRef]

Golovchenko, E.

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, IEEE J. Quantum Electron. 26, 1815 (1990).
[CrossRef]

Guzdar, P. N.

B. Khubchandani, P. N. Guzdar, and R. Roy, Phys. Rev. E 66, 066609 (2002).
[CrossRef]

Hart, D. L.

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

D. L. Hart, A. F. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef]

Headley, C.

C. Headley and G. P. Agrawal, J. Opt. Soc. Am. B 13, 2170 (1996).
[CrossRef]

C. Headley and G. P. Agrawal, IEEE J. Quantum Electron. QE-31, 2058 (1995).
[CrossRef]

Inoue, K.

H. Takesue and K. Inoue, Phys. Rev. A 70, 031802(R) (2004).
[CrossRef]

Jalili, A.

L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, Opt. Commun. 193, 289 (2001).
[CrossRef]

Jenkins, J.

Judy, A. F.

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

D. L. Hart, A. F. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef]

Kennedy, T. A. B.

D. L. Hart, A. F. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef]

S. Trillo, S. Wabnitz, and T. A. B. Kennedy, Phys. Rev. A 50, 1732 (1994).
[CrossRef]

Khubchandani, B.

B. Khubchandani, P. N. Guzdar, and R. Roy, Phys. Rev. E 66, 066609 (2002).
[CrossRef]

Kumar, P.

Landahl, E.

E. Landahl, D. Baiocchi, and J. R. Thompson, Opt. Commun. 150, 339 (1998).
[CrossRef]

Lee, Y.

L. Garcia, J. Jenkins, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, J. Opt. Soc. Am. B 19, 2727 (2002).
[CrossRef]

L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, Opt. Commun. 193, 289 (2001).
[CrossRef]

Lin, Q.

Q. Lin, F. Yaman, and G. P. Agrawal, Phys. Rev. A 75, 023803 (2007).
[CrossRef]

Q. Lin, F. Yaman, and G. P. Agrawal, Opt. Lett. 31, 1286 (2006).
[CrossRef]

Liu, X.

X. Liu, X. Zhou, and C. Lu, Phys. Rev. A 72, 013811 (2005).
[CrossRef]

X. Liu, X. Zhou, and C. Lu, Opt. Lett. 30, 2257 (2005).
[CrossRef]

Liu, X.-M.

X.-M. Liu, Phys. Rev. A 77, 043818 (2008).
[CrossRef]

Lu, C.

X. Liu, X. Zhou, and C. Lu, Phys. Rev. A 72, 013811 (2005).
[CrossRef]

X. Liu, X. Zhou, and C. Lu, Opt. Lett. 30, 2257 (2005).
[CrossRef]

Mamyshev, P. V.

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, IEEE J. Quantum Electron. 26, 1815 (1990).
[CrossRef]

Mitra, P. P.

P. P. Mitra and J. B. Stark, Nature 411, 1027 (2001).
[CrossRef]

Muga, N. J.

N. A. Silva, N. J. Muga, and A. N. Pinto, Opt. Commun. 284, 3408 (2011).
[CrossRef]

N. A. Silva, N. J. Muga, and A. N. Pinto, J. Lightwave Technol. 27, 4979 (2009).
[CrossRef]

Pilipetskii, A. N.

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, IEEE J. Quantum Electron. 26, 1815 (1990).
[CrossRef]

Pinto, A. N.

N. A. Silva, N. J. Muga, and A. N. Pinto, Opt. Commun. 284, 3408 (2011).
[CrossRef]

N. A. Silva, N. J. Muga, and A. N. Pinto, J. Lightwave Technol. 27, 4979 (2009).
[CrossRef]

Poole, N.

L. Garcia, J. Jenkins, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, J. Opt. Soc. Am. B 19, 2727 (2002).
[CrossRef]

L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, Opt. Commun. 193, 289 (2001).
[CrossRef]

Roy, R.

B. Khubchandani, P. N. Guzdar, and R. Roy, Phys. Rev. E 66, 066609 (2002).
[CrossRef]

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

D. L. Hart, A. F. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef]

J. R. Thompson and R. Roy, Phys. Rev. A 44, 7605 (1991).
[CrossRef]

J. R. Thompson and R. Roy, Opt. Lett. 16, 557 (1991).
[CrossRef]

J. R. Thompson and R. Roy, Phys. Rev. A 43, 4987 (1991).
[CrossRef]

Salit, K.

L. Garcia, J. Jenkins, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, J. Opt. Soc. Am. B 19, 2727 (2002).
[CrossRef]

L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, Opt. Commun. 193, 289 (2001).
[CrossRef]

Sharping, J. E.

Sidereas, P.

L. Garcia, J. Jenkins, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, J. Opt. Soc. Am. B 19, 2727 (2002).
[CrossRef]

L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, Opt. Commun. 193, 289 (2001).
[CrossRef]

Silva, N. A.

N. A. Silva, N. J. Muga, and A. N. Pinto, Opt. Commun. 284, 3408 (2011).
[CrossRef]

N. A. Silva, N. J. Muga, and A. N. Pinto, J. Lightwave Technol. 27, 4979 (2009).
[CrossRef]

Stark, J. B.

P. P. Mitra and J. B. Stark, Nature 411, 1027 (2001).
[CrossRef]

Stoev, K.

D. L. Hart, A. F. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef]

Takesue, H.

H. Takesue and K. Inoue, Phys. Rev. A 70, 031802(R) (2004).
[CrossRef]

Thompson, J. R.

L. Garcia, J. Jenkins, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, J. Opt. Soc. Am. B 19, 2727 (2002).
[CrossRef]

L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, Opt. Commun. 193, 289 (2001).
[CrossRef]

E. Landahl, D. Baiocchi, and J. R. Thompson, Opt. Commun. 150, 339 (1998).
[CrossRef]

J. Chang, D. Baiocchi, J. Vas, and J. R. Thompson, Opt. Commun. 139, 227 (1997).
[CrossRef]

J. R. Thompson and R. Roy, Phys. Rev. A 44, 7605 (1991).
[CrossRef]

J. R. Thompson and R. Roy, Phys. Rev. A 43, 4987 (1991).
[CrossRef]

J. R. Thompson and R. Roy, Opt. Lett. 16, 557 (1991).
[CrossRef]

Trillo, S.

J. Fatome, C. Finot, A. Armaroli, and S. Trillo, Opt. Lett. 38, 181 (2013).
[CrossRef]

S. Trillo, S. Wabnitz, and T. A. B. Kennedy, Phys. Rev. A 50, 1732 (1994).
[CrossRef]

Vanholsbeeck, F.

Vas, J.

J. Chang, D. Baiocchi, J. Vas, and J. R. Thompson, Opt. Commun. 139, 227 (1997).
[CrossRef]

Wabnitz, S.

S. Trillo, S. Wabnitz, and T. A. B. Kennedy, Phys. Rev. A 50, 1732 (1994).
[CrossRef]

Yaman, F.

Q. Lin, F. Yaman, and G. P. Agrawal, Phys. Rev. A 75, 023803 (2007).
[CrossRef]

Q. Lin, F. Yaman, and G. P. Agrawal, Opt. Lett. 31, 1286 (2006).
[CrossRef]

Zhou, X.

X. Liu, X. Zhou, and C. Lu, Phys. Rev. A 72, 013811 (2005).
[CrossRef]

X. Liu, X. Zhou, and C. Lu, Opt. Lett. 30, 2257 (2005).
[CrossRef]

IEEE J. Quantum Electron. (2)

C. Headley and G. P. Agrawal, IEEE J. Quantum Electron. QE-31, 2058 (1995).
[CrossRef]

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, IEEE J. Quantum Electron. 26, 1815 (1990).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (2)

Nature (1)

P. P. Mitra and J. B. Stark, Nature 411, 1027 (2001).
[CrossRef]

Opt. Commun. (4)

J. Chang, D. Baiocchi, J. Vas, and J. R. Thompson, Opt. Commun. 139, 227 (1997).
[CrossRef]

E. Landahl, D. Baiocchi, and J. R. Thompson, Opt. Commun. 150, 339 (1998).
[CrossRef]

L. Garcia, A. Jalili, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, Opt. Commun. 193, 289 (2001).
[CrossRef]

N. A. Silva, N. J. Muga, and A. N. Pinto, Opt. Commun. 284, 3408 (2011).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. A (8)

D. L. Hart, A. F. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef]

J. R. Thompson and R. Roy, Phys. Rev. A 44, 7605 (1991).
[CrossRef]

S. Trillo, S. Wabnitz, and T. A. B. Kennedy, Phys. Rev. A 50, 1732 (1994).
[CrossRef]

J. R. Thompson and R. Roy, Phys. Rev. A 43, 4987 (1991).
[CrossRef]

H. Takesue and K. Inoue, Phys. Rev. A 70, 031802(R) (2004).
[CrossRef]

Q. Lin, F. Yaman, and G. P. Agrawal, Phys. Rev. A 75, 023803 (2007).
[CrossRef]

X.-M. Liu, Phys. Rev. A 77, 043818 (2008).
[CrossRef]

X. Liu, X. Zhou, and C. Lu, Phys. Rev. A 72, 013811 (2005).
[CrossRef]

Phys. Rev. E (2)

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

B. Khubchandani, P. N. Guzdar, and R. Roy, Phys. Rev. E 66, 066609 (2002).
[CrossRef]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

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Figures (3)

Fig. 1.
Fig. 1.

Normalized pulse profile. (a) Input time trace showing beating due to 366 GHz pump detuning, 2 ns modulation due to 0.5 GHz mode structure, and 5 ns envelope. (b) Input spectrum showing 0.5 GHz mode structure in blueshifted pump. (c) Single-shot output spectrum at z=100m for P0=5.5W and Ω=366GHz, showing up to fourth-order FWM sideband visibility.

Fig. 2.
Fig. 2.

Evolution along fiber length of normalized power in first-order sidebands (ρ3 and ρ4) for peak pump power P0=5.5W. Solid curve, SSRS and phase noise included; dotted curve, SSRS included but without phase noise; dots and error bars, experimental data [8]. Phase noise stabilizes otherwise depletive effects of SSRS.

Fig. 3.
Fig. 3.

Evolution along fiber length of normalized power in second-order sidebands (ρ5 and ρ6) for peak pump power P0=5.5W. Solid curve, SSRS and phase noise included; dotted curve, SSRS included but without phase noise; dots and error bars, experimental data [8]. Phase noise stabilizes otherwise depletive effects of SSRS.

Equations (2)

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

Upz+iβp(2)22UpT2+iΓ(z,T)Up+αUp2=iγp(|Up|2+2|Us|2)Upgp2|Us|2Up+iUsHp(ω+ΩR)fN(z,ω)eiωTdωUsz+dUsT+iβs(2)22UsT2+iΓ(z,T)Us+αUs2=iγs(|Us|2+2|Up|2)Us+gs2|Up|2Us+iUpHp(ωΩR)fN*(z,ω)eiωTdω,
U(0,τ)=exp(τ22τp2){1+δρ12[exp(i(Ω+Δν)τ2)+exp(i(ΩΔν)τ2)]+1+δρ2exp(iΩτ2)},

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