Abstract

We present a theoretical and experimental study of the modulation instability process in a dispersion oscillating passive fiber-ring resonator in the low dispersion region. Generally, the modulation of the dispersion along the cavity length is responsible for the emergence of a regime characterised by multiple parametric resonances (or Faraday instabilities). We show that, under weak dispersion conditions, a huge number of Faraday sidebands can grow under the influence of fourth order dispersion. We specifically designed a piecewise uniform fiber-ring cavity and report on experiments that confirm our theoretical predictions. We recorded the dynamics of this system revealing strong interactions between the different sidebands in agreement with numerical simulations.

© 2017 Optical Society of America

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Corrections

8 May 2017: Corrections were made to Eqs. (3) and (6).


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References

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  1. R. Vallée, “Temporal instabilities in the output of an all-fiber ring cavity,” Opt. Commun. 81, 419–426 (1991).
    [Crossref]
  2. M. Nakazawa, K. Suzuki, and H. A. Haus, “Modulational instability oscillation in nonlinear dispersive ring cavity,” Phys. Rev. A 38, 5193–5196 (1988).
    [Crossref]
  3. M. Haelterman, S. Trillo, and S. Wabnitz, “Dissipative modulation instability in a nonlinear dispersive ring cavity,” Opt. Commun. 91, 401–407 (1992).
    [Crossref]
  4. S. Coen and M. Haelterman, “Continuous-wave ultrahigh-repetition-rate pulse-train generation through modulational instability in a passive fiber cavity,” Opt. Lett. 26, 39–41 (2001).
    [Crossref]
  5. G.-L. Oppo, “Formation and control of Turing patterns and phase fronts in photonics and chemistry,” J. Math. Chem. 45, 95 (2008).
    [Crossref]
  6. R. Vallée, “Role of the group velocity dispersion in the onset of instabilities in a nonlinear ring cavity,” Opt. Commun. 93, 389–399 (1992).
    [Crossref]
  7. S. Coen and M. Haelterman, “Modulational Instability Induced by Cavity Boundary Conditions in a Normally Dispersive Optical Fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
    [Crossref]
  8. S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveia-Neto, “Modulation instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation,” Phys. Rev. A 43, 6162–6165 (1991).
    [Crossref] [PubMed]
  9. J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St.J. Russell, “Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber,” Opt. Lett. 28, 2225–2227 (2003).
    [Crossref] [PubMed]
  10. S. Pitois and G. Millot, “Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber,” Opt. Commun. 226, 415–422 (2003).
    [Crossref]
  11. M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, A. Mussot, A. Armaroli, and F. Biancalana, “Fourth-order dispersion mediated modulation instability in dispersion oscillating fibers,” Opt. Lett. 38, 3464–3467 (2013).
    [Crossref] [PubMed]
  12. A. Armaroli and F. Biancalana, “Suppression and splitting of modulational instability sidebands in periodically tapered optical fibers because of fourth-order dispersion,” Opt. Lett. 39, 4804–4807 (2014).
    [Crossref] [PubMed]
  13. A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, “Optical Fiber Systems Are Convectively Unstable,” Phys. Rev. Lett. 101, 113904 (2008).
    [Crossref] [PubMed]
  14. F. Leo, A. Mussot, P. Kockaert, P. Emplit, M. Haelterman, and M. Taki, “Nonlinear Symmetry Breaking Induced by Third-Order Dispersion in Optical Fiber Cavities,” Phys. Rev. Lett. 110, 104103 (2013).
    [Crossref] [PubMed]
  15. Y. Xu and S. Coen, “Experimental observation of the spontaneous breaking of the time-reversal symmetry in a synchronously pumped passive Kerr resonator,” Opt. Lett. 39, 3492 (2014).
    [Crossref] [PubMed]
  16. P. Parra-Rivas, D. Gomila, F. Leo, S. Coen, and L. Gelens, “Third-order chromatic dispersion stabilizes Kerr frequency combs,” Optics Letters 39, 2971 (2014).
    [Crossref] [PubMed]
  17. M. Tlidi, A. Mussot, E. Louvergneaux, G. Kozyreff, A. G. Vladimirov, and M. Taki, “Control and removal of modulational instabilities in low-dispersion photonic crystal fiber cavities,” Opt. Lett. 32, 662–664 (2007).
    [Crossref] [PubMed]
  18. M. Conforti, A. Mussot, A. Kudlinski, and S. Trillo, “Modulational instability in dispersion oscillating fiber ring cavities,” Opt. Lett. 39, 4200–4203 (2014).
    [Crossref] [PubMed]
  19. M. Conforti, F. Copie, A. Mussot, A. Kudlinski, and S. Trillo, “Parametric instabilities in modulated fiber ring cavities,” Opt. Lett. 41, 5027–5030 (2016).
    [Crossref] [PubMed]
  20. F. Copie, M. Conforti, A. Kudlinski, A. Mussot, and S. Trillo, “Competing Turing and Faraday Instabilities in Longitudinally Modulated Passive Resonators,” Phys. Rev. Lett. 116, 143901 (2016).
    [Crossref] [PubMed]
  21. F. Copie, M. Conforti, A. Kudlinski, S. Trillo, and A. Mussot, “Dynamics of Turing and Faraday instabilities in a longitudinally modulated fiber-ring cavity,” Opt. Lett. 42, 435 (2017).
    [Crossref] [PubMed]
  22. N. Tarasov, A. M. Perego, D. V. Churkin, K. Staliunas, and S. K. Turitsyn, “Mode-locking via dissipative Faraday instability,” Nat. Commun. 7, 12441 (2016).
    [Crossref] [PubMed]
  23. L. A. Lugiato and R. Lefever, “Spatial Dissipative Structures in Passive Optical Systems,” Phys. Rev. Lett. 58, 2209–2211 (1987).
    [Crossref] [PubMed]
  24. S. Coen, M. Haelterman, P. Emplit, L. Delage, L. M. Simohamed, and F. Reynaud, “Bistable switching induced by modulational instability in a normally dispersive all-fibre ring cavity,” J. Opt. B: Quantum Semiclass. Opt. 1, 36 (1999).
    [Crossref]
  25. D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6, 463–468 (2012).
    [Crossref]
  26. B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
    [Crossref] [PubMed]
  27. S.-W. Huang, “Multispectral Kerr frequency comb initiated by Faraday ripples,” https://arxiv.org/abs/1610.06657 (2016).

2017 (1)

2016 (3)

F. Copie, M. Conforti, A. Kudlinski, A. Mussot, and S. Trillo, “Competing Turing and Faraday Instabilities in Longitudinally Modulated Passive Resonators,” Phys. Rev. Lett. 116, 143901 (2016).
[Crossref] [PubMed]

M. Conforti, F. Copie, A. Mussot, A. Kudlinski, and S. Trillo, “Parametric instabilities in modulated fiber ring cavities,” Opt. Lett. 41, 5027–5030 (2016).
[Crossref] [PubMed]

N. Tarasov, A. M. Perego, D. V. Churkin, K. Staliunas, and S. K. Turitsyn, “Mode-locking via dissipative Faraday instability,” Nat. Commun. 7, 12441 (2016).
[Crossref] [PubMed]

2014 (4)

2013 (2)

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, A. Mussot, A. Armaroli, and F. Biancalana, “Fourth-order dispersion mediated modulation instability in dispersion oscillating fibers,” Opt. Lett. 38, 3464–3467 (2013).
[Crossref] [PubMed]

F. Leo, A. Mussot, P. Kockaert, P. Emplit, M. Haelterman, and M. Taki, “Nonlinear Symmetry Breaking Induced by Third-Order Dispersion in Optical Fiber Cavities,” Phys. Rev. Lett. 110, 104103 (2013).
[Crossref] [PubMed]

2012 (2)

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6, 463–468 (2012).
[Crossref]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

2008 (2)

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, “Optical Fiber Systems Are Convectively Unstable,” Phys. Rev. Lett. 101, 113904 (2008).
[Crossref] [PubMed]

G.-L. Oppo, “Formation and control of Turing patterns and phase fronts in photonics and chemistry,” J. Math. Chem. 45, 95 (2008).
[Crossref]

2007 (1)

2003 (2)

J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St.J. Russell, “Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber,” Opt. Lett. 28, 2225–2227 (2003).
[Crossref] [PubMed]

S. Pitois and G. Millot, “Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber,” Opt. Commun. 226, 415–422 (2003).
[Crossref]

2001 (1)

1999 (1)

S. Coen, M. Haelterman, P. Emplit, L. Delage, L. M. Simohamed, and F. Reynaud, “Bistable switching induced by modulational instability in a normally dispersive all-fibre ring cavity,” J. Opt. B: Quantum Semiclass. Opt. 1, 36 (1999).
[Crossref]

1997 (1)

S. Coen and M. Haelterman, “Modulational Instability Induced by Cavity Boundary Conditions in a Normally Dispersive Optical Fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
[Crossref]

1992 (2)

M. Haelterman, S. Trillo, and S. Wabnitz, “Dissipative modulation instability in a nonlinear dispersive ring cavity,” Opt. Commun. 91, 401–407 (1992).
[Crossref]

R. Vallée, “Role of the group velocity dispersion in the onset of instabilities in a nonlinear ring cavity,” Opt. Commun. 93, 389–399 (1992).
[Crossref]

1991 (2)

R. Vallée, “Temporal instabilities in the output of an all-fiber ring cavity,” Opt. Commun. 81, 419–426 (1991).
[Crossref]

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveia-Neto, “Modulation instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation,” Phys. Rev. A 43, 6162–6165 (1991).
[Crossref] [PubMed]

1988 (1)

M. Nakazawa, K. Suzuki, and H. A. Haus, “Modulational instability oscillation in nonlinear dispersive ring cavity,” Phys. Rev. A 38, 5193–5196 (1988).
[Crossref]

1987 (1)

L. A. Lugiato and R. Lefever, “Spatial Dissipative Structures in Passive Optical Systems,” Phys. Rev. Lett. 58, 2209–2211 (1987).
[Crossref] [PubMed]

Akhmediev, N.

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, “Optical Fiber Systems Are Convectively Unstable,” Phys. Rev. Lett. 101, 113904 (2008).
[Crossref] [PubMed]

Armaroli, A.

Biancalana, F.

Bouwmans, G.

Cavalcanti, S. B.

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveia-Neto, “Modulation instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation,” Phys. Rev. A 43, 6162–6165 (1991).
[Crossref] [PubMed]

Churkin, D. V.

N. Tarasov, A. M. Perego, D. V. Churkin, K. Staliunas, and S. K. Turitsyn, “Mode-locking via dissipative Faraday instability,” Nat. Commun. 7, 12441 (2016).
[Crossref] [PubMed]

Coen, S.

P. Parra-Rivas, D. Gomila, F. Leo, S. Coen, and L. Gelens, “Third-order chromatic dispersion stabilizes Kerr frequency combs,” Optics Letters 39, 2971 (2014).
[Crossref] [PubMed]

Y. Xu and S. Coen, “Experimental observation of the spontaneous breaking of the time-reversal symmetry in a synchronously pumped passive Kerr resonator,” Opt. Lett. 39, 3492 (2014).
[Crossref] [PubMed]

J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St.J. Russell, “Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber,” Opt. Lett. 28, 2225–2227 (2003).
[Crossref] [PubMed]

S. Coen and M. Haelterman, “Continuous-wave ultrahigh-repetition-rate pulse-train generation through modulational instability in a passive fiber cavity,” Opt. Lett. 26, 39–41 (2001).
[Crossref]

S. Coen, M. Haelterman, P. Emplit, L. Delage, L. M. Simohamed, and F. Reynaud, “Bistable switching induced by modulational instability in a normally dispersive all-fibre ring cavity,” J. Opt. B: Quantum Semiclass. Opt. 1, 36 (1999).
[Crossref]

S. Coen and M. Haelterman, “Modulational Instability Induced by Cavity Boundary Conditions in a Normally Dispersive Optical Fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
[Crossref]

Conforti, M.

Copie, F.

Cressoni, J. C.

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveia-Neto, “Modulation instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation,” Phys. Rev. A 43, 6162–6165 (1991).
[Crossref] [PubMed]

da Cruz, H. R.

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveia-Neto, “Modulation instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation,” Phys. Rev. A 43, 6162–6165 (1991).
[Crossref] [PubMed]

Delage, L.

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, “Optical Fiber Systems Are Convectively Unstable,” Phys. Rev. Lett. 101, 113904 (2008).
[Crossref] [PubMed]

S. Coen, M. Haelterman, P. Emplit, L. Delage, L. M. Simohamed, and F. Reynaud, “Bistable switching induced by modulational instability in a normally dispersive all-fibre ring cavity,” J. Opt. B: Quantum Semiclass. Opt. 1, 36 (1999).
[Crossref]

Dias, F.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

Droques, M.

Dudley, J. M.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

Emplit, P.

F. Leo, A. Mussot, P. Kockaert, P. Emplit, M. Haelterman, and M. Taki, “Nonlinear Symmetry Breaking Induced by Third-Order Dispersion in Optical Fiber Cavities,” Phys. Rev. Lett. 110, 104103 (2013).
[Crossref] [PubMed]

S. Coen, M. Haelterman, P. Emplit, L. Delage, L. M. Simohamed, and F. Reynaud, “Bistable switching induced by modulational instability in a normally dispersive all-fibre ring cavity,” J. Opt. B: Quantum Semiclass. Opt. 1, 36 (1999).
[Crossref]

Gelens, L.

P. Parra-Rivas, D. Gomila, F. Leo, S. Coen, and L. Gelens, “Third-order chromatic dispersion stabilizes Kerr frequency combs,” Optics Letters 39, 2971 (2014).
[Crossref] [PubMed]

Genty, G.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

Gomila, D.

P. Parra-Rivas, D. Gomila, F. Leo, S. Coen, and L. Gelens, “Third-order chromatic dispersion stabilizes Kerr frequency combs,” Optics Letters 39, 2971 (2014).
[Crossref] [PubMed]

Gouveia-Neto, A. S.

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveia-Neto, “Modulation instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation,” Phys. Rev. A 43, 6162–6165 (1991).
[Crossref] [PubMed]

Haelterman, M.

F. Leo, A. Mussot, P. Kockaert, P. Emplit, M. Haelterman, and M. Taki, “Nonlinear Symmetry Breaking Induced by Third-Order Dispersion in Optical Fiber Cavities,” Phys. Rev. Lett. 110, 104103 (2013).
[Crossref] [PubMed]

S. Coen and M. Haelterman, “Continuous-wave ultrahigh-repetition-rate pulse-train generation through modulational instability in a passive fiber cavity,” Opt. Lett. 26, 39–41 (2001).
[Crossref]

S. Coen, M. Haelterman, P. Emplit, L. Delage, L. M. Simohamed, and F. Reynaud, “Bistable switching induced by modulational instability in a normally dispersive all-fibre ring cavity,” J. Opt. B: Quantum Semiclass. Opt. 1, 36 (1999).
[Crossref]

S. Coen and M. Haelterman, “Modulational Instability Induced by Cavity Boundary Conditions in a Normally Dispersive Optical Fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
[Crossref]

M. Haelterman, S. Trillo, and S. Wabnitz, “Dissipative modulation instability in a nonlinear dispersive ring cavity,” Opt. Commun. 91, 401–407 (1992).
[Crossref]

Harvey, J. D.

Haus, H. A.

M. Nakazawa, K. Suzuki, and H. A. Haus, “Modulational instability oscillation in nonlinear dispersive ring cavity,” Phys. Rev. A 38, 5193–5196 (1988).
[Crossref]

Herink, G.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6, 463–468 (2012).
[Crossref]

Jalali, B.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6, 463–468 (2012).
[Crossref]

Knight, J. C.

Kockaert, P.

F. Leo, A. Mussot, P. Kockaert, P. Emplit, M. Haelterman, and M. Taki, “Nonlinear Symmetry Breaking Induced by Third-Order Dispersion in Optical Fiber Cavities,” Phys. Rev. Lett. 110, 104103 (2013).
[Crossref] [PubMed]

Kozyreff, G.

Kudlinski, A.

Lacourt, P. A.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

Larger, L.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

Lefever, R.

L. A. Lugiato and R. Lefever, “Spatial Dissipative Structures in Passive Optical Systems,” Phys. Rev. Lett. 58, 2209–2211 (1987).
[Crossref] [PubMed]

Leo, F.

P. Parra-Rivas, D. Gomila, F. Leo, S. Coen, and L. Gelens, “Third-order chromatic dispersion stabilizes Kerr frequency combs,” Optics Letters 39, 2971 (2014).
[Crossref] [PubMed]

F. Leo, A. Mussot, P. Kockaert, P. Emplit, M. Haelterman, and M. Taki, “Nonlinear Symmetry Breaking Induced by Third-Order Dispersion in Optical Fiber Cavities,” Phys. Rev. Lett. 110, 104103 (2013).
[Crossref] [PubMed]

Leonhardt, R.

Louvergneaux, E.

Lugiato, L. A.

L. A. Lugiato and R. Lefever, “Spatial Dissipative Structures in Passive Optical Systems,” Phys. Rev. Lett. 58, 2209–2211 (1987).
[Crossref] [PubMed]

Martinelli, G.

Merolla, J. M.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

Millot, G.

S. Pitois and G. Millot, “Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber,” Opt. Commun. 226, 415–422 (2003).
[Crossref]

Mussot, A.

F. Copie, M. Conforti, A. Kudlinski, S. Trillo, and A. Mussot, “Dynamics of Turing and Faraday instabilities in a longitudinally modulated fiber-ring cavity,” Opt. Lett. 42, 435 (2017).
[Crossref] [PubMed]

M. Conforti, F. Copie, A. Mussot, A. Kudlinski, and S. Trillo, “Parametric instabilities in modulated fiber ring cavities,” Opt. Lett. 41, 5027–5030 (2016).
[Crossref] [PubMed]

F. Copie, M. Conforti, A. Kudlinski, A. Mussot, and S. Trillo, “Competing Turing and Faraday Instabilities in Longitudinally Modulated Passive Resonators,” Phys. Rev. Lett. 116, 143901 (2016).
[Crossref] [PubMed]

M. Conforti, A. Mussot, A. Kudlinski, and S. Trillo, “Modulational instability in dispersion oscillating fiber ring cavities,” Opt. Lett. 39, 4200–4203 (2014).
[Crossref] [PubMed]

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, A. Mussot, A. Armaroli, and F. Biancalana, “Fourth-order dispersion mediated modulation instability in dispersion oscillating fibers,” Opt. Lett. 38, 3464–3467 (2013).
[Crossref] [PubMed]

F. Leo, A. Mussot, P. Kockaert, P. Emplit, M. Haelterman, and M. Taki, “Nonlinear Symmetry Breaking Induced by Third-Order Dispersion in Optical Fiber Cavities,” Phys. Rev. Lett. 110, 104103 (2013).
[Crossref] [PubMed]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, “Optical Fiber Systems Are Convectively Unstable,” Phys. Rev. Lett. 101, 113904 (2008).
[Crossref] [PubMed]

M. Tlidi, A. Mussot, E. Louvergneaux, G. Kozyreff, A. G. Vladimirov, and M. Taki, “Control and removal of modulational instabilities in low-dispersion photonic crystal fiber cavities,” Opt. Lett. 32, 662–664 (2007).
[Crossref] [PubMed]

Nakazawa, M.

M. Nakazawa, K. Suzuki, and H. A. Haus, “Modulational instability oscillation in nonlinear dispersive ring cavity,” Phys. Rev. A 38, 5193–5196 (1988).
[Crossref]

Oppo, G.-L.

G.-L. Oppo, “Formation and control of Turing patterns and phase fronts in photonics and chemistry,” J. Math. Chem. 45, 95 (2008).
[Crossref]

Parra-Rivas, P.

P. Parra-Rivas, D. Gomila, F. Leo, S. Coen, and L. Gelens, “Third-order chromatic dispersion stabilizes Kerr frequency combs,” Optics Letters 39, 2971 (2014).
[Crossref] [PubMed]

Perego, A. M.

N. Tarasov, A. M. Perego, D. V. Churkin, K. Staliunas, and S. K. Turitsyn, “Mode-locking via dissipative Faraday instability,” Nat. Commun. 7, 12441 (2016).
[Crossref] [PubMed]

Pitois, S.

S. Pitois and G. Millot, “Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber,” Opt. Commun. 226, 415–422 (2003).
[Crossref]

Reynaud, F.

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, “Optical Fiber Systems Are Convectively Unstable,” Phys. Rev. Lett. 101, 113904 (2008).
[Crossref] [PubMed]

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D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6, 463–468 (2012).
[Crossref]

Russell, P. St.J.

Simohamed, L. M.

S. Coen, M. Haelterman, P. Emplit, L. Delage, L. M. Simohamed, and F. Reynaud, “Bistable switching induced by modulational instability in a normally dispersive all-fibre ring cavity,” J. Opt. B: Quantum Semiclass. Opt. 1, 36 (1999).
[Crossref]

Solli, D. R.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6, 463–468 (2012).
[Crossref]

Staliunas, K.

N. Tarasov, A. M. Perego, D. V. Churkin, K. Staliunas, and S. K. Turitsyn, “Mode-locking via dissipative Faraday instability,” Nat. Commun. 7, 12441 (2016).
[Crossref] [PubMed]

Stefani, A.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
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M. Nakazawa, K. Suzuki, and H. A. Haus, “Modulational instability oscillation in nonlinear dispersive ring cavity,” Phys. Rev. A 38, 5193–5196 (1988).
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B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
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Taki, M.

F. Leo, A. Mussot, P. Kockaert, P. Emplit, M. Haelterman, and M. Taki, “Nonlinear Symmetry Breaking Induced by Third-Order Dispersion in Optical Fiber Cavities,” Phys. Rev. Lett. 110, 104103 (2013).
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A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, “Optical Fiber Systems Are Convectively Unstable,” Phys. Rev. Lett. 101, 113904 (2008).
[Crossref] [PubMed]

M. Tlidi, A. Mussot, E. Louvergneaux, G. Kozyreff, A. G. Vladimirov, and M. Taki, “Control and removal of modulational instabilities in low-dispersion photonic crystal fiber cavities,” Opt. Lett. 32, 662–664 (2007).
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N. Tarasov, A. M. Perego, D. V. Churkin, K. Staliunas, and S. K. Turitsyn, “Mode-locking via dissipative Faraday instability,” Nat. Commun. 7, 12441 (2016).
[Crossref] [PubMed]

Tlidi, M.

Trillo, S.

Turitsyn, S. K.

N. Tarasov, A. M. Perego, D. V. Churkin, K. Staliunas, and S. K. Turitsyn, “Mode-locking via dissipative Faraday instability,” Nat. Commun. 7, 12441 (2016).
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Wetzel, B.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
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S. Coen, M. Haelterman, P. Emplit, L. Delage, L. M. Simohamed, and F. Reynaud, “Bistable switching induced by modulational instability in a normally dispersive all-fibre ring cavity,” J. Opt. B: Quantum Semiclass. Opt. 1, 36 (1999).
[Crossref]

Nat. Commun. (1)

N. Tarasov, A. M. Perego, D. V. Churkin, K. Staliunas, and S. K. Turitsyn, “Mode-locking via dissipative Faraday instability,” Nat. Commun. 7, 12441 (2016).
[Crossref] [PubMed]

Nat. Photonics (1)

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6, 463–468 (2012).
[Crossref]

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[Crossref]

R. Vallée, “Temporal instabilities in the output of an all-fiber ring cavity,” Opt. Commun. 81, 419–426 (1991).
[Crossref]

M. Haelterman, S. Trillo, and S. Wabnitz, “Dissipative modulation instability in a nonlinear dispersive ring cavity,” Opt. Commun. 91, 401–407 (1992).
[Crossref]

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M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, A. Mussot, A. Armaroli, and F. Biancalana, “Fourth-order dispersion mediated modulation instability in dispersion oscillating fibers,” Opt. Lett. 38, 3464–3467 (2013).
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M. Conforti, A. Mussot, A. Kudlinski, and S. Trillo, “Modulational instability in dispersion oscillating fiber ring cavities,” Opt. Lett. 39, 4200–4203 (2014).
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S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveia-Neto, “Modulation instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation,” Phys. Rev. A 43, 6162–6165 (1991).
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[Crossref]

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S. Coen and M. Haelterman, “Modulational Instability Induced by Cavity Boundary Conditions in a Normally Dispersive Optical Fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
[Crossref]

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, “Optical Fiber Systems Are Convectively Unstable,” Phys. Rev. Lett. 101, 113904 (2008).
[Crossref] [PubMed]

F. Leo, A. Mussot, P. Kockaert, P. Emplit, M. Haelterman, and M. Taki, “Nonlinear Symmetry Breaking Induced by Third-Order Dispersion in Optical Fiber Cavities,” Phys. Rev. Lett. 110, 104103 (2013).
[Crossref] [PubMed]

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Sci. Rep. (1)

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

Other (1)

S.-W. Huang, “Multispectral Kerr frequency comb initiated by Faraday ripples,” https://arxiv.org/abs/1610.06657 (2016).

Supplementary Material (1)

NameDescription
» Visualization 1: MP4 (2831 KB)      Evolution of the spectrum for the first 400 round-trips of 40 consecutive runs of the experiment

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Figures (9)

Fig. 1
Fig. 1 Schematic representation of a dispersion modulated passive fiber-ring cavity. A monochromatic pump (at pulsation ω0) drives a loop composed of two fibers with different dispersion (represented in blue and red). The output field is composed of a superposition of the input and intracavity field in proportions governed by the reflection and transmission coefficients of the coupler (ρ and θ respectively, ρ2 + θ2 = 1).
Fig. 2
Fig. 2 MI in the Faraday regime with only GVD: (a) Evolution of the GVD as a function of the pump wavelength λP for the two fibers composing the ring. (b) Bistable response of the cavity, the operating point is marked by a red bullet. (c) 2D plot of the parametric gain spectrum as a function of the pump wavelength. The theoretical position of the first sidebands calculated from Eq. (7) in gray and Eq. (8) in green are superimposed. (d) Closeup view of (c) in the vicinity of λ 0 a (rotated by 90 degrees anticlockwise). (e–g) Parametric gain spectra for three pump wavelengths indicated by colored arrows in (d). β4 = 0 s4/m, L = 43 m.
Fig. 3
Fig. 3 MI in the Faraday regime when accounting for FOD: (a,b) as Fig. 2; (c) The theoretical position of the sidebands for m = 1 calculated from Eq. (5) is superimposed in gray. The position of the FOD branches calculated from Eq. (9) is highlighted by dashed black lines in (d). β4 = −10 · 10−55 s4/m, L = 43 m.
Fig. 4
Fig. 4 (a) GVD as a function of the wavelength for the two fibers which constitute the ring cavity. The shaded region corresponds to the accessible range of pump wavelengths. Longitudinal profiles of (b) β2 and (c) β4 for three consecutive round-trips. The average values of β2 and β4 are represented in dashed red lines.
Fig. 5
Fig. 5 (a) Experimental setup. (b) Schematic representation of the short bursts pumping method used in this work. The input pump pulses are in light red and a sketch of the corresponding signal power is represented by a dashed red line. The evolution of the signal power when the driving field is not turned off after the first burst is reported as a black curve for comparison. Inset of (b) displays a zoom over three consecutive round-trips.
Fig. 6
Fig. 6 (a) Experimental evolution of the output spectra of the cavity as a function of the pump wavelength. The analytical estimation (Eq. (9)) of the position of the HOD branch is in dashed black lines. Eight spectra along this figure (indicated by black triangles) are reported in (b) for clarity. The positions and orders of the high-frequency cut-off sidebands are highlighted by arrows for the first and last spectra.
Fig. 7
Fig. 7 (a) Experimental spectrum at the output of the cavity showing 87 pairs of sidebands symmetrically located around the pump. (b) Analytical gain spectrum obtained from Floquet analysis. (c) Positions of the sidebands as a function of the integer m for both experiments and analytics (Eq. 5). Here λP = 1550.3 nm.
Fig. 8
Fig. 8 (b) 2D color logarithmic plot of the real time evolution of the spectrum for the first 1500 round-trips of a burst. The beginning of the burst corresponds to the round-trip 0. (a, c) Snapshots of (b) for round-trips 400 and 1500 respectively. (d–f) Corresponding numerical simulations.
Fig. 9
Fig. 9 Power spectrum after 400 round-trips of 3 consecutive shots: (a) experiments; (b) simulations. Only the random noise conditions differ from one shot to the other.

Equations (9)

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i E ( z , t ) z + q = 2 N i q β q ( z ) q ! q E ( z , t ) t q + γ | E ( z , t ) | 2 E ( z , t ) = ( δ L i α L ) E ( z , t ) + i θ E i n ,
z [ u ˜ v ˜ ] = [ ( α + i ζ ) g ( z ) h ( z ) ( α + i ζ ) ] [ u ˜ v ˜ ] ,
{ ζ = q = 2 i β 2 q 1 ( z ) ( 2 q 1 ) ! ω 2 q 1 , g ( z ) = q = 1 i β 2 q ( z ) ( 2 q ) ! ω 2 q + γ P u δ L , h ( z ) = q = 1 i β 2 q ( z ) ( 2 q ) ! ω 2 q + 3 γ P u δ L
( β 2 a v ω 2 2 + β 4 a v ω 4 2 + 2 γ P u δ ) 2 γ 2 P u 2 = ( m π L ) 2 ,
ω m = ± 6 β 2 a v β 4 a v ± 2 9 ( β 2 a v β 4 a v ) 2 + 6 β 4 a v { ± ( m π L ) 2 + γ 2 P u 2 + ( δ L 2 γ P u ) } .
{ G ( ω ) = ln ( max | σ ± | ) / L , σ ± = D 2 ± D 2 4 e 2 ζ L D = e ζ L [ 2 cos ( k a L a ) cos ( k b L b ) g a h b , + g b h a k a k b sin ( k a L a ) sin ( k b L b ) ] , k a , b = g a , b h a , b ,
ω m = { 2 β 2 a v ( δ L 2 γ P u ) } ± [ 2 β 2 a v ( m π L ) 2 + ( γ P u ) 2 ] ,
ω = 2 β 2 a v ( δ L 2 γ P u ) ,
ω F O D = ± 6 β 2 a β 4 a ± 2 9 ( β 2 a β 4 a ) 2 + 6 β 4 a ( δ L 2 γ P u ) .

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