C. Söller, B. Brecht, P. J. Mosley, L. Y. Zang, A. Podlipensky, N. Y. Joly, P. St.J. Russell, and C. Silberhorn, “Bridging visible and telecom wavelengths with a single-mode broadband photon pair source,” Phys. Rev. A81, 031801 (2010).

[CrossRef]

B. Deconinck and J. N. Kutz, “Computing spectra of linear operators using the Floquet-Fourier-Hill method,” J. Comp. Phys.219, 296–321 (2006).

[CrossRef]

D. E. Pelinovsky and J. Yang, “Parametric resonance and radiative decay of dispersion-managed solitons,” SIAM J. Appl. Math.64, 1360 (2004).

[CrossRef]

P. St.J. Russell, “Photonic crystal fibers,” Science299, 358–362 (2003).

[CrossRef]
[PubMed]

F. Biancalana, D. V. Skryabin, and P. St.J. Russell, “Four-wave mixing instabilities in photonic-crystal and tapered fibers,” Phys. Rev. E68, 046603 (2003).

[CrossRef]

A. Kumar, A. Labruyere, and P. Tchofo-Dinda, “Modulational instability in fiber systems with periodic loss compensation and dispersion management,” Opt. Commun.219, 221–232 (2003).

[CrossRef]

F. K. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, “Nonlinear excitations in arrays of Bose-Einstein condensates,” Phys. Rev. A64, 043606 (2001).

[CrossRef]

H. W. Broer and C. Simó, “Resonance tongues in Hill’s equations: a geometric approach,” J. Diff. Equations166, 290–327 (2000).

[CrossRef]

D. Y. Tang, W. S. Man, H. Tam, and M. Demokan, “Modulational instability in a fiber soliton ring laser induced by periodic dispersion variation,” Phys. Rev. A61, 023804 (2000).

[CrossRef]

F. K. Abdullaev and J. Garnier, “Modulational instability of electromagnetic waves in birefringent fibers with periodic and random dispersion.” Phys. Rev. E60, 1042–1050 (1999).

[CrossRef]

R. Lai and A. J. Sievers, “Modulational instability of nonlinear spin waves in easy-axis antiferromagnetic chains,” Phys. Rev. B57, 3433–3443 (1998).

[CrossRef]

F. K. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, “Modulational instability in optical fibers with variable dispersion,” Phys. Rev. A220, 213–218 (1996).

N. J. Smith and N. J. Doran, “Modulational instabilities in fibers with periodic dispersion management.” Opt. Lett.21, 570–572 (1996).

[CrossRef]
[PubMed]

J. C. Bronski and J. N. Kutz, “Modulational stability of plane waves in nonreturn-to-zero communications systems with dispersion management.” Opt. Lett.21, 937–939 (1996).

[CrossRef]
[PubMed]

K. Kikuchi, C. Lorattanasane, F. Futami, and S. Kaneko, “Observation of quasi-phase matched four-wave mixing assisted by periodic power variation in a long-distance optical amplifier chain,” IEEE Photon. Technol. Lett.7, 1378–1380 (1995).

[CrossRef]

R. Bauer and L. Melnikov, “Multi-soliton fission and quasi-periodicity in a fiber with a periodically modulated core diameter,” Opt. Commun.115, 190–198 (1995).

[CrossRef]

V. A. Labay, J. Bornemann, and A. Labay, “Matrix singular value decomposition for pole-free solutions of homogeneous matrix equations as applied to numerical modeling methods,” IEEE Microw. Guided Wave Lett.2, 49–51 (1992).

[CrossRef]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett.56, 135–138 (1986).

[CrossRef]
[PubMed]

N. N. Akhmediev and V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrödinger equation,” JETP69, 1089–1093 (1986).

A. Hasegawa, “Observation of self-trapping instability of a plasma cyclotron wave in a computer experiment,” Phys. Rev. Lett.24, 1165–1168 (1970).

[CrossRef]

C. K. W. Tam, “Amplitude dispersion and nonlinear instability of whistlers,” Phys. Fluids12, 1028–1035 (1969).

[CrossRef]

T. Taniuti and H. Washimi, “Self-trapping and instability of hydromagnetic waves along the magnetic field in a cold plasma,” Phys. Rev. Lett.21, 209–212 (1968).

[CrossRef]

V. I. Karpman, “Self-modulation of Nonlinear Plane Waves in Dispersive Media,” JETP Lett.6, 277–279 (1967).

T. B. Benjamin and J. E. Feir, “The disintegration of wave trains on deep water. Part 1. Theory,” J. Fluid Mech.27, 417–430 (1967).

[CrossRef]

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett.3, 307–310 (1966).

G. B. Whitham, “Non-linear dispersive waves,” Proc. R. Soc. Lond., Ser. A283, 238–261 (1965).

[CrossRef]

F. K. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, “Nonlinear excitations in arrays of Bose-Einstein condensates,” Phys. Rev. A64, 043606 (2001).

[CrossRef]

F. K. Abdullaev and J. Garnier, “Modulational instability of electromagnetic waves in birefringent fibers with periodic and random dispersion.” Phys. Rev. E60, 1042–1050 (1999).

[CrossRef]

F. K. Abdullaev, S. A. Darmanyan, S. Bischoff, and M. P. Sørensen, “Modulational instability of electromagnetic waves in media with varying nonlinearity,” J. Opt. Soc. Am. B14, 27–33 (1997).

[CrossRef]

F. K. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, “Modulational instability in optical fibers with variable dispersion,” Phys. Rev. A220, 213–218 (1996).

G. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2006).

N. N. Akhmediev and V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrödinger equation,” JETP69, 1089–1093 (1986).

V. I. Arnold, A. Weinstein, and K. Vogtmann, Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics) (Springer, 1989).

V. I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations (Springer, 1988).

[CrossRef]

F. K. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, “Nonlinear excitations in arrays of Bose-Einstein condensates,” Phys. Rev. A64, 043606 (2001).

[CrossRef]

R. Bauer and L. Melnikov, “Multi-soliton fission and quasi-periodicity in a fiber with a periodically modulated core diameter,” Opt. Commun.115, 190–198 (1995).

[CrossRef]

T. B. Benjamin and J. E. Feir, “The disintegration of wave trains on deep water. Part 1. Theory,” J. Fluid Mech.27, 417–430 (1967).

[CrossRef]

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett.3, 307–310 (1966).

F. Biancalana, D. V. Skryabin, and P. St.J. Russell, “Four-wave mixing instabilities in photonic-crystal and tapered fibers,” Phys. Rev. E68, 046603 (2003).

[CrossRef]

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, L. Bigot, and A. Mussot, Université Lille 1, Laboratoire PhLAM, IRCICA, 59655 Villeneuve d’Ascq, France (private communication, 2012).

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, L. Bigot, and A. Mussot, “Demonstration of modulation instability assisted by a periodic dispersion landscape in an optical fiber,” in “CLEO: Science and Innovations,” (Optical Society of America, 2012), p. CTh4B.7.

V. A. Labay, J. Bornemann, and A. Labay, “Matrix singular value decomposition for pole-free solutions of homogeneous matrix equations as applied to numerical modeling methods,” IEEE Microw. Guided Wave Lett.2, 49–51 (1992).

[CrossRef]

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, L. Bigot, and A. Mussot, Université Lille 1, Laboratoire PhLAM, IRCICA, 59655 Villeneuve d’Ascq, France (private communication, 2012).

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, L. Bigot, and A. Mussot, “Demonstration of modulation instability assisted by a periodic dispersion landscape in an optical fiber,” in “CLEO: Science and Innovations,” (Optical Society of America, 2012), p. CTh4B.7.

C. Söller, B. Brecht, P. J. Mosley, L. Y. Zang, A. Podlipensky, N. Y. Joly, P. St.J. Russell, and C. Silberhorn, “Bridging visible and telecom wavelengths with a single-mode broadband photon pair source,” Phys. Rev. A81, 031801 (2010).

[CrossRef]

H. W. Broer and C. Simó, “Resonance tongues in Hill’s equations: a geometric approach,” J. Diff. Equations166, 290–327 (2000).

[CrossRef]

F. K. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, “Nonlinear excitations in arrays of Bose-Einstein condensates,” Phys. Rev. A64, 043606 (2001).

[CrossRef]

F. K. Abdullaev, S. A. Darmanyan, S. Bischoff, and M. P. Sørensen, “Modulational instability of electromagnetic waves in media with varying nonlinearity,” J. Opt. Soc. Am. B14, 27–33 (1997).

[CrossRef]

F. K. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, “Modulational instability in optical fibers with variable dispersion,” Phys. Rev. A220, 213–218 (1996).

B. Deconinck and J. N. Kutz, “Computing spectra of linear operators using the Floquet-Fourier-Hill method,” J. Comp. Phys.219, 296–321 (2006).

[CrossRef]

D. Y. Tang, W. S. Man, H. Tam, and M. Demokan, “Modulational instability in a fiber soliton ring laser induced by periodic dispersion variation,” Phys. Rev. A61, 023804 (2000).

[CrossRef]

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, L. Bigot, and A. Mussot, “Demonstration of modulation instability assisted by a periodic dispersion landscape in an optical fiber,” in “CLEO: Science and Innovations,” (Optical Society of America, 2012), p. CTh4B.7.

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, L. Bigot, and A. Mussot, Université Lille 1, Laboratoire PhLAM, IRCICA, 59655 Villeneuve d’Ascq, France (private communication, 2012).

T. B. Benjamin and J. E. Feir, “The disintegration of wave trains on deep water. Part 1. Theory,” J. Fluid Mech.27, 417–430 (1967).

[CrossRef]

K. Kikuchi, C. Lorattanasane, F. Futami, and S. Kaneko, “Observation of quasi-phase matched four-wave mixing assisted by periodic power variation in a long-distance optical amplifier chain,” IEEE Photon. Technol. Lett.7, 1378–1380 (1995).

[CrossRef]

F. K. Abdullaev and J. Garnier, “Modulational instability of electromagnetic waves in birefringent fibers with periodic and random dispersion.” Phys. Rev. E60, 1042–1050 (1999).

[CrossRef]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett.56, 135–138 (1986).

[CrossRef]
[PubMed]

A. Hasegawa, “Observation of self-trapping instability of a plasma cyclotron wave in a computer experiment,” Phys. Rev. Lett.24, 1165–1168 (1970).

[CrossRef]

C. Söller, B. Brecht, P. J. Mosley, L. Y. Zang, A. Podlipensky, N. Y. Joly, P. St.J. Russell, and C. Silberhorn, “Bridging visible and telecom wavelengths with a single-mode broadband photon pair source,” Phys. Rev. A81, 031801 (2010).

[CrossRef]

K. Kikuchi, C. Lorattanasane, F. Futami, and S. Kaneko, “Observation of quasi-phase matched four-wave mixing assisted by periodic power variation in a long-distance optical amplifier chain,” IEEE Photon. Technol. Lett.7, 1378–1380 (1995).

[CrossRef]

V. I. Karpman, “Self-modulation of Nonlinear Plane Waves in Dispersive Media,” JETP Lett.6, 277–279 (1967).

K. Kikuchi, C. Lorattanasane, F. Futami, and S. Kaneko, “Observation of quasi-phase matched four-wave mixing assisted by periodic power variation in a long-distance optical amplifier chain,” IEEE Photon. Technol. Lett.7, 1378–1380 (1995).

[CrossRef]

F. K. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, “Modulational instability in optical fibers with variable dispersion,” Phys. Rev. A220, 213–218 (1996).

F. K. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, “Nonlinear excitations in arrays of Bose-Einstein condensates,” Phys. Rev. A64, 043606 (2001).

[CrossRef]

N. N. Akhmediev and V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrödinger equation,” JETP69, 1089–1093 (1986).

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, L. Bigot, and A. Mussot, “Demonstration of modulation instability assisted by a periodic dispersion landscape in an optical fiber,” in “CLEO: Science and Innovations,” (Optical Society of America, 2012), p. CTh4B.7.

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, L. Bigot, and A. Mussot, Université Lille 1, Laboratoire PhLAM, IRCICA, 59655 Villeneuve d’Ascq, France (private communication, 2012).

A. Kumar, A. Labruyere, and P. Tchofo-Dinda, “Modulational instability in fiber systems with periodic loss compensation and dispersion management,” Opt. Commun.219, 221–232 (2003).

[CrossRef]

V. A. Labay, J. Bornemann, and A. Labay, “Matrix singular value decomposition for pole-free solutions of homogeneous matrix equations as applied to numerical modeling methods,” IEEE Microw. Guided Wave Lett.2, 49–51 (1992).

[CrossRef]

V. A. Labay, J. Bornemann, and A. Labay, “Matrix singular value decomposition for pole-free solutions of homogeneous matrix equations as applied to numerical modeling methods,” IEEE Microw. Guided Wave Lett.2, 49–51 (1992).

[CrossRef]

A. Kumar, A. Labruyere, and P. Tchofo-Dinda, “Modulational instability in fiber systems with periodic loss compensation and dispersion management,” Opt. Commun.219, 221–232 (2003).

[CrossRef]

R. Lai and A. J. Sievers, “Modulational instability of nonlinear spin waves in easy-axis antiferromagnetic chains,” Phys. Rev. B57, 3433–3443 (1998).

[CrossRef]

L. D. Landau and E. M. Lifshitz, Mechanics, Third Edition: Volume 1 (Course of Theoretical Physics) (Butterworth-Heinemann, 1976).

F. K. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, “Modulational instability in optical fibers with variable dispersion,” Phys. Rev. A220, 213–218 (1996).

L. D. Landau and E. M. Lifshitz, Mechanics, Third Edition: Volume 1 (Course of Theoretical Physics) (Butterworth-Heinemann, 1976).

K. Kikuchi, C. Lorattanasane, F. Futami, and S. Kaneko, “Observation of quasi-phase matched four-wave mixing assisted by periodic power variation in a long-distance optical amplifier chain,” IEEE Photon. Technol. Lett.7, 1378–1380 (1995).

[CrossRef]

D. Y. Tang, W. S. Man, H. Tam, and M. Demokan, “Modulational instability in a fiber soliton ring laser induced by periodic dispersion variation,” Phys. Rev. A61, 023804 (2000).

[CrossRef]

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, L. Bigot, and A. Mussot, “Demonstration of modulation instability assisted by a periodic dispersion landscape in an optical fiber,” in “CLEO: Science and Innovations,” (Optical Society of America, 2012), p. CTh4B.7.

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, L. Bigot, and A. Mussot, Université Lille 1, Laboratoire PhLAM, IRCICA, 59655 Villeneuve d’Ascq, France (private communication, 2012).

R. Bauer and L. Melnikov, “Multi-soliton fission and quasi-periodicity in a fiber with a periodically modulated core diameter,” Opt. Commun.115, 190–198 (1995).

[CrossRef]

C. Söller, B. Brecht, P. J. Mosley, L. Y. Zang, A. Podlipensky, N. Y. Joly, P. St.J. Russell, and C. Silberhorn, “Bridging visible and telecom wavelengths with a single-mode broadband photon pair source,” Phys. Rev. A81, 031801 (2010).

[CrossRef]

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, L. Bigot, and A. Mussot, Université Lille 1, Laboratoire PhLAM, IRCICA, 59655 Villeneuve d’Ascq, France (private communication, 2012).

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, L. Bigot, and A. Mussot, “Demonstration of modulation instability assisted by a periodic dispersion landscape in an optical fiber,” in “CLEO: Science and Innovations,” (Optical Society of America, 2012), p. CTh4B.7.

D. E. Pelinovsky and J. Yang, “Parametric resonance and radiative decay of dispersion-managed solitons,” SIAM J. Appl. Math.64, 1360 (2004).

[CrossRef]

C. Söller, B. Brecht, P. J. Mosley, L. Y. Zang, A. Podlipensky, N. Y. Joly, P. St.J. Russell, and C. Silberhorn, “Bridging visible and telecom wavelengths with a single-mode broadband photon pair source,” Phys. Rev. A81, 031801 (2010).

[CrossRef]

C. Söller, B. Brecht, P. J. Mosley, L. Y. Zang, A. Podlipensky, N. Y. Joly, P. St.J. Russell, and C. Silberhorn, “Bridging visible and telecom wavelengths with a single-mode broadband photon pair source,” Phys. Rev. A81, 031801 (2010).

[CrossRef]

J. Rarity, J. Fulconis, J. Duligall, W. Wadsworth, and P. St.J. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express13, 534–544 (2005).

[CrossRef]
[PubMed]

P. St.J. Russell, “Photonic crystal fibers,” Science299, 358–362 (2003).

[CrossRef]
[PubMed]

F. Biancalana, D. V. Skryabin, and P. St.J. Russell, “Four-wave mixing instabilities in photonic-crystal and tapered fibers,” Phys. Rev. E68, 046603 (2003).

[CrossRef]

F. K. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, “Nonlinear excitations in arrays of Bose-Einstein condensates,” Phys. Rev. A64, 043606 (2001).

[CrossRef]

R. Lai and A. J. Sievers, “Modulational instability of nonlinear spin waves in easy-axis antiferromagnetic chains,” Phys. Rev. B57, 3433–3443 (1998).

[CrossRef]

C. Söller, B. Brecht, P. J. Mosley, L. Y. Zang, A. Podlipensky, N. Y. Joly, P. St.J. Russell, and C. Silberhorn, “Bridging visible and telecom wavelengths with a single-mode broadband photon pair source,” Phys. Rev. A81, 031801 (2010).

[CrossRef]

H. W. Broer and C. Simó, “Resonance tongues in Hill’s equations: a geometric approach,” J. Diff. Equations166, 290–327 (2000).

[CrossRef]

F. Biancalana, D. V. Skryabin, and P. St.J. Russell, “Four-wave mixing instabilities in photonic-crystal and tapered fibers,” Phys. Rev. E68, 046603 (2003).

[CrossRef]

C. Söller, B. Brecht, P. J. Mosley, L. Y. Zang, A. Podlipensky, N. Y. Joly, P. St.J. Russell, and C. Silberhorn, “Bridging visible and telecom wavelengths with a single-mode broadband photon pair source,” Phys. Rev. A81, 031801 (2010).

[CrossRef]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett.56, 135–138 (1986).

[CrossRef]
[PubMed]

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett.3, 307–310 (1966).

C. K. W. Tam, “Amplitude dispersion and nonlinear instability of whistlers,” Phys. Fluids12, 1028–1035 (1969).

[CrossRef]

D. Y. Tang, W. S. Man, H. Tam, and M. Demokan, “Modulational instability in a fiber soliton ring laser induced by periodic dispersion variation,” Phys. Rev. A61, 023804 (2000).

[CrossRef]

D. Y. Tang, W. S. Man, H. Tam, and M. Demokan, “Modulational instability in a fiber soliton ring laser induced by periodic dispersion variation,” Phys. Rev. A61, 023804 (2000).

[CrossRef]

T. Taniuti and H. Washimi, “Self-trapping and instability of hydromagnetic waves along the magnetic field in a cold plasma,” Phys. Rev. Lett.21, 209–212 (1968).

[CrossRef]

S. Ambomo, C. M. Ngabireng, and P. Tchofo-Dinda, “Critical behavior with dramatic enhancement of modulational instability gain in fiber systems with periodic variation dispersion,” J. Opt. Soc. Am. B25, 425–433 (2008).

[CrossRef]

A. Kumar, A. Labruyere, and P. Tchofo-Dinda, “Modulational instability in fiber systems with periodic loss compensation and dispersion management,” Opt. Commun.219, 221–232 (2003).

[CrossRef]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett.56, 135–138 (1986).

[CrossRef]
[PubMed]

F. Verhulst, “Perturbation analysis of parametric resonance,” in Encyclopedia of Complexity and Systems Science, R. A. Meyers, ed. (SpringerNew York, 2009), pp. 6625–6639.

V. I. Arnold, A. Weinstein, and K. Vogtmann, Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics) (Springer, 1989).

T. Taniuti and H. Washimi, “Self-trapping and instability of hydromagnetic waves along the magnetic field in a cold plasma,” Phys. Rev. Lett.21, 209–212 (1968).

[CrossRef]

V. I. Arnold, A. Weinstein, and K. Vogtmann, Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics) (Springer, 1989).

G. B. Whitham, “Non-linear dispersive waves,” Proc. R. Soc. Lond., Ser. A283, 238–261 (1965).

[CrossRef]

D. E. Pelinovsky and J. Yang, “Parametric resonance and radiative decay of dispersion-managed solitons,” SIAM J. Appl. Math.64, 1360 (2004).

[CrossRef]

C. Söller, B. Brecht, P. J. Mosley, L. Y. Zang, A. Podlipensky, N. Y. Joly, P. St.J. Russell, and C. Silberhorn, “Bridging visible and telecom wavelengths with a single-mode broadband photon pair source,” Phys. Rev. A81, 031801 (2010).

[CrossRef]

V. A. Labay, J. Bornemann, and A. Labay, “Matrix singular value decomposition for pole-free solutions of homogeneous matrix equations as applied to numerical modeling methods,” IEEE Microw. Guided Wave Lett.2, 49–51 (1992).

[CrossRef]

K. Kikuchi, C. Lorattanasane, F. Futami, and S. Kaneko, “Observation of quasi-phase matched four-wave mixing assisted by periodic power variation in a long-distance optical amplifier chain,” IEEE Photon. Technol. Lett.7, 1378–1380 (1995).

[CrossRef]

B. Deconinck and J. N. Kutz, “Computing spectra of linear operators using the Floquet-Fourier-Hill method,” J. Comp. Phys.219, 296–321 (2006).

[CrossRef]

H. W. Broer and C. Simó, “Resonance tongues in Hill’s equations: a geometric approach,” J. Diff. Equations166, 290–327 (2000).

[CrossRef]

T. B. Benjamin and J. E. Feir, “The disintegration of wave trains on deep water. Part 1. Theory,” J. Fluid Mech.27, 417–430 (1967).

[CrossRef]

F. K. Abdullaev, S. A. Darmanyan, S. Bischoff, and M. P. Sørensen, “Modulational instability of electromagnetic waves in media with varying nonlinearity,” J. Opt. Soc. Am. B14, 27–33 (1997).

[CrossRef]

S. Ambomo, C. M. Ngabireng, and P. Tchofo-Dinda, “Critical behavior with dramatic enhancement of modulational instability gain in fiber systems with periodic variation dispersion,” J. Opt. Soc. Am. B25, 425–433 (2008).

[CrossRef]

N. N. Akhmediev and V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrödinger equation,” JETP69, 1089–1093 (1986).

V. I. Karpman, “Self-modulation of Nonlinear Plane Waves in Dispersive Media,” JETP Lett.6, 277–279 (1967).

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett.3, 307–310 (1966).

R. Bauer and L. Melnikov, “Multi-soliton fission and quasi-periodicity in a fiber with a periodically modulated core diameter,” Opt. Commun.115, 190–198 (1995).

[CrossRef]

A. Kumar, A. Labruyere, and P. Tchofo-Dinda, “Modulational instability in fiber systems with periodic loss compensation and dispersion management,” Opt. Commun.219, 221–232 (2003).

[CrossRef]

J. Rarity, J. Fulconis, J. Duligall, W. Wadsworth, and P. St.J. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express13, 534–544 (2005).

[CrossRef]
[PubMed]

S. V. Afshar and T. M. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part I: Kerr nonlinearity,” Opt. Express17, 2298–2318 (2009).

[CrossRef]

N. J. Smith and N. J. Doran, “Modulational instabilities in fibers with periodic dispersion management.” Opt. Lett.21, 570–572 (1996).

[CrossRef]
[PubMed]

J. C. Bronski and J. N. Kutz, “Modulational stability of plane waves in nonreturn-to-zero communications systems with dispersion management.” Opt. Lett.21, 937–939 (1996).

[CrossRef]
[PubMed]

F. Matera, A. Mecozzi, M. Romagnoli, and M. Settembre, “Sideband instability induced by periodic power variation in long-distance fiber links,” Opt. Lett.18, 1499–1501 (1993).

[CrossRef]
[PubMed]

C. K. W. Tam, “Amplitude dispersion and nonlinear instability of whistlers,” Phys. Fluids12, 1028–1035 (1969).

[CrossRef]

F. K. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, “Nonlinear excitations in arrays of Bose-Einstein condensates,” Phys. Rev. A64, 043606 (2001).

[CrossRef]

D. Y. Tang, W. S. Man, H. Tam, and M. Demokan, “Modulational instability in a fiber soliton ring laser induced by periodic dispersion variation,” Phys. Rev. A61, 023804 (2000).

[CrossRef]

F. K. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, “Modulational instability in optical fibers with variable dispersion,” Phys. Rev. A220, 213–218 (1996).

C. Söller, B. Brecht, P. J. Mosley, L. Y. Zang, A. Podlipensky, N. Y. Joly, P. St.J. Russell, and C. Silberhorn, “Bridging visible and telecom wavelengths with a single-mode broadband photon pair source,” Phys. Rev. A81, 031801 (2010).

[CrossRef]

R. Lai and A. J. Sievers, “Modulational instability of nonlinear spin waves in easy-axis antiferromagnetic chains,” Phys. Rev. B57, 3433–3443 (1998).

[CrossRef]

F. K. Abdullaev and J. Garnier, “Modulational instability of electromagnetic waves in birefringent fibers with periodic and random dispersion.” Phys. Rev. E60, 1042–1050 (1999).

[CrossRef]

F. Biancalana, D. V. Skryabin, and P. St.J. Russell, “Four-wave mixing instabilities in photonic-crystal and tapered fibers,” Phys. Rev. E68, 046603 (2003).

[CrossRef]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett.56, 135–138 (1986).

[CrossRef]
[PubMed]

T. Taniuti and H. Washimi, “Self-trapping and instability of hydromagnetic waves along the magnetic field in a cold plasma,” Phys. Rev. Lett.21, 209–212 (1968).

[CrossRef]

A. Hasegawa, “Observation of self-trapping instability of a plasma cyclotron wave in a computer experiment,” Phys. Rev. Lett.24, 1165–1168 (1970).

[CrossRef]

G. B. Whitham, “Non-linear dispersive waves,” Proc. R. Soc. Lond., Ser. A283, 238–261 (1965).

[CrossRef]

P. St.J. Russell, “Photonic crystal fibers,” Science299, 358–362 (2003).

[CrossRef]
[PubMed]

D. E. Pelinovsky and J. Yang, “Parametric resonance and radiative decay of dispersion-managed solitons,” SIAM J. Appl. Math.64, 1360 (2004).

[CrossRef]

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, L. Bigot, and A. Mussot, “Demonstration of modulation instability assisted by a periodic dispersion landscape in an optical fiber,” in “CLEO: Science and Innovations,” (Optical Society of America, 2012), p. CTh4B.7.

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, L. Bigot, and A. Mussot, Université Lille 1, Laboratoire PhLAM, IRCICA, 59655 Villeneuve d’Ascq, France (private communication, 2012).

F. Verhulst, “Perturbation analysis of parametric resonance,” in Encyclopedia of Complexity and Systems Science, R. A. Meyers, ed. (SpringerNew York, 2009), pp. 6625–6639.

G. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2006).

V. I. Arnold, A. Weinstein, and K. Vogtmann, Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics) (Springer, 1989).

L. D. Landau and E. M. Lifshitz, Mechanics, Third Edition: Volume 1 (Course of Theoretical Physics) (Butterworth-Heinemann, 1976).

V. I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations (Springer, 1988).

[CrossRef]

“Comsol Multiphysics”, http://www.comsol.com .