Abstract

We investigate the modulational instability (MI) of an optical beam near the zero group dispersion wavelength of a relaxing saturable nonlinear system. Considering a suitable theoretical model, we identify and discuss significant features of higher order dispersion (HOD), especially the role of the fourth-order dispersion (FOD) in the MI spectrum of relaxing saturable systems. The influence of FOD is to suppress MI in the anomalous group dispersion regime, to promote MI sidebands in the normal group dispersion regime, and the evolution of nonconventional sidebands are observed. Particularly, the inclusion of a finite value of the response time extends the range of unstable frequencies down to infinite frequencies. This happens because the finite response time in the nonlinear response is equivalent to assuming a complex nonlinearity. Therefore, in addition to the real part of the nonlinearity (which governs the parametric MI process), the contribution from the imaginary part of the nonlinear response (which models the Raman process) extends the domain of MI through the self-phase-matched process, even when the phase matching for the parametric MI process is not feasible. In the regime of the slow response, MI is suppressed regardless of the signs of the dispersion coefficients. To give a better insight into the MI phenomena, the maximum instability gain and the optimum modulation frequency are drawn as a function of the delay time. Thus, in this paper, the MI dynamics of a relaxing saturable nonlinear system is emphasized and the influence of HOD is highlighted.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  37. 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]
  38. P. T. Dinda, C. Ngabireng, K. Porsezian, and B. Kalithasan, “Modulational instability in optical fibers with arbitrary higher-order dispersion and delayed Raman response,” Opt. Commun. 266, 142–150 (2006).
    [CrossRef]
  39. P. T. Dinda and K. Porsezian, “Impact of fourth-order dispersion in the modulational instability spectra of wave propagation in glass fibers with saturable nonlinearity,” J. Opt. Soc. Am. B 27, 1143–1152 (2010).
    [CrossRef]

2011

2010

R. V. J. Raja, K. Porsezian, and K. Nithyanandan, “Modulational-instability-induced supercontinuum generation with saturable nonlinear response,” Phys. Rev. A 82, 013825 (2010).
[CrossRef]

L. Zhang, S. Wen, X. Fu, J. Deng, J. Zhang, and D. Fan, “Spatiotemporal instability in dispersive nonlinear Kerr medium with a finite response time,” Opt. Commun. 283, 2251–2257 (2010).
[CrossRef]

R. V. J. Raja, A. Husakou, J. Hermann, and K. Porsezian, “Supercontinuum generation in liquid-filled photonic crystal fiber with slow nonlinear response,” J. Opt. Soc. Am. B 27, 1763–1768 (2010).
[CrossRef]

P. T. Dinda and K. Porsezian, “Impact of fourth-order dispersion in the modulational instability spectra of wave propagation in glass fibers with saturable nonlinearity,” J. Opt. Soc. Am. B 27, 1143–1152 (2010).
[CrossRef]

2009

2008

X. Liu, J. W. Haus, and S. Shahriar, “Modulation instability for a relaxational Kerr medium,” Opt. Commun. 281, 2907–2912 (2008).
[CrossRef]

2006

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[CrossRef]

Y.-F. Chen, K. Beckwitt, F. W. Wise, B. G. Aitken, J. S. Sanghera, and I. D. Aggarwal, “Measurement of fifth- and seventh-order non-linearities of glasses,” J. Opt. Soc. Am. B 23, 347–352 (2006).
[CrossRef]

P. T. Dinda, C. Ngabireng, K. Porsezian, and B. Kalithasan, “Modulational instability in optical fibers with arbitrary higher-order dispersion and delayed Raman response,” Opt. Commun. 266, 142–150 (2006).
[CrossRef]

2005

2004

H. Leblond and C. Cambournac, “Spatial modulation instability of coherent light in a weakly-relaxing Kerr medium,” J. Opt. A 6, 461–468 (2004).
[CrossRef]

2003

I. Velchev, R. Pattnaik, and J. Toulouse, “Two-beam modulation instability in noninstantaneous nonlinear media,” Phys. Rev. Lett. 91, 093905 (2003).
[CrossRef]

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

W. Shuang-Chun, S. Wen-Hua, Z. Hua, F. Xi-Quan, Q. Lie-Jia, and F. Dian-Yuan, “Influence of higher-order dispersions and Raman delayed response on modulation instability in microstructured fibres,” Chin. Phys. Lett. 20, 852–854 (2003).
[CrossRef]

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]

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]

2002

2001

1994

F. K. Abdullaev, S. A. Darmanyan, S. Bischoff, P. L. Christiansen, and M. P. Sorensen, “Modulational instability in optical fibers near the zero dispersion point,” Opt. Commun. 108, 60–64 (1994).
[CrossRef]

1993

1991

1989

1988

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443–454 (1988).
[CrossRef]

1987

1986

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

G. R. Olbright and N. Peyghambarian, “Interferometric measurement of the nonlinear index of refraction, n2, of CdSxSe1−x-doped glasses,” Appl. Phys. Lett. 48, 1184–1186 (1986).
[CrossRef]

1985

S. Yao, C. Karaguleff, A. Gabel, R. Fortenberry, C. T. Seaton, and G. I. Stegeman, “Ultrafast carrier and grating lifetimes in semiconductor-doped glasses,” Appl. Phys. Lett. 46, 801–802 (1985).
[CrossRef]

1984

1979

R. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Progr. Quantum Electron. 5, 1–68 (1979).
[CrossRef]

1973

A. Hasegawa and F. Tappert, “Generation of a train of soliton pulses by induced modulational instability in optical fibers,” Appl. Phys. Lett. 23, 142–244 (1973).
[CrossRef]

Abdullaev, F. K.

F. K. Abdullaev, S. A. Darmanyan, S. Bischoff, P. L. Christiansen, and M. P. Sorensen, “Modulational instability in optical fibers near the zero dispersion point,” Opt. Commun. 108, 60–64 (1994).
[CrossRef]

Abouou, M. N. Z.

Aggarwal, I. D.

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

Aitken, B. G.

Akhmediev, N.

Beckwitt, K.

Bischoff, S.

F. K. Abdullaev, S. A. Darmanyan, S. Bischoff, P. L. Christiansen, and M. P. Sorensen, “Modulational instability in optical fibers near the zero dispersion point,” Opt. Commun. 108, 60–64 (1994).
[CrossRef]

Borges, N. M.

Cambournac, C.

Cavalcanti, S. B.

J. M. Hickmann, S. B. Cavalcanti, N. M. Borges, E. A. Gouveia, and A. S. Gouveia-Neto, “Modulational instability in semiconductor-doped glass fibers with saturable nonlinearity,” Opt. Lett. 18, 182–184 (1993).
[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]

Chauvet, M.

Chen, C.-H.

Chen, Y.-F.

Christiansen, P. L.

F. K. Abdullaev, S. A. Darmanyan, S. Bischoff, P. L. Christiansen, and M. P. Sorensen, “Modulational instability in optical fibers near the zero dispersion point,” Opt. Commun. 108, 60–64 (1994).
[CrossRef]

Chu, W.-H.

Coen, S.

Coutaz, J.-L.

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]

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]

da Silva, G. L.

Darmanyan, S. A.

F. K. Abdullaev, S. A. Darmanyan, S. Bischoff, P. L. Christiansen, and M. P. Sorensen, “Modulational instability in optical fibers near the zero dispersion point,” Opt. Commun. 108, 60–64 (1994).
[CrossRef]

Deng, J.

L. Zhang, S. Wen, X. Fu, J. Deng, J. Zhang, and D. Fan, “Spatiotemporal instability in dispersive nonlinear Kerr medium with a finite response time,” Opt. Commun. 283, 2251–2257 (2010).
[CrossRef]

Dian-Yuan, F.

W. Shuang-Chun, S. Wen-Hua, Z. Hua, F. Xi-Quan, Q. Lie-Jia, and F. Dian-Yuan, “Influence of higher-order dispersions and Raman delayed response on modulation instability in microstructured fibres,” Chin. Phys. Lett. 20, 852–854 (2003).
[CrossRef]

Dinda, P. T.

M. N. Z. Abouou, P. T. Dinda, C. M. Ngabireng, B. Kibler, and F. Smektala, “Impact of the material absorption on the modulational instability spectra of wave propagation in high-index glass fibers,” J. Opt. Soc. Am. B 28, 1518–1528 (2011).
[CrossRef]

P. T. Dinda and K. Porsezian, “Impact of fourth-order dispersion in the modulational instability spectra of wave propagation in glass fibers with saturable nonlinearity,” J. Opt. Soc. Am. B 27, 1143–1152 (2010).
[CrossRef]

P. T. Dinda, C. Ngabireng, K. Porsezian, and B. Kalithasan, “Modulational instability in optical fibers with arbitrary higher-order dispersion and delayed Raman response,” Opt. Commun. 266, 142–150 (2006).
[CrossRef]

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

Dudley, J. M.

Emplit, P.

Fan, D.

L. Zhang, S. Wen, X. Fu, J. Deng, J. Zhang, and D. Fan, “Spatiotemporal instability in dispersive nonlinear Kerr medium with a finite response time,” Opt. Commun. 283, 2251–2257 (2010).
[CrossRef]

Fatome, J.

Finot, C.

Flytzanis, C.

Fortenberry, R.

S. Yao, C. Karaguleff, A. Gabel, R. Fortenberry, C. T. Seaton, and G. I. Stegeman, “Ultrafast carrier and grating lifetimes in semiconductor-doped glasses,” Appl. Phys. Lett. 46, 801–802 (1985).
[CrossRef]

Fu, X.

L. Zhang, S. Wen, X. Fu, J. Deng, J. Zhang, and D. Fan, “Spatiotemporal instability in dispersive nonlinear Kerr medium with a finite response time,” Opt. Commun. 283, 2251–2257 (2010).
[CrossRef]

Gabel, A.

S. Yao, C. Karaguleff, A. Gabel, R. Fortenberry, C. T. Seaton, and G. I. Stegeman, “Ultrafast carrier and grating lifetimes in semiconductor-doped glasses,” Appl. Phys. Lett. 46, 801–802 (1985).
[CrossRef]

Gatz, S.

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[CrossRef]

Gleria, I.

Gouveia, E. A.

Gouveia-Neto, A. S.

J. M. Hickmann, S. B. Cavalcanti, N. M. Borges, E. A. Gouveia, and A. S. Gouveia-Neto, “Modulational instability in semiconductor-doped glass fibers with saturable nonlinearity,” Opt. Lett. 18, 182–184 (1993).
[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]

Haelterman, M.

Hammani, K.

Harvey, J. D.

Hasegawa, A.

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

A. Hasegawa, “Generation of a train of soliton pulses by induced modulational instability in optical fibers,” Opt. Lett. 9, 288–290 (1984).
[CrossRef]

A. Hasegawa and F. Tappert, “Generation of a train of soliton pulses by induced modulational instability in optical fibers,” Appl. Phys. Lett. 23, 142–244 (1973).
[CrossRef]

Haus, J. W.

X. Liu, J. W. Haus, and S. Shahriar, “Modulation instability for a relaxational Kerr medium,” Opt. Commun. 281, 2907–2912 (2008).
[CrossRef]

Hellwarth, R.

R. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Progr. Quantum Electron. 5, 1–68 (1979).
[CrossRef]

Hermann, J.

Herrmann, J.

Hickmann, J. M.

Hua, Z.

W. Shuang-Chun, S. Wen-Hua, Z. Hua, F. Xi-Quan, Q. Lie-Jia, and F. Dian-Yuan, “Influence of higher-order dispersions and Raman delayed response on modulation instability in microstructured fibres,” Chin. Phys. Lett. 20, 852–854 (2003).
[CrossRef]

Husakou, A.

Jeng, C. C.

M.-F. Shih, C. C. Jeng, F. W. Sheu, and C. Y. Lin, “Spatiotemporal optical modulation instability of coherent light in noninstantaneous nonlinear media,” Phys. Rev. Lett. 88, 133902 (2002).
[CrossRef]

Jeng, C.-C.

Kalithasan, B.

P. T. Dinda, C. Ngabireng, K. Porsezian, and B. Kalithasan, “Modulational instability in optical fibers with arbitrary higher-order dispersion and delayed Raman response,” Opt. Commun. 266, 142–150 (2006).
[CrossRef]

Karaguleff, C.

S. Yao, C. Karaguleff, A. Gabel, R. Fortenberry, C. T. Seaton, and G. I. Stegeman, “Ultrafast carrier and grating lifetimes in semiconductor-doped glasses,” Appl. Phys. Lett. 46, 801–802 (1985).
[CrossRef]

Kenney-Wallace, G. A.

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443–454 (1988).
[CrossRef]

Kibler, B.

Knight, J. C.

Kull, M.

Kumar, A.

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

Labruyere, A.

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

Lantz, E.

Leblond, H.

H. Leblond and C. Cambournac, “Spatial modulation instability of coherent light in a weakly-relaxing Kerr medium,” J. Opt. A 6, 461–468 (2004).
[CrossRef]

Leonhardt, R.

Lie-Jia, Q.

W. Shuang-Chun, S. Wen-Hua, Z. Hua, F. Xi-Quan, Q. Lie-Jia, and F. Dian-Yuan, “Influence of higher-order dispersions and Raman delayed response on modulation instability in microstructured fibres,” Chin. Phys. Lett. 20, 852–854 (2003).
[CrossRef]

Lin, C. Y.

M.-F. Shih, C. C. Jeng, F. W. Sheu, and C. Y. Lin, “Spatiotemporal optical modulation instability of coherent light in noninstantaneous nonlinear media,” Phys. Rev. Lett. 88, 133902 (2002).
[CrossRef]

Liu, X.

X. Liu, J. W. Haus, and S. Shahriar, “Modulation instability for a relaxational Kerr medium,” Opt. Commun. 281, 2907–2912 (2008).
[CrossRef]

Liu, Y.-H.

Lotshaw, W. T.

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443–454 (1988).
[CrossRef]

Lukasik, J.

Lyra, M. L.

Maillotte, H.

McMorrow, D.

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443–454 (1988).
[CrossRef]

Millot, G.

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36, 2140–2142 (2011).
[CrossRef]

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]

Ngabireng, C.

P. T. Dinda, C. Ngabireng, K. Porsezian, and B. Kalithasan, “Modulational instability in optical fibers with arbitrary higher-order dispersion and delayed Raman response,” Opt. Commun. 266, 142–150 (2006).
[CrossRef]

Ngabireng, C. M.

Nithyanandan, K.

R. V. J. Raja, K. Porsezian, and K. Nithyanandan, “Modulational-instability-induced supercontinuum generation with saturable nonlinear response,” Phys. Rev. A 82, 013825 (2010).
[CrossRef]

Olbright, G. R.

G. R. Olbright and N. Peyghambarian, “Interferometric measurement of the nonlinear index of refraction, n2, of CdSxSe1−x-doped glasses,” Appl. Phys. Lett. 48, 1184–1186 (1986).
[CrossRef]

Pattnaik, R.

I. Velchev, R. Pattnaik, and J. Toulouse, “Two-beam modulation instability in noninstantaneous nonlinear media,” Phys. Rev. Lett. 91, 093905 (2003).
[CrossRef]

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[CrossRef]

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[CrossRef]

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P. T. Dinda and K. Porsezian, “Impact of fourth-order dispersion in the modulational instability spectra of wave propagation in glass fibers with saturable nonlinearity,” J. Opt. Soc. Am. B 27, 1143–1152 (2010).
[CrossRef]

R. V. J. Raja, A. Husakou, J. Hermann, and K. Porsezian, “Supercontinuum generation in liquid-filled photonic crystal fiber with slow nonlinear response,” J. Opt. Soc. Am. B 27, 1763–1768 (2010).
[CrossRef]

R. V. J. Raja, K. Porsezian, and K. Nithyanandan, “Modulational-instability-induced supercontinuum generation with saturable nonlinear response,” Phys. Rev. A 82, 013825 (2010).
[CrossRef]

P. T. Dinda, C. Ngabireng, K. Porsezian, and B. Kalithasan, “Modulational instability in optical fibers with arbitrary higher-order dispersion and delayed Raman response,” Opt. Commun. 266, 142–150 (2006).
[CrossRef]

Potasek, M. J.

Raja, R. V. J.

R. V. J. Raja, K. Porsezian, and K. Nithyanandan, “Modulational-instability-induced supercontinuum generation with saturable nonlinear response,” Phys. Rev. A 82, 013825 (2010).
[CrossRef]

R. V. J. Raja, A. Husakou, J. Hermann, and K. Porsezian, “Supercontinuum generation in liquid-filled photonic crystal fiber with slow nonlinear response,” J. Opt. Soc. Am. B 27, 1763–1768 (2010).
[CrossRef]

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Roussignol, P.

Sanghera, J. S.

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[CrossRef]

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[CrossRef]

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M.-F. Shih, C. C. Jeng, F. W. Sheu, and C. Y. Lin, “Spatiotemporal optical modulation instability of coherent light in noninstantaneous nonlinear media,” Phys. Rev. Lett. 88, 133902 (2002).
[CrossRef]

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W.-H. Chu, C.-C. Jeng, C.-H. Chen, Y.-H. Liu, and M.-F. Shih, “Induced spatiotemporal modulation instability in a noninstantaneous self-defocusing medium,” Opt. Lett. 30, 1846–1848 (2005).
[CrossRef]

M.-F. Shih, C. C. Jeng, F. W. Sheu, and C. Y. Lin, “Spatiotemporal optical modulation instability of coherent light in noninstantaneous nonlinear media,” Phys. Rev. Lett. 88, 133902 (2002).
[CrossRef]

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W. Shuang-Chun, S. Wen-Hua, Z. Hua, F. Xi-Quan, Q. Lie-Jia, and F. Dian-Yuan, “Influence of higher-order dispersions and Raman delayed response on modulation instability in microstructured fibres,” Chin. Phys. Lett. 20, 852–854 (2003).
[CrossRef]

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K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138(1986).
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I. Velchev, R. Pattnaik, and J. Toulouse, “Two-beam modulation instability in noninstantaneous nonlinear media,” Phys. Rev. Lett. 91, 093905 (2003).
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I. Velchev, R. Pattnaik, and J. Toulouse, “Two-beam modulation instability in noninstantaneous nonlinear media,” Phys. Rev. Lett. 91, 093905 (2003).
[CrossRef]

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Wadsworth, W. J.

Wen, S.

L. Zhang, S. Wen, X. Fu, J. Deng, J. Zhang, and D. Fan, “Spatiotemporal instability in dispersive nonlinear Kerr medium with a finite response time,” Opt. Commun. 283, 2251–2257 (2010).
[CrossRef]

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W. Shuang-Chun, S. Wen-Hua, Z. Hua, F. Xi-Quan, Q. Lie-Jia, and F. Dian-Yuan, “Influence of higher-order dispersions and Raman delayed response on modulation instability in microstructured fibres,” Chin. Phys. Lett. 20, 852–854 (2003).
[CrossRef]

Wetzel, B.

Wise, F. W.

Wong, G. K. L.

Wright, E. M.

Xi-Quan, F.

W. Shuang-Chun, S. Wen-Hua, Z. Hua, F. Xi-Quan, Q. Lie-Jia, and F. Dian-Yuan, “Influence of higher-order dispersions and Raman delayed response on modulation instability in microstructured fibres,” Chin. Phys. Lett. 20, 852–854 (2003).
[CrossRef]

Yao, S.

S. Yao, C. Karaguleff, A. Gabel, R. Fortenberry, C. T. Seaton, and G. I. Stegeman, “Ultrafast carrier and grating lifetimes in semiconductor-doped glasses,” Appl. Phys. Lett. 46, 801–802 (1985).
[CrossRef]

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L. Zhang, S. Wen, X. Fu, J. Deng, J. Zhang, and D. Fan, “Spatiotemporal instability in dispersive nonlinear Kerr medium with a finite response time,” Opt. Commun. 283, 2251–2257 (2010).
[CrossRef]

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A. Hasegawa and F. Tappert, “Generation of a train of soliton pulses by induced modulational instability in optical fibers,” Appl. Phys. Lett. 23, 142–244 (1973).
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[CrossRef]

Chin. Phys. Lett.

W. Shuang-Chun, S. Wen-Hua, Z. Hua, F. Xi-Quan, Q. Lie-Jia, and F. Dian-Yuan, “Influence of higher-order dispersions and Raman delayed response on modulation instability in microstructured fibres,” Chin. Phys. Lett. 20, 852–854 (2003).
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R. V. J. Raja, A. Husakou, J. Hermann, and K. Porsezian, “Supercontinuum generation in liquid-filled photonic crystal fiber with slow nonlinear response,” J. Opt. Soc. Am. B 27, 1763–1768 (2010).
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[CrossRef]

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, 889–900 (1989).
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C. Cambournac, H. Maillotte, E. Lantz, J. M. Dudley, and M. Chauvet, “Spatiotemporal behavior of periodic arrays of spatial solitons in a planar waveguide with relaxing Kerr nonlinearity,” J. Opt. Soc. Am. B 19, 574–585 (2002).
[CrossRef]

P. T. Dinda and K. Porsezian, “Impact of fourth-order dispersion in the modulational instability spectra of wave propagation in glass fibers with saturable nonlinearity,” J. Opt. Soc. Am. B 27, 1143–1152 (2010).
[CrossRef]

Opt. Commun.

L. Zhang, S. Wen, X. Fu, J. Deng, J. Zhang, and D. Fan, “Spatiotemporal instability in dispersive nonlinear Kerr medium with a finite response time,” Opt. Commun. 283, 2251–2257 (2010).
[CrossRef]

X. Liu, J. W. Haus, and S. Shahriar, “Modulation instability for a relaxational Kerr medium,” Opt. Commun. 281, 2907–2912 (2008).
[CrossRef]

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

F. K. Abdullaev, S. A. Darmanyan, S. Bischoff, P. L. Christiansen, and M. P. Sorensen, “Modulational instability in optical fibers near the zero dispersion point,” Opt. Commun. 108, 60–64 (1994).
[CrossRef]

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]

P. T. Dinda, C. Ngabireng, K. Porsezian, and B. Kalithasan, “Modulational instability in optical fibers with arbitrary higher-order dispersion and delayed Raman response,” Opt. Commun. 266, 142–150 (2006).
[CrossRef]

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[CrossRef]

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I. Velchev, R. Pattnaik, and J. Toulouse, “Two-beam modulation instability in noninstantaneous nonlinear media,” Phys. Rev. Lett. 91, 093905 (2003).
[CrossRef]

M.-F. Shih, C. C. Jeng, F. W. Sheu, and C. Y. Lin, “Spatiotemporal optical modulation instability of coherent light in noninstantaneous nonlinear media,” Phys. Rev. Lett. 88, 133902 (2002).
[CrossRef]

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Figures (16)

Fig. 1.
Fig. 1.

MI gain spectra G(Ω) in the regime of fast response for different combinations of Γ and τ [i.e., A(Γ=0,τ=0), B(Γ=0.01,τ=0.01), and C(Γ=0.1,τ=0.01)]. The system parameters are fixed (as stated earlier) and are maintained constant throughout the discussion.

Fig. 2.
Fig. 2.

MI spectrum G(Ω) in the regime of slow response for τ=0.1ps and Γ(A=0,B=0.01,C=0.01)W1.

Fig. 3.
Fig. 3.

Plot of OMF and Gmax as a function of delay time for different saturation parameters Γ.

Fig. 4.
Fig. 4.

MI spectrum as a function in the regime of fast response. Curve A is the instantaneous Kerr case. Curves B and C are for τ=0.01ps with Γ taking 0.01 and 0.1W1, respectively. Curve D is for the τ=0.1 and Γ=0.01W1.

Fig. 5.
Fig. 5.

MI spectrum G(Ω) in the regime of slow response for τ=0.1ps and Γ(A=0,B=0.01,C=0.1)W1.

Fig. 6.
Fig. 6.

Plot of OMF and Gmax as a function of delay time for different saturation parameter Γ.

Fig. 7.
Fig. 7.

MI spectrum for some representative values of τ and Γ. Curves A and B are for τ=0.01ps with Γ taking 0.01 and 0.1W1, respectively. Curves C and D are for τ=0.1ps with Γ taking 0.01 and 0.1W1, respectively.

Fig. 8.
Fig. 8.

Plot of (a) OMF and (b) Gmax as a function of the delay time for different saturation parameters Γ.

Fig. 9.
Fig. 9.

MI spectrum in the regime of fast response (τ=0.01ps).

Fig. 10.
Fig. 10.

MI spectrum G(Ω) in the regime of slow response for τ=0.1ps and Γ(A=0,B=0.01,C=0.1)W1.

Fig. 11.
Fig. 11.

Plot of (a) OMF and (b) Gmax as a function of delay time for β2>0 and β4<0.

Fig. 12.
Fig. 12.

Illustration of FOD in the MI spectrum for Γ=0.01W1 at β4=(A=3,B=5,C=7)ps4km1.

Fig. 13.
Fig. 13.

MI spectrum at fast and slow response represented by the red solid line (τ=0.01ps) and the green dashed line (τ=0.1ps), respectively for Γ(A=0.01;B=0.01)W1.

Fig. 14.
Fig. 14.

Plot of (a) OMF and (b) Gmax as a function of delay time for Γ=0.01W1 at β2=0 and β2=60ps2km1.

Fig. 15.
Fig. 15.

MI spectrum at dispersionless limit for different values of τ. Curves τ(A=0.01,B=0.05,C=0.1,D=1)ps.

Fig. 16.
Fig. 16.

Plot of OMF and Gmax as a function of delay for Γ=0.01W1.

Equations (30)

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

Ez+n=24βkin1n!nEtn=γf(Γ|E|2)ΓE,
f(Γ|E|2)=Γ|E|21+Γ|E|2,
Ez+iβ222Et2β363Et3iβ4244Et4=iγNE,
Nt=1τ[N+f˜(Γ,|E|2)],
Es=E0exp[if˜(Γ|E0|2)z],
Ns=f˜(Γ,|E0|2).
Ep=(E0+a(z,t))exp[if˜(Γ|E0|2)z],
Np=f˜(Γ,|E0|2)+n(z,t),
iaz=β222at2+iβ363at3β4244at4+γnE0,
int=1τ[n+Γf˜(Γ,|E0|2)E0(a+a*)].
a(z,t)=a1exp[i(KzΩt)]+a2exp[i(KzΩt)],
[K+D(Ω)+γ˜E02γ˜E02γ˜E02K+E(Ω)+γ˜E02],
D(Ω)β2Ω22β3Ω36+β4Ω424,
E(Ω)β2Ω22+β3Ω36+β4Ω424,
γ˜γ(1+iΩτ)(1+ΓE02)2.
K=β3Ω36±[(β2Ω22+β4Ω424)(β2Ω22+β4Ω424+2γ˜E02)]1/2.
G(Ω)=2Im(K)=2γ˜2E04(γ˜E02+β2Ω22+β4Ω424)2.
Ω2<Ω12,Ω22<Ω2<Ω32.
Ω126β2β412β4β224β4γP3,
Ω2212β2β44γPβ2,
Ω3212β2β4.
ΩOMF12γPβ2,
ΩOMF112β2β42γPβ2.
Ω126β2β412β4β224β4γP3,
ΩOMF2γPβ2.
Ω2212β2β44γPβ2,
Ω3212β2β4.
OMF12β2β42γPβ2.
Ω1[48γP|β4|]1/4,
ΩOMF[24γPβ2]1/4.

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