Abstract

We analyze the modulational instability (MI) of light waves in glass fibers with a local saturable nonlinear refractive index. We identify and discuss the salient features of the effect of the fourth order of the fiber dispersion, in the MI spectra. Particularly, we find that in fibers with negative sign of the second-order dispersion and positive sign of the fourth-order dispersion (FOD), the two existing types of MI processes, called processes of type I, which generate a single pair of sidebands, and processes of type II, which lead to two pairs of sidebands, become highly sensitive to the magnitude of the FOD, both quantitatively and qualitatively. We demonstrate the existence of a critical FOD and two branches of critical pump powers, from which we construct the global map of the MI behaviors in the system, including clear delimitations of the respective domains of the existence of MI processes of types I and II.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  29. 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]
  30. P. Tchofo Dinda, C. M. Ngabireng, K. Porsezian, and B. Kalithansan, “Modulational instability in optical fibers with arbitrary higher-order dispersion and delayed Raman response,” Opt. Commun. 266, 142–150 (2006).
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    [CrossRef]
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    [CrossRef]
  37. A. Labruyere, S. Ambomo, C. Ngabireng, P. Tchofo Dinda, K. Nakkeeran, and K. Porsezian, “Suppression of sideband frequency shifts in the modulational instability spectra of wave propagation in optical fiber systems,” Opt. Lett. 32, 1287–1289 (2007).
    [CrossRef] [PubMed]

2009 (1)

2008 (1)

2007 (2)

2006 (2)

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

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

2005 (1)

K. Porsezian, K. Senthilnathan, and S. Devipriya, “Modulational instability in fiber Bragg grating with non-Kerr nonlinearity,” IEEE J. Quantum Electron. 41, 789–796 (2005).
[CrossRef]

2003 (3)

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]

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]

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)

1998 (1)

1996 (3)

1995 (2)

N. Da Dalt, C. De Angelis, G. F. Nalesso, and M. Santagiustina, “Dynamics of induced modulational instability in waveguides with saturable nonlinearity,” Opt. Commun. 121, 69–72 (1995).
[CrossRef]

I. Kang, T. D. Krauss, F. W. Wise, B. G. Aitken, and N. F. Borrelli, “Femtosecond measurement of enhanced optical nonlinearities of sulfide glasses and heavy-metal-doped oxide glasses,” J. Opt. Soc. Am. B 12, 2053–2059 (1995).
[CrossRef]

1993 (2)

1991 (4)

1990 (1)

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78, 137–142 (1990).
[CrossRef]

1989 (4)

E. J. Greer, D. M. Patrick, P. G. J. Wigley, and J. R. Taylor, “Generation of 2 THz repetition rate pulse trains through induced modulational instability,” Electron. Lett. 25, 1246–1248 (1989).
[CrossRef]

S. Sudo, H. Itoh, K. Okamoto, and K. Kubodora, “Generation of 5 THz repetition optical pulses by modulation instability in optical fibers,” Appl. Phys. Lett. 54, 993–994 (1989).
[CrossRef]

K. W. DeLong, A. Gabel, C. T. Seaton, and G. I. Stegeman, “Nonlinear transmission, degenerate four-wave mixing, photodarkening, and the effects of carrier-density-dependent nonlinearities in semiconductor-doped glasses,” J. Opt. Soc. Am. B 6, 1306–1313 (1989).
[CrossRef]

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989).
[CrossRef]

1988 (2)

C. N. Ironside, T. J. Cullen, B. S. Bhumbra, J. Bell, W. C. Banyai, N. Finlayson, C. T. Seaton, and G. I. Stegeman, “Nonlinear-optical effects in ion-exchanged semiconductor-doped glass waveguides,” J. Opt. Soc. Am. B 5, 492–495 (1988).
[CrossRef]

L. H. Acioli, A. S. L. Gomes, and J. R. Rios Leite, “Measurement of high-order optical nonlinear susceptibilities in semiconductor-doped glasses,” Appl. Phys. Lett. 53, 1788–1790 (1988).
[CrossRef]

1987 (1)

1986 (1)

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

1985 (1)

1984 (1)

1983 (1)

1980 (1)

A. Hasegawa and W. F. Brinkman, “Tunable coherent IR and FIR sources utilizing modulational instability,” IEEE J. Quantum Electron. 16, 694–697 (1980).
[CrossRef]

Abdullaev, F. Kh.

F. Kh. Abdullaev, S. A. Darmanyan, A. Kobyakov, F. Lederer, K. Porsezian, and B. Kalithansan, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220, 213–218 (1996).
[CrossRef]

Acioli, L. H.

L. H. Acioli, A. S. L. Gomes, and J. R. Rios Leite, “Measurement of high-order optical nonlinear susceptibilities in semiconductor-doped glasses,” Appl. Phys. Lett. 53, 1788–1790 (1988).
[CrossRef]

Aggarwal, I. D.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2008).

Aitken, B. G.

Ambomo, S.

Banyai, W. C.

Beckwitt, K.

Bell, J.

Bhumbra, B. S.

Borges, N. M.

Borrelli, N. F.

I. Kang, T. D. Krauss, F. W. Wise, B. G. Aitken, and N. F. Borrelli, “Femtosecond measurement of enhanced optical nonlinearities of sulfide glasses and heavy-metal-doped oxide glasses,” J. Opt. Soc. Am. B 12, 2053–2059 (1995).
[CrossRef]

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989).
[CrossRef]

Brinkman, W. F.

A. Hasegawa and W. F. Brinkman, “Tunable coherent IR and FIR sources utilizing modulational instability,” IEEE J. Quantum Electron. 16, 694–697 (1980).
[CrossRef]

Cambrell, G. K.

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] [PubMed]

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]

Chen, Y. F.

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] [PubMed]

Cullen, T. J.

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]

Da Dalt, N.

N. Da Dalt, C. De Angelis, G. F. Nalesso, and M. Santagiustina, “Dynamics of induced modulational instability in waveguides with saturable nonlinearity,” Opt. Commun. 121, 69–72 (1995).
[CrossRef]

Da Silva, G. L.

Darmanyan, S. A.

F. Kh. Abdullaev, S. A. Darmanyan, A. Kobyakov, F. Lederer, K. Porsezian, and B. Kalithansan, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220, 213–218 (1996).
[CrossRef]

De Angelis, C.

N. Da Dalt, C. De Angelis, G. F. Nalesso, and M. Santagiustina, “Dynamics of induced modulational instability in waveguides with saturable nonlinearity,” Opt. Commun. 121, 69–72 (1995).
[CrossRef]

de Sterke, C. M.

DeLong, K. W.

Devipriya, S.

K. Porsezian, K. Senthilnathan, and S. Devipriya, “Modulational instability in fiber Bragg grating with non-Kerr nonlinearity,” IEEE J. Quantum Electron. 41, 789–796 (2005).
[CrossRef]

Doran, N. J.

Drummond, P. D.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78, 137–142 (1990).
[CrossRef]

Dudley, J. M.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78, 137–142 (1990).
[CrossRef]

Dumbaugh, W. H.

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989).
[CrossRef]

Finlayson, N.

Flytzanis, C.

Gabel, A.

Gatz, S.

Gleria, I.

Gomes, A. S. L.

L. H. Acioli, A. S. L. Gomes, and J. R. Rios Leite, “Measurement of high-order optical nonlinear susceptibilities in semiconductor-doped glasses,” Appl. Phys. Lett. 53, 1788–1790 (1988).
[CrossRef]

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] [PubMed]

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]

Greer, E. J.

E. J. Greer, D. M. Patrick, P. G. J. Wigley, and J. R. Taylor, “Generation of 2 THz repetition rate pulse trains through induced modulational instability,” Electron. Lett. 25, 1246–1248 (1989).
[CrossRef]

Haelterman, M.

Hall, D. W.

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989).
[CrossRef]

Harvey, J. D.

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]

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78, 137–142 (1990).
[CrossRef]

Hasegawa, A.

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

A. Hasegawa and W. F. Brinkman, “Tunable coherent IR and FIR sources utilizing modulational instability,” IEEE J. Quantum Electron. 16, 694–697 (1980).
[CrossRef]

Herrmann, J.

Hickmann, J. M.

Ironside, C. N.

Itoh, H.

S. Sudo, H. Itoh, K. Okamoto, and K. Kubodora, “Generation of 5 THz repetition optical pulses by modulation instability in optical fibers,” Appl. Phys. Lett. 54, 993–994 (1989).
[CrossRef]

Jain, R. K.

Kalithansan, B.

S. Ambomo, C. M. Ngabireng, P. Tchofo Dinda, A. Labruyere, K. Porsezian, and B. Kalithansan, “Critical behavior with dramatic enhancement of modulational instability gain in fiber systems with periodic variation dispersion,” J. Opt. Soc. Am. B 25, 425–433 (2008).
[CrossRef]

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

F. Kh. Abdullaev, S. A. Darmanyan, A. Kobyakov, F. Lederer, K. Porsezian, and B. Kalithansan, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220, 213–218 (1996).
[CrossRef]

Kang, I.

Kennedy, T. A. B.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78, 137–142 (1990).
[CrossRef]

Knight, J. C.

Kobyakov, A.

F. Kh. Abdullaev, S. A. Darmanyan, A. Kobyakov, F. Lederer, K. Porsezian, and B. Kalithansan, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220, 213–218 (1996).
[CrossRef]

Krauss, T. D.

Kubodora, K.

S. Sudo, H. Itoh, K. Okamoto, and K. Kubodora, “Generation of 5 THz repetition optical pulses by modulation instability in optical fibers,” Appl. Phys. Lett. 54, 993–994 (1989).
[CrossRef]

Kull, M.

Kumar, A.

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]

Labruyere, A.

Langbein, U.

Lederer, F.

F. Kh. Abdullaev, S. A. Darmanyan, A. Kobyakov, F. Lederer, K. Porsezian, and B. Kalithansan, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220, 213–218 (1996).
[CrossRef]

U. Langbein, F. Lederer, T. Peschel, and H. E. Ponath, “Nonlinear guided waves in saturable nonlinear media,” Opt. Lett. 10, 571–573 (1985).
[CrossRef] [PubMed]

Leonhardt, R.

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]

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78, 137–142 (1990).
[CrossRef]

Lind, R. C.

Lukasik, J.

Lyra, M. L.

Millot, G.

Nakkeeran, K.

Nalesso, G. F.

N. Da Dalt, C. De Angelis, G. F. Nalesso, and M. Santagiustina, “Dynamics of induced modulational instability in waveguides with saturable nonlinearity,” Opt. Commun. 121, 69–72 (1995).
[CrossRef]

Newhouse, M. A.

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989).
[CrossRef]

Ngabireng, C.

Ngabireng, C. M.

S. Ambomo, C. M. Ngabireng, P. Tchofo Dinda, A. Labruyere, K. Porsezian, and B. Kalithansan, “Critical behavior with dramatic enhancement of modulational instability gain in fiber systems with periodic variation dispersion,” J. Opt. Soc. Am. B 25, 425–433 (2008).
[CrossRef]

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

Okamoto, K.

S. Sudo, H. Itoh, K. Okamoto, and K. Kubodora, “Generation of 5 THz repetition optical pulses by modulation instability in optical fibers,” Appl. Phys. Lett. 54, 993–994 (1989).
[CrossRef]

Patrick, D. M.

E. J. Greer, D. M. Patrick, P. G. J. Wigley, and J. R. Taylor, “Generation of 2 THz repetition rate pulse trains through induced modulational instability,” Electron. Lett. 25, 1246–1248 (1989).
[CrossRef]

Peschel, T.

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]

S. Pitois, M. Haelterman, and G. Millot, “Bragg modulational instability induced by a dynamic grating in an optical fiber,” Opt. Lett. 26, 780–782 (2001).
[CrossRef]

Ponath, H. E.

Porsezian, K.

S. Ambomo, C. M. Ngabireng, P. Tchofo Dinda, A. Labruyere, K. Porsezian, and B. Kalithansan, “Critical behavior with dramatic enhancement of modulational instability gain in fiber systems with periodic variation dispersion,” J. Opt. Soc. Am. B 25, 425–433 (2008).
[CrossRef]

A. Labruyere, S. Ambomo, C. Ngabireng, P. Tchofo Dinda, K. Nakkeeran, and K. Porsezian, “Suppression of sideband frequency shifts in the modulational instability spectra of wave propagation in optical fiber systems,” Opt. Lett. 32, 1287–1289 (2007).
[CrossRef] [PubMed]

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

K. Porsezian, K. Senthilnathan, and S. Devipriya, “Modulational instability in fiber Bragg grating with non-Kerr nonlinearity,” IEEE J. Quantum Electron. 41, 789–796 (2005).
[CrossRef]

F. Kh. Abdullaev, S. A. Darmanyan, A. Kobyakov, F. Lederer, K. Porsezian, and B. Kalithansan, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220, 213–218 (1996).
[CrossRef]

Ricard, D.

Rios Leite, J. R.

L. H. Acioli, A. S. L. Gomes, and J. R. Rios Leite, “Measurement of high-order optical nonlinear susceptibilities in semiconductor-doped glasses,” Appl. Phys. Lett. 53, 1788–1790 (1988).
[CrossRef]

Roussignol, P.

Sanghera, J. S.

Santagiustina, M.

N. Da Dalt, C. De Angelis, G. F. Nalesso, and M. Santagiustina, “Dynamics of induced modulational instability in waveguides with saturable nonlinearity,” Opt. Commun. 121, 69–72 (1995).
[CrossRef]

Seaton, C. T.

Senthilnathan, K.

K. Porsezian, K. Senthilnathan, and S. Devipriya, “Modulational instability in fiber Bragg grating with non-Kerr nonlinearity,” IEEE J. Quantum Electron. 41, 789–796 (2005).
[CrossRef]

Seve, E.

Smith, N. J.

Sombra, A. S. B.

St. J. Russell, P.

Stegeman, G. I.

Sudo, S.

S. Sudo, H. Itoh, K. Okamoto, and K. Kubodora, “Generation of 5 THz repetition optical pulses by modulation instability in optical fibers,” Appl. Phys. Lett. 54, 993–994 (1989).
[CrossRef]

Tai, K.

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

Taylor, J. R.

E. J. Greer, D. M. Patrick, P. G. J. Wigley, and J. R. Taylor, “Generation of 2 THz repetition rate pulse trains through induced modulational instability,” Electron. Lett. 25, 1246–1248 (1989).
[CrossRef]

Tchofo Dinda, P.

Tomita, A.

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

Wadsworth, W. J.

Wang, X. H.

Weidman, D. L.

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989).
[CrossRef]

Wigley, P. G. J.

E. J. Greer, D. M. Patrick, P. G. J. Wigley, and J. R. Taylor, “Generation of 2 THz repetition rate pulse trains through induced modulational instability,” Electron. Lett. 25, 1246–1248 (1989).
[CrossRef]

Wise, F. K.

Wise, F. W.

Wong, G. K. L.

Xiang, A.

X. Zhong and A. Xiang, “Modulation polarization instability of light in a nonlinear birefringent dispersive medium,” Opt. Fiber Technol. 13, 271–279 (2007).
[CrossRef]

Zhong, X.

X. Zhong and A. Xiang, “Modulation polarization instability of light in a nonlinear birefringent dispersive medium,” Opt. Fiber Technol. 13, 271–279 (2007).
[CrossRef]

Appl. Phys. Lett. (3)

S. Sudo, H. Itoh, K. Okamoto, and K. Kubodora, “Generation of 5 THz repetition optical pulses by modulation instability in optical fibers,” Appl. Phys. Lett. 54, 993–994 (1989).
[CrossRef]

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989).
[CrossRef]

L. H. Acioli, A. S. L. Gomes, and J. R. Rios Leite, “Measurement of high-order optical nonlinear susceptibilities in semiconductor-doped glasses,” Appl. Phys. Lett. 53, 1788–1790 (1988).
[CrossRef]

Electron. Lett. (1)

E. J. Greer, D. M. Patrick, P. G. J. Wigley, and J. R. Taylor, “Generation of 2 THz repetition rate pulse trains through induced modulational instability,” Electron. Lett. 25, 1246–1248 (1989).
[CrossRef]

IEEE J. Quantum Electron. (2)

K. Porsezian, K. Senthilnathan, and S. Devipriya, “Modulational instability in fiber Bragg grating with non-Kerr nonlinearity,” IEEE J. Quantum Electron. 41, 789–796 (2005).
[CrossRef]

A. Hasegawa and W. F. Brinkman, “Tunable coherent IR and FIR sources utilizing modulational instability,” IEEE J. Quantum Electron. 16, 694–697 (1980).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (12)

S. Ambomo, C. M. Ngabireng, P. Tchofo Dinda, A. Labruyere, K. Porsezian, and B. Kalithansan, “Critical behavior with dramatic enhancement of modulational instability gain in fiber systems with periodic variation dispersion,” J. Opt. Soc. Am. B 25, 425–433 (2008).
[CrossRef]

C. M. de Sterke, “Theory of modulational instability in fiber Bragg gratings,” J. Opt. Soc. Am. B 15, 2660–2667 (1998).
[CrossRef]

G. L. Da Silva, I. Gleria, M. L. Lyra, and A. S. B. Sombra, “Modulational instability in lossless fibers with saturable delayed nonlinear response,” J. Opt. Soc. Am. B 26, 183–188 (2009).
[CrossRef]

S. Gatz and J. Herrmann, “Soliton propagation in materials with saturable nonlinearity,” J. Opt. Soc. Am. B 8, 2296–2302 (1991).
[CrossRef]

J. Herrmann, “propagation of ultrashort light pulses in fibers with saturable nonlinearity in the normal-dispersion region,” J. Opt. Soc. Am. B 8, 1507–1511 (1991).
[CrossRef]

K. W. DeLong, A. Gabel, C. T. Seaton, and G. I. Stegeman, “Nonlinear transmission, degenerate four-wave mixing, photodarkening, and the effects of carrier-density-dependent nonlinearities in semiconductor-doped glasses,” J. Opt. Soc. Am. B 6, 1306–1313 (1989).
[CrossRef]

I. Kang, T. D. Krauss, F. W. Wise, B. G. Aitken, and N. F. Borrelli, “Femtosecond measurement of enhanced optical nonlinearities of sulfide glasses and heavy-metal-doped oxide glasses,” J. Opt. Soc. Am. B 12, 2053–2059 (1995).
[CrossRef]

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

P. Roussignol, D. Ricard, J. Lukasik, and C. Flytzanis, “New results on optical phase conjugation in semiconductor-doped glasses,” J. Opt. Soc. Am. B 4, 5–13 (1987).
[CrossRef]

C. N. Ironside, T. J. Cullen, B. S. Bhumbra, J. Bell, W. C. Banyai, N. Finlayson, C. T. Seaton, and G. I. Stegeman, “Nonlinear-optical effects in ion-exchanged semiconductor-doped glass waveguides,” J. Opt. Soc. Am. B 5, 492–495 (1988).
[CrossRef]

J. L. Coutaz and M. Kull, “Saturation of nonlinear index of refraction in semiconductor-doped glass,” J. Opt. Soc. Am. B 8, 95–98 (1991).
[CrossRef]

X. H. Wang and G. K. Cambrell, “Simulation of strong nonlinear effects in optical waveguides,” J. Opt. Soc. Am. B 10, 2048–2055 (1993).
[CrossRef]

Opt. Commun. (5)

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. Tchofo Dinda, C. M. Ngabireng, K. Porsezian, and B. Kalithansan, “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. Tchofo Dinda, “Modulational instability in fiber systems with periodic loss compensation and dispersion management,” Opt. Commun. 219, 221–232 (2003).
[CrossRef]

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78, 137–142 (1990).
[CrossRef]

N. Da Dalt, C. De Angelis, G. F. Nalesso, and M. Santagiustina, “Dynamics of induced modulational instability in waveguides with saturable nonlinearity,” Opt. Commun. 121, 69–72 (1995).
[CrossRef]

Opt. Fiber Technol. (1)

X. Zhong and A. Xiang, “Modulation polarization instability of light in a nonlinear birefringent dispersive medium,” Opt. Fiber Technol. 13, 271–279 (2007).
[CrossRef]

Opt. Lett. (8)

U. Langbein, F. Lederer, T. Peschel, and H. E. Ponath, “Nonlinear guided waves in saturable nonlinear media,” Opt. Lett. 10, 571–573 (1985).
[CrossRef] [PubMed]

A. Labruyere, S. Ambomo, C. Ngabireng, P. Tchofo Dinda, K. Nakkeeran, and K. Porsezian, “Suppression of sideband frequency shifts in the modulational instability spectra of wave propagation in optical fiber systems,” Opt. Lett. 32, 1287–1289 (2007).
[CrossRef] [PubMed]

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] [PubMed]

P. Tchofo Dinda, G. Millot, E. Seve, and M. Haelterman, “Demonstration of nonlinear gap in the modulational instability spectra of wave propagation in highly birefringents fibers,” Opt. Lett. 21, 1640–1642 (1996).
[CrossRef]

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

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

S. Pitois, M. Haelterman, and G. Millot, “Bragg modulational instability induced by a dynamic grating in an optical fiber,” Opt. Lett. 26, 780–782 (2001).
[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] [PubMed]

Phys. Lett. A (1)

F. Kh. Abdullaev, S. A. Darmanyan, A. Kobyakov, F. Lederer, K. Porsezian, and B. Kalithansan, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220, 213–218 (1996).
[CrossRef]

Phys. Rev. A (1)

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]

Phys. Rev. Lett. (1)

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

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2008).

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Figures (8)

Fig. 1
Fig. 1

Plot of the OMF as a function of pump power P 0 , for positive β 2 and negative β 4 . β 2 = 2.5 ps 2 / km .

Fig. 2
Fig. 2

Plot of the OMF as a function of pump power P 0 , for negative β 2 and negative β 4 . β 2 = 2.5 ps 2 / km .

Fig. 3
Fig. 3

Schematic representation of the MI map in the fiber system for negative β 2 and positive β 4 .

Fig. 4
Fig. 4

Plot of the OMF as a function of β 4 , for negative β 2 and positive β 4 . β 2 = 2.5 ps 2 / km .

Fig. 5
Fig. 5

Plot of the OMF as a function of pump power P 0 , for negative β 2 and positive β 4 . β 2 = 2.5 ps 2 / km .

Fig. 6
Fig. 6

Plots of the gain spectra in the region of negative β 2 and positive β 4 , for different values of β 4 , and pump powers of P 0 = 10   W and P 0 = 35   W . β 2 = 2.5 ps 2 / km , γ = 3 W 1 / km , and L = 350   m (200 m) for P 0 = 10   W ( P 0 = 35   W ) . The solid curves correspond to the results obtained by direct numerical simulation of the NLSE (2). The initial intensity of the spectral components at z = 0 was a weak noise. The dotted curves correspond to the results obtained by our analytical formula (13).

Fig. 7
Fig. 7

Plots of the gain spectra in the same conditions as in Fig. 6 but with P 0 = P S = 100   W and P 0 = 285   W . Here L = 150   m .

Fig. 8
Fig. 8

Plots of the gain spectra in the same conditions as in Fig. 6 but with P 0 = 325   W and P 0 = 450   W . Here L = 150   m .

Equations (39)

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Ω cmi = 2 γ P 0 / | β 2 | .
A z + i β 2 2 2 A t 2 β 3 6 3 A t 3 i β 4 24 4 A t 4 i γ g ( | A | 2 ) A = 0 ,
g ( | A | 2 ) = | A | 2 1 + Γ | A | 2 ,
γ η γ s g = η n 2 ω c A eff ,
A s = P 0   exp [ i ϕ ( z ) ] ,
ϕ ( z ) = γ P 0 z 1 + Γ P 0 .
A ( z , t ) = ( P 0 + q ( z , t ) ) exp ( i ϕ ) ,
q ( z , t ) = u ( z ) e i Ω t + v ( z ) e i Ω t ,
d Y d z = i M Y = i [ D ( Ω ) + γ ̃ P 0 γ ̃ P 0 γ ̃ P 0 D ̃ ( Ω ) γ ̃ P 0 ] Y ,
Y = [ u ( z ) v ( z ) ] ,
D ( Ω ) β 2 Ω 2 2 β 3 Ω 3 6 + β 4 Ω 4 24 ,
D ̃ ( Ω ) β 2 Ω 2 2 + β 3 Ω 3 6 + β 4 Ω 4 24 ,
γ ̃ γ / Q 2 ,
Q 1 + Γ P 0 .
K 2 + [ D ̃ ( Ω ) D ( Ω ) ] K γ P 0 Q 2 [ D ̃ ( Ω ) + D ( Ω ) ] D ( Ω ) D ̃ ( Ω ) = 0 ,
K = β 3 Ω 3 6 ± ( γ ̃ P 0 + β 2 Ω 2 2 + β 4 Ω 4 24 ) 2 γ ̃ 2 P 0 2 .
G ( Ω ) = 2   Im ( K ) = 2 γ ̃ 2 P 0 2 ( γ ̃ P 0 + β 2 Ω 2 2 + β 4 Ω 4 24 ) 2 .
β 2 2 Ω 2 + β 4 Ω 4 24 + γ ̃ P 0 = 0 ,
β 2 Ω + β 4 Ω 3 6 = 0.
Ω 1 , 2 = 6 β 2 β 4 ± 6 β 4 β 2 2 2 3 γ ̃ β 4 P 0 ,
Ω 0 = 6 β 2 β 4 .
Ω opt = Ω 0 [ 1 + 1 + P 0 P 0 c ] 1 / 2 ,
P 0 c = 3 | β 2 | 2 Q 2 2 | β 4 | γ .
Ω opt = Ω 0 [ P 0 / P 0 c + 1 1 ] 1 / 2 .
Ω opt 2 γ P 0 | β 2 | = Ω cmi .
Ω opt 2 Ω 0 2 P 0 / P 0 c 1 Γ 24 γ | β 4 | P 0 .
Ω 1 , 2 = Ω 0 [ 1 ± 1 P 0 / P 0 c ] 1 / 2 .
P 0 > P 0 c .
ξ Γ 2 P 0 2 + ( 2 Γ ξ 1 ) P 0 + ξ < 0 ,
ξ 3 | β 2 | 2 / ( 2 γ | β 4 | ) .
P c 1 < P 0 < P c 2 ,
P c 1 1 2 Γ ξ Δ 2 ξ Γ 2 ,
P c 2 1 2 Γ ξ + Δ 2 ξ Γ 2 ,
Δ = 1 4 Γ ξ .
β 4 > β 4 c 6 | β 2 | 2 Γ γ .
P 0 > ξ .
Ω 2 2 Ω 0 = 2 3 | β 2 | | β 4 | .
Ω 1 , 2 = Ω 0 [ σ 2 σ 4 ± 1 σ 4 1 σ 4 η P 0 / P 0 c s g ] 1 / 2 ,
P 0 c s g η P 0 c = 3 | β 2 | 2 Q 2 2 | β 4 | γ s g .

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