Abstract

We report the modulational instability (MI) analysis in silicon-on-insulator waveguides under fourth-order dispersion. The two-photon absorption (TPA) generates four symmetric optimum frequencies in the MI gain spectrum. The free-carrier absorption is found to enhance the value of the central MI gain. The chirp amplifies the intensity of the main pulse train peaks, leading to input profile independence. It shifts the occurrence of these peaks at short propagation distances. The absorption coefficients counteract the chirp, creating a pump dependence, and the high values of TPA destroy drastically the spontaneous breakup mechanism, leading to pump depletion.

© 2013 Optical Society of America

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2012 (4)

2011 (4)

J. Wen, H. Liu, N. Huang, Q. Sun, and W. Zhao, “Influence of the initial chirp on the supercontinuum generation in silicon-on-insulator waveguide,” Appl. Phys. B 104, 867–871 (2011).
[CrossRef]

J. H. Li, K. S. Chiang, and K. W. Chow, “Modulation instabilities in two-core optical fibers,” J. Opt. Soc. Am. B 28, 1693–1701 (2011).
[CrossRef]

C. M. Ngabireng, S. Ambomo, P. T. Dinda, and A. B. Moubissi, “Loss effects in the spectra of polarization modulational instability in weakly birefringent optical fibers,” J. Opt. 13, 085201 (2011).
[CrossRef]

M. Erkintalo, K. Hammami, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107, 253901 (2011).
[CrossRef]

2010 (3)

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

J. C. Travers, “Blue extension of optical fibre supercontinuum generation,” J. Opt. 12, 113001 (2010).
[CrossRef]

2009 (4)

A. M. Kamchatnov and M. Salerno, “Dark soliton oscillations in Bose–Einstein condensates with multi-body interactions,” J. Phys. B 42, 185303 (2009).

P. Das, M. Vyas, and P. K. Panigrahi, “Loss of superfluidity in the Bose–Einstein condensate in an optical lattice with cubic and quintic nonlinearity,” J. Phys. B. 42, 245304 (2009).

V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: the beginning,” Physica D 238, 540–548 (2009).
[CrossRef]

C. G. L. Tiofack, A. Mohamadou, T. C. Kofané, and A. B. Moubissi, “Generation of pulse trains in nonlinear optical fibers through the generalized complex Ginzburg–Landau equation,” Phys. Rev. E 80, 066604 (2009).
[CrossRef]

2008 (2)

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

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Femtosecond pulse propagation in silicon waveguides: variational approach and its advantages,” Opt. Commun. 281, 5889–5893 (2008).
[CrossRef]

2007 (4)

F. Ndzana, A. Mohamadou, and T. C. Kofané, “Modulational instability in the cubic quintic nonlinear Schrödinger equation through the variational approach,” Opt. Commun. 275, 421–428 (2007).
[CrossRef]

A. Demircan and U. Bandelow, “Analysis of the interplay between soliton fission and modulation instability in supercontinuum generation,” Appl. Phys. B 86, 31–39 (2007).
[CrossRef]

L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32, 391–393 (2007).
[CrossRef]

L. Yin and G. P. Agrawal, “Impact of two-photon absorption on self-phase modulation in silicon waveguides,” Opt. Lett. 32, 2031–2033 (2007).
[CrossRef]

2006 (3)

R. E. Kennedy, S. V. Popov, and J. R. Taylor, “Ytterbium gain band self-induced modulation instability laser,” Opt. Lett. 31, 167–169 (2006).
[CrossRef]

B. Jalali and S. Fathpour, “Silicon photonics,” IEEE J. Lightwave Technol. 24, 4600–4615 (2006).
[CrossRef]

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12, 1678–1687 (2006).
[CrossRef]

2005 (5)

E. Brainis, D. Amans, and S. Massar, “Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: numerical study,” Phys. Rev. A 71, 023808 (2005).
[CrossRef]

A. Dermican and U. Bandelow, “Supercontinuum generation by the modulation instability,” Opt. Commun. 244, 181–185 (2005).
[CrossRef]

M. Nurhuda and E. Van Groesen, “Effects of delayed Kerr nonlinearity and ionization on the filamentary ultrashort laser pulses in air,” Phys. Rev. E 71, 066502 (2005).
[CrossRef]

M. Lipson, “Guiding, modulating, and emitting light on silicon challenges and opportunities,” J. Lightwave Technol. 23, 4222–4238 (2005).
[CrossRef]

C. M. Ngabireng, P. T. Dinda, A. Tonello, K. Nakkeeran, P. K. A. Wai, and T. C. Kofané, “Radiating and nonradiating behavior of hyperbolic-secant, raised-cosine, and Gaussian input light pulses in dispersion-managed fiber systems,” Phys. Rev. E 72, 036613 (2005).
[CrossRef]

2004 (1)

2003 (1)

S. C. Wen, W. H. Su, H. Zhang, X. Q. Fu, L. J. Qian, and D. Y. Fan, “Influence of higher-order dispersions and raman delayed response on modulation instability in microstructured fibres,” Chin. Phys. Lett. 20, 852–854 (2003).
[CrossRef]

2002 (1)

H. K. Tsang, C. S. Wong, and T. K. Liang, “Optical dispersion, two-photon absorption, and self-phase modulation in silicon waveguides at 1.5 m wavelength,” Appl. Phys. Lett. 80, 416–418 (2002).
[CrossRef]

1999 (1)

R. S. Tasgal and B. A. Malomed, “Modulational instabilities in the dual-core nonlinear optical fiber,” Phys. Scr. 60, 418–422 (1999).
[CrossRef]

1998 (1)

1997 (1)

1996 (1)

S. B. Cavalcanti and M. Lyra, “Modulation instability of ultrashort pulses via a generalized nonlinear Schrödinger equation with deviating argument,” Phys. Lett. A 211, 276–280 (1996).
[CrossRef]

1995 (1)

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

1994 (1)

Y. Kodama, A. Maruta, and A. Hasegawa, “Long distance communications with solitons,” Quantum Opt. 6, 463–516 (1994).
[CrossRef]

1993 (1)

G. P. Agrawal, “Effect of two-photon absorption on the amplification of ultrashort optical pulses,” Phys. Rev. E 48, 2316–2318 (1993).
[CrossRef]

1990 (2)

P. Drummond, T. Kennedy, and J. Dudley, “Cross-phase modulation instability in high birefringence fibers,” Opt. Commun. 78, 137–142 (1990).
[CrossRef]

J. E. Rothenberg, “Modulational instability of copropagating frequencies for normal dispersion,” Phys. Rev. Lett. 64, 813 (1990).
[CrossRef]

1989 (3)

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]

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).
[CrossRef]

1987 (1)

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
[CrossRef]

1986 (1)

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

1984 (1)

1970 (1)

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

1969 (2)

V. I. Karpman and E. M. Krushkal, “Modulated waves in nonlinear dispersive media,” Sov. Phys. JETP 28, 277–281 (1969).

W. J. Cody, “Rational Chebyshev approximations for the error function,”Math. Comput. 23, 631–637 (1969).
[CrossRef]

1968 (1)

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]

1967 (1)

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]

1965 (1)

V. I. Talanov, “Self-focusing of wave beams,” JETP Lett. 2, 138–141 (1965).

1964 (1)

L. A. Ostrovsky, “Electromagnetic waves in nonlinear media with dispersion,” Sov. Phys. Tech. Phys. 8, 679–683 (1964).

Abdullaev, F. Kh.

Agrawal, G. P.

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Femtosecond pulse propagation in silicon waveguides: variational approach and its advantages,” Opt. Commun. 281, 5889–5893 (2008).
[CrossRef]

L. Yin and G. P. Agrawal, “Impact of two-photon absorption on self-phase modulation in silicon waveguides,” Opt. Lett. 32, 2031–2033 (2007).
[CrossRef]

L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32, 391–393 (2007).
[CrossRef]

G. P. Agrawal, “Effect of two-photon absorption on the amplification of ultrashort optical pulses,” Phys. Rev. E 48, 2316–2318 (1993).
[CrossRef]

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
[CrossRef]

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

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

G. P. Agrawal, Applications of Nonlinear Fiber Optics(Academic, 2008).

Akhmediev, N.

M. Erkintalo, K. Hammami, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107, 253901 (2011).
[CrossRef]

N. Akhmediev and A. Ankiewicz, Solitons. Nonlinear Pulses and Beams (Chapman and Hall, 1997).

Amans, D.

E. Brainis, D. Amans, and S. Massar, “Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: numerical study,” Phys. Rev. A 71, 023808 (2005).
[CrossRef]

Ambomo, S.

C. M. Ngabireng, S. Ambomo, P. T. Dinda, and A. B. Moubissi, “Loss effects in the spectra of polarization modulational instability in weakly birefringent optical fibers,” J. Opt. 13, 085201 (2011).
[CrossRef]

Andrés, P.

Angelis, C. D.

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

Ankiewicz, A.

N. Akhmediev and A. Ankiewicz, Solitons. Nonlinear Pulses and Beams (Chapman and Hall, 1997).

Bandelow, U.

A. Demircan and U. Bandelow, “Analysis of the interplay between soliton fission and modulation instability in supercontinuum generation,” Appl. Phys. B 86, 31–39 (2007).
[CrossRef]

A. Dermican and U. Bandelow, “Supercontinuum generation by the modulation instability,” Opt. Commun. 244, 181–185 (2005).
[CrossRef]

Benjamin, T. B.

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]

Bhadra, S. K.

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Femtosecond pulse propagation in silicon waveguides: variational approach and its advantages,” Opt. Commun. 281, 5889–5893 (2008).
[CrossRef]

Bischoff, S.

Bouri, C.

Brainis, E.

E. Brainis, D. Amans, and S. Massar, “Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: numerical study,” Phys. Rev. A 71, 023808 (2005).
[CrossRef]

Castelló-Lurbe, D.

Cavalcanti, S. B.

S. B. Cavalcanti and M. Lyra, “Modulation instability of ultrashort pulses via a generalized nonlinear Schrödinger equation with deviating argument,” Phys. Lett. A 211, 276–280 (1996).
[CrossRef]

Chiang, K. S.

J. H. Li, K. S. Chiang, B. A. Malomed, and K. W. Chow, “Modulation instabilities in birefringent two-core optical fibres,” J. Phys. B 45, 165404 (2012).

J. H. Li, K. S. Chiang, and K. W. Chow, “Modulation instabilities in two-core optical fibers,” J. Opt. Soc. Am. B 28, 1693–1701 (2011).
[CrossRef]

Chow, K. W.

J. H. Li, K. S. Chiang, B. A. Malomed, and K. W. Chow, “Modulation instabilities in birefringent two-core optical fibres,” J. Phys. B 45, 165404 (2012).

J. H. Li, K. S. Chiang, and K. W. Chow, “Modulation instabilities in two-core optical fibers,” J. Opt. Soc. Am. B 28, 1693–1701 (2011).
[CrossRef]

Cody, W. J.

W. J. Cody, “Rational Chebyshev approximations for the error function,”Math. Comput. 23, 631–637 (1969).
[CrossRef]

Dalt, N. D.

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

Darmanyan, S. A.

Das, P.

P. Das, M. Vyas, and P. K. Panigrahi, “Loss of superfluidity in the Bose–Einstein condensate in an optical lattice with cubic and quintic nonlinearity,” J. Phys. B. 42, 245304 (2009).

Demircan, A.

A. Demircan and U. Bandelow, “Analysis of the interplay between soliton fission and modulation instability in supercontinuum generation,” Appl. Phys. B 86, 31–39 (2007).
[CrossRef]

Dermican, A.

A. Dermican and U. Bandelow, “Supercontinuum generation by the modulation instability,” Opt. Commun. 244, 181–185 (2005).
[CrossRef]

Dinda, P. T.

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C. M. Ngabireng, S. Ambomo, P. T. Dinda, and A. B. Moubissi, “Loss effects in the spectra of polarization modulational instability in weakly birefringent optical fibers,” J. Opt. 13, 085201 (2011).
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C. M. Ngabireng, P. T. Dinda, A. Tonello, K. Nakkeeran, P. K. A. Wai, and T. C. Kofané, “Radiating and nonradiating behavior of hyperbolic-secant, raised-cosine, and Gaussian input light pulses in dispersion-managed fiber systems,” Phys. Rev. E 72, 036613 (2005).
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R. J. R. Vasantha, K. Porsezian, and K. Nithyanandan, “Modulational-instability-induced supercontinuum generation with saturable nonlinear response,” Phys. Rev. A 82, 013825 (2010).
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S. C. Wen, W. H. Su, H. Zhang, X. Q. Fu, L. J. Qian, and D. Y. Fan, “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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S. C. Wen, W. H. Su, H. Zhang, X. Q. Fu, L. J. Qian, and D. Y. Fan, “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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J. Wen, H. Liu, N. Huang, Q. Sun, and W. Zhao, “Influence of the initial chirp on the supercontinuum generation in silicon-on-insulator waveguide,” Appl. Phys. B 104, 867–871 (2011).
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J. Wen, H. Liu, N. Huang, Q. Sun, and W. Zhao, “Influence of the initial chirp on the supercontinuum generation in silicon-on-insulator waveguide,” Appl. Phys. B 104, 867–871 (2011).
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Appl. Phys. Lett. (2)

H. K. Tsang, C. S. Wong, and T. K. Liang, “Optical dispersion, two-photon absorption, and self-phase modulation in silicon waveguides at 1.5 m wavelength,” Appl. Phys. Lett. 80, 416–418 (2002).
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[CrossRef]

Chin. Phys. Lett. (1)

S. C. Wen, W. H. Su, H. Zhang, X. Q. Fu, L. J. Qian, and D. Y. Fan, “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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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).
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IEEE J. Lightwave Technol. (1)

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