Abstract

Modulation instability (MI) of cw states of a two-core fiber, incorporating the effects of coupling-coefficient dispersion (CCD), is studied by solving a pair of generalized, linearly coupled nonlinear Schrödinger equations. CCD refers to the property that the coupling coefficient depends on the optical wavelength, and earlier studies of MI do not account for this physics. CCD does not seriously affect the symmetric/antisymmetric cw, but can drastically modify the MI of the asymmetric state. Generally, new MI frequency bands are produced, and CCD reduces (enhances) the original MI band in the anomalous (normal) dispersion regime. Another remarkable result is the existence of a critical value for the CCD, where the MI gain spectrum undergoes an abrupt change. In the anomalous dispersion regime, a new low-frequency MI band is generated. In the normal dispersion regime, an MI band vanishes, reappears, and then moves up in frequency on crossing this critical value. In both dispersion regimes, the relative magnitude of the low-frequency band and the high-frequency band depends strongly on the total input power. It is possible to switch the dominant MI frequency between a low frequency and a high frequency by tuning the total input power, providing a promising scheme to manipulate MI-related nonlinear effects in two-core fibers. The MI bands are independent of the third-order dispersion, but can be shifted significantly by self-steepening at a sufficiently high total input power. The evolution of MI from a cw input is also demonstrated with a wave propagation study.

© 2011 Optical Society of America

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2010 (3)

2009 (4)

X. Dai, Y. Xiang, S. Wen, and D. Fan, “Modulation instability of copropagating light beams in nonlinear metamaterials,” J. Opt. Soc. Am. B 26, 564–571 (2009).
[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers, and continuous wave supercontinuum generation,” Opt. Express 17, 21497–21508 (2009).
[CrossRef] [PubMed]

H. S. Chiu and K. W. Chow, “Effect of birefringence on the modulation instabilities of a system of coherently coupled nonlinear Schrödinger equations,” Phys. Rev. A 79, 065803 (2009).
[CrossRef]

M. Liu and K. S. Chiang, “Propagation of ultrashort pulses in a nonlinear two-core photonic crystal fiber,” Appl. Phys. B 98, 815–820 (2009).
[CrossRef]

2007 (2)

2006 (4)

2004 (2)

T. Tanemura, Y. Ozeki, and K. Kikuchi, “Modulational instability and parametric amplification induced by loss dispersion in optical fibers,” Phys. Rev. Lett. 93, 163902 (2004).
[CrossRef] [PubMed]

S. C. Tsang, K. S. Chiang, and K. W. Chow, “Soliton interaction in a two-core optical fiber,” Opt. Commun. 229, 431–439 (2004).
[CrossRef]

2003 (4)

2002 (5)

2001 (4)

W. C. Xu, S. M. Zhang, W. C. Chen, A. P. Luo, and S. H. Liu, “Modulation instability of femtosecond pulses in dispersion-decreasing fibers,” Opt. Commun. 199, 355–360 (2001).
[CrossRef]

G. Millot, P. Tchofo Dinda, E. Seve, and S. Wabnitz, “Modulational instability and stimulated Raman scattering in normally dispersive highly birefringent fibers,” Opt. Fiber Technol. 7, 170–205 (2001).
[CrossRef]

L. D. Carr, J. N. Kutz, and W. P. Reinhardt, “Stability of stationary states in the cubic nonlinear Schrodinger equation: applications to the Bose–Einstein condensate,” Phys. Rev. E 63, 066604 (2001).
[CrossRef]

J. M. Chávez Boggio, S. Tenenbaum, and H. L. Fragnito, “Amplification of broadband noise pumped by two lasers in optical fibers,” J. Opt. Soc. Am. B 18, 1428–1435 (2001).
[CrossRef]

1999 (3)

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

P. Shum, K. S. Chiang, and W. A. Gambling, “Switching dynamics of short optical pulses in a nonlinear directional coupler,” IEEE J. Quantum Electron. 35, 79–83 (1999).
[CrossRef]

P. M. Ramos and C. R. Paiva, “All-optical pulse switching in twin-core fiber couplers with intermodal dispersion,” IEEE J. Quantum Electron. 35, 983–989 (1999).
[CrossRef]

1998 (1)

1997 (3)

K. S. Chiang, “Propagation of short optical pulses in directional couplers with Kerr nonlinearity,” J. Opt. Soc. Am. B 14, 1437–1443 (1997).
[CrossRef]

K. S. Chiang, “Coupled-mode equations for pulse switching in parallel waveguides,” IEEE J. Quantum Electron. 33, 950–954(1997).
[CrossRef]

K. S. Chiang, Y. T. Chow, D. J. Richardson, D. Taverner, L. Dong, L. Reekie, and K. M. Lo, “Experimental demonstration of intermodal dispersion in a two-core optical fiber,” Opt. Commun. 143, 189–192 (1997).
[CrossRef]

1995 (1)

1993 (1)

1990 (1)

I. M. Uzunov, “Influence of intrapulse Raman scattering on the modulational instability in optical fibers,” Opt. Quantum Electron. 22, 529–533 (1990).
[CrossRef]

1989 (1)

1987 (1)

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

1985 (1)

1982 (1)

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. 18, 1580–1583 (1982).
[CrossRef]

1972 (1)

Agrawal, G. P.

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

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

Akhmediev, N.

Akhmediev, N. N.

V. Rastogi, K. S. Chiang, and N. N. Akhmediev, “Soliton states in a nonlinear directional coupler with intermodal dispersion,” Phys. Lett. A 301, 27–34 (2002).
[CrossRef]

Bellanca, G.

Betlej, A.

Birks, T. A.

Bise, R. T.

Boggio, J. M. Chávez

Cambournac, C.

Carr, L. D.

L. D. Carr, J. N. Kutz, and W. P. Reinhardt, “Stability of stationary states in the cubic nonlinear Schrodinger equation: applications to the Bose–Einstein condensate,” Phys. Rev. E 63, 066604 (2001).
[CrossRef]

Chauvet, M.

Chen, W. C.

W. C. Xu, S. M. Zhang, W. C. Chen, A. P. Luo, and S. H. Liu, “Modulation instability of femtosecond pulses in dispersion-decreasing fibers,” Opt. Commun. 199, 355–360 (2001).
[CrossRef]

Chen, X.

Chiang, K. S.

M. Liu and K. S. Chiang, “Pulse propagation in a decoupled two-core fiber,” Opt. Express 18, 21261–21268 (2010).
[CrossRef] [PubMed]

M. Liu and K. S. Chiang, “Propagation of ultrashort pulses in a nonlinear two-core photonic crystal fiber,” Appl. Phys. B 98, 815–820 (2009).
[CrossRef]

S. C. Tsang, K. S. Chiang, and K. W. Chow, “Soliton interaction in a two-core optical fiber,” Opt. Commun. 229, 431–439 (2004).
[CrossRef]

V. Rastogi, K. S. Chiang, and N. N. Akhmediev, “Soliton states in a nonlinear directional coupler with intermodal dispersion,” Phys. Lett. A 301, 27–34 (2002).
[CrossRef]

P. Shum, K. S. Chiang, and W. A. Gambling, “Switching dynamics of short optical pulses in a nonlinear directional coupler,” IEEE J. Quantum Electron. 35, 79–83 (1999).
[CrossRef]

K. S. Chiang, “Propagation of short optical pulses in directional couplers with Kerr nonlinearity,” J. Opt. Soc. Am. B 14, 1437–1443 (1997).
[CrossRef]

K. S. Chiang, Y. T. Chow, D. J. Richardson, D. Taverner, L. Dong, L. Reekie, and K. M. Lo, “Experimental demonstration of intermodal dispersion in a two-core optical fiber,” Opt. Commun. 143, 189–192 (1997).
[CrossRef]

K. S. Chiang, “Coupled-mode equations for pulse switching in parallel waveguides,” IEEE J. Quantum Electron. 33, 950–954(1997).
[CrossRef]

K. S. Chiang, “Intermodal dispersion in two-core optical fibers,” Opt. Lett. 20, 997–999 (1995).
[CrossRef] [PubMed]

Chiu, H. S.

H. S. Chiu and K. W. Chow, “Effect of birefringence on the modulation instabilities of a system of coherently coupled nonlinear Schrödinger equations,” Phys. Rev. A 79, 065803 (2009).
[CrossRef]

Chow, K. W.

H. S. Chiu and K. W. Chow, “Effect of birefringence on the modulation instabilities of a system of coherently coupled nonlinear Schrödinger equations,” Phys. Rev. A 79, 065803 (2009).
[CrossRef]

S. C. Tsang, K. S. Chiang, and K. W. Chow, “Soliton interaction in a two-core optical fiber,” Opt. Commun. 229, 431–439 (2004).
[CrossRef]

Chow, Y. T.

K. S. Chiang, Y. T. Chow, D. J. Richardson, D. Taverner, L. Dong, L. Reekie, and K. M. Lo, “Experimental demonstration of intermodal dispersion in a two-core optical fiber,” Opt. Commun. 143, 189–192 (1997).
[CrossRef]

Christodoulides, D. N.

Conforti, M.

Dai, X.

De Angelis, C.

Dias, F.

DiGiovanni, D. J.

Dinda, P. Tchofo

Dong, L.

K. S. Chiang, Y. T. Chow, D. J. Richardson, D. Taverner, L. Dong, L. Reekie, and K. M. Lo, “Experimental demonstration of intermodal dispersion in a two-core optical fiber,” Opt. Commun. 143, 189–192 (1997).
[CrossRef]

Du, J.

Dudley, J. M.

Emplit, P.

Fan, D.

Fan, D. Y.

Fejer, M. M.

Fini, J.

Fragnito, H. L.

Gambling, W. A.

P. Shum, K. S. Chiang, and W. A. Gambling, “Switching dynamics of short optical pulses in a nonlinear directional coupler,” IEEE J. Quantum Electron. 35, 79–83 (1999).
[CrossRef]

Genty, G.

Haelterman, M.

Honzatko, P.

P. Peterka, P. Honzatko, J. Kanka, V. Matejec, and I. Kasik, “Generation of high-repetition rate pulse trains in a fiber laser through a twin-core fiber,” Proc. SPIE 5036, 376–381 (2003).
[CrossRef]

Höök, A.

Ishida, Y.

Jankovic, L.

Jensen, S. M.

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. 18, 1580–1583 (1982).
[CrossRef]

Kanka, J.

P. Peterka, P. Honzatko, J. Kanka, V. Matejec, and I. Kasik, “Generation of high-repetition rate pulse trains in a fiber laser through a twin-core fiber,” Proc. SPIE 5036, 376–381 (2003).
[CrossRef]

Karlsson, M.

Kasik, I.

P. Peterka, P. Honzatko, J. Kanka, V. Matejec, and I. Kasik, “Generation of high-repetition rate pulse trains in a fiber laser through a twin-core fiber,” Proc. SPIE 5036, 376–381 (2003).
[CrossRef]

Kazovsky, L. G.

Kibler, B.

Kikuchi, K.

T. Tanemura, Y. Ozeki, and K. Kikuchi, “Modulational instability and parametric amplification induced by loss dispersion in optical fibers,” Phys. Rev. Lett. 93, 163902 (2004).
[CrossRef] [PubMed]

T. Tanemura and K. Kikuchi, “Unified analysis of modulational instability induced by cross-phase modulation in optical fibers,” J. Opt. Soc. Am. B 20, 2502–2514 (2003).
[CrossRef]

Kitayama, K.-I.

Kivshar, Y. S.

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

Knight, J. C.

Kutz, J. N.

L. D. Carr, J. N. Kutz, and W. P. Reinhardt, “Stability of stationary states in the cubic nonlinear Schrodinger equation: applications to the Bose–Einstein condensate,” Phys. Rev. E 63, 066604 (2001).
[CrossRef]

Lantz, E.

Li, L.

J. Wang, L. Li, Z. Li, G. Zhou, D. Mihalache, and B. A. Malomed, “Generation, compression, and propagation of pulse trains under higher order effects,” Opt. Commun. 263, 328–336 (2006).
[CrossRef]

Li, Z.

J. Wang, L. Li, Z. Li, G. Zhou, D. Mihalache, and B. A. Malomed, “Generation, compression, and propagation of pulse trains under higher order effects,” Opt. Commun. 263, 328–336 (2006).
[CrossRef]

Liu, M.

M. Liu and K. S. Chiang, “Pulse propagation in a decoupled two-core fiber,” Opt. Express 18, 21261–21268 (2010).
[CrossRef] [PubMed]

M. Liu and K. S. Chiang, “Propagation of ultrashort pulses in a nonlinear two-core photonic crystal fiber,” Appl. Phys. B 98, 815–820 (2009).
[CrossRef]

Liu, S. H.

W. C. Xu, S. M. Zhang, W. C. Chen, A. P. Luo, and S. H. Liu, “Modulation instability of femtosecond pulses in dispersion-decreasing fibers,” Opt. Commun. 199, 355–360 (2001).
[CrossRef]

Liu, Y.

Lo, K. M.

K. S. Chiang, Y. T. Chow, D. J. Richardson, D. Taverner, L. Dong, L. Reekie, and K. M. Lo, “Experimental demonstration of intermodal dispersion in a two-core optical fiber,” Opt. Commun. 143, 189–192 (1997).
[CrossRef]

Locatelli, A.

Luo, A. P.

W. C. Xu, S. M. Zhang, W. C. Chen, A. P. Luo, and S. H. Liu, “Modulation instability of femtosecond pulses in dispersion-decreasing fibers,” Opt. Commun. 199, 355–360 (2001).
[CrossRef]

Maillotte, H.

Makris, K. G.

Malomed, B. A.

J. Wang, L. Li, Z. Li, G. Zhou, D. Mihalache, and B. A. Malomed, “Generation, compression, and propagation of pulse trains under higher order effects,” Opt. Commun. 263, 328–336 (2006).
[CrossRef]

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

Marhic, M. E.

Martijn de Sterke, C.

Matejec, V.

P. Peterka, P. Honzatko, J. Kanka, V. Matejec, and I. Kasik, “Generation of high-repetition rate pulse trains in a fiber laser through a twin-core fiber,” Proc. SPIE 5036, 376–381 (2003).
[CrossRef]

McKinstrie, C. J.

Mihalache, D.

J. Wang, L. Li, Z. Li, G. Zhou, D. Mihalache, and B. A. Malomed, “Generation, compression, and propagation of pulse trains under higher order effects,” Opt. Commun. 263, 328–336 (2006).
[CrossRef]

Millot, G.

G. Millot, S. Pitois, and P. Tchofo Dinda, “Modulational instability processes in optical isotropic fibers under dual-frequency circular polarization pumping,” J. Opt. Soc. Am. B 19, 454–460(2002).
[CrossRef]

G. Millot, P. Tchofo Dinda, E. Seve, and S. Wabnitz, “Modulational instability and stimulated Raman scattering in normally dispersive highly birefringent fibers,” Opt. Fiber Technol. 7, 170–205 (2001).
[CrossRef]

Osgood, R. M.

Ozeki, Y.

T. Tanemura, Y. Ozeki, and K. Kikuchi, “Modulational instability and parametric amplification induced by loss dispersion in optical fibers,” Phys. Rev. Lett. 93, 163902 (2004).
[CrossRef] [PubMed]

Paiva, C. R.

P. M. Ramos and C. R. Paiva, “All-optical pulse switching in twin-core fiber couplers with intermodal dispersion,” IEEE J. Quantum Electron. 35, 983–989 (1999).
[CrossRef]

Panoiu, N. C.

Parini, A.

Peterka, P.

P. Peterka, P. Honzatko, J. Kanka, V. Matejec, and I. Kasik, “Generation of high-repetition rate pulse trains in a fiber laser through a twin-core fiber,” Proc. SPIE 5036, 376–381 (2003).
[CrossRef]

Phillips, C. R.

Pitois, S.

Porsezian, K.

Radic, S.

Ramos, P. M.

P. M. Ramos and C. R. Paiva, “All-optical pulse switching in twin-core fiber couplers with intermodal dispersion,” IEEE J. Quantum Electron. 35, 983–989 (1999).
[CrossRef]

Rastogi, V.

V. Rastogi, K. S. Chiang, and N. N. Akhmediev, “Soliton states in a nonlinear directional coupler with intermodal dispersion,” Phys. Lett. A 301, 27–34 (2002).
[CrossRef]

Reekie, L.

K. S. Chiang, Y. T. Chow, D. J. Richardson, D. Taverner, L. Dong, L. Reekie, and K. M. Lo, “Experimental demonstration of intermodal dispersion in a two-core optical fiber,” Opt. Commun. 143, 189–192 (1997).
[CrossRef]

Reinhardt, W. P.

L. D. Carr, J. N. Kutz, and W. P. Reinhardt, “Stability of stationary states in the cubic nonlinear Schrodinger equation: applications to the Bose–Einstein condensate,” Phys. Rev. E 63, 066604 (2001).
[CrossRef]

Richardson, D. J.

K. S. Chiang, Y. T. Chow, D. J. Richardson, D. Taverner, L. Dong, L. Reekie, and K. M. Lo, “Experimental demonstration of intermodal dispersion in a two-core optical fiber,” Opt. Commun. 143, 189–192 (1997).
[CrossRef]

Seve, E.

G. Millot, P. Tchofo Dinda, E. Seve, and S. Wabnitz, “Modulational instability and stimulated Raman scattering in normally dispersive highly birefringent fibers,” Opt. Fiber Technol. 7, 170–205 (2001).
[CrossRef]

Shum, P.

P. Shum, K. S. Chiang, and W. A. Gambling, “Switching dynamics of short optical pulses in a nonlinear directional coupler,” IEEE J. Quantum Electron. 35, 79–83 (1999).
[CrossRef]

Simaeys, G. V.

Snyder, A. W.

Stegeman, G. I.

Suntsov, S.

Tanemura, T.

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[CrossRef] [PubMed]

T. Tanemura and K. Kikuchi, “Unified analysis of modulational instability induced by cross-phase modulation in optical fibers,” J. Opt. Soc. Am. B 20, 2502–2514 (2003).
[CrossRef]

Taru, T.

Tasgal, R. S.

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

Taverner, D.

K. S. Chiang, Y. T. Chow, D. J. Richardson, D. Taverner, L. Dong, L. Reekie, and K. M. Lo, “Experimental demonstration of intermodal dispersion in a two-core optical fiber,” Opt. Commun. 143, 189–192 (1997).
[CrossRef]

Tenenbaum, S.

Trillo, S.

Tsang, S. C.

S. C. Tsang, K. S. Chiang, and K. W. Chow, “Soliton interaction in a two-core optical fiber,” Opt. Commun. 229, 431–439 (2004).
[CrossRef]

Ultanir, E. A.

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[CrossRef]

Wabnitz, S.

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[CrossRef]

S. Trillo, S. Wabnitz, G. I. Stegeman, and E. M. Wright, “Parametric amplification and modulation instabilities in dispersive nonlinear directional couplers with relaxing nonlinearity,” J. Opt. Soc. Am. B 6, 889–900 (1989).
[CrossRef]

Wang, J.

J. Wang, L. Li, Z. Li, G. Zhou, D. Mihalache, and B. A. Malomed, “Generation, compression, and propagation of pulse trains under higher order effects,” Opt. Commun. 263, 328–336 (2006).
[CrossRef]

Wang, Z.

Wen, S.

Wen, S. C.

Wong, K. K. Y.

Wright, E. M.

Xiang, Y.

Xie, C.

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W. C. Xu, S. M. Zhang, W. C. Chen, A. P. Luo, and S. H. Liu, “Modulation instability of femtosecond pulses in dispersion-decreasing fibers,” Opt. Commun. 199, 355–360 (2001).
[CrossRef]

Zhang, S. M.

W. C. Xu, S. M. Zhang, W. C. Chen, A. P. Luo, and S. H. Liu, “Modulation instability of femtosecond pulses in dispersion-decreasing fibers,” Opt. Commun. 199, 355–360 (2001).
[CrossRef]

Zhou, G.

J. Wang, L. Li, Z. Li, G. Zhou, D. Mihalache, and B. A. Malomed, “Generation, compression, and propagation of pulse trains under higher order effects,” Opt. Commun. 263, 328–336 (2006).
[CrossRef]

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[CrossRef]

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[CrossRef]

P. Shum, K. S. Chiang, and W. A. Gambling, “Switching dynamics of short optical pulses in a nonlinear directional coupler,” IEEE J. Quantum Electron. 35, 79–83 (1999).
[CrossRef]

P. M. Ramos and C. R. Paiva, “All-optical pulse switching in twin-core fiber couplers with intermodal dispersion,” IEEE J. Quantum Electron. 35, 983–989 (1999).
[CrossRef]

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. 18, 1580–1583 (1982).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (15)

S. Trillo, S. Wabnitz, G. I. Stegeman, and E. M. Wright, “Parametric amplification and modulation instabilities in dispersive nonlinear directional couplers with relaxing nonlinearity,” J. Opt. Soc. Am. B 6, 889–900 (1989).
[CrossRef]

K. S. Chiang, “Propagation of short optical pulses in directional couplers with Kerr nonlinearity,” J. Opt. Soc. Am. B 14, 1437–1443 (1997).
[CrossRef]

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[CrossRef]

J. M. Chávez Boggio, S. Tenenbaum, and H. L. Fragnito, “Amplification of broadband noise pumped by two lasers in optical fibers,” J. Opt. Soc. Am. B 18, 1428–1435 (2001).
[CrossRef]

G. Millot, S. Pitois, and P. Tchofo Dinda, “Modulational instability processes in optical isotropic fibers under dual-frequency circular polarization pumping,” J. Opt. Soc. Am. B 19, 454–460(2002).
[CrossRef]

G. V. Simaeys, P. Emplit, and M. Haelterman, “Experimental study of the reversible behavior of modulational instability in optical fibers,” J. Opt. Soc. Am. B 19, 477–486 (2002).
[CrossRef]

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]

S. C. Wen and D. Y. Fan, “Spatiotemporal instabilities in nonlinear Kerr media in the presence of arbitrary higher-order dispersions,” J. Opt. Soc. Am. B 19, 1653–1659 (2002).
[CrossRef]

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Fiber-optical parametric amplifiers with linearly or circularly polarized waves,” J. Opt. Soc. Am. B 20, 2425–2433 (2003).
[CrossRef]

T. Tanemura and K. Kikuchi, “Unified analysis of modulational instability induced by cross-phase modulation in optical fibers,” J. Opt. Soc. Am. B 20, 2502–2514 (2003).
[CrossRef]

E. A. Ultanir, D. N. Christodoulides, G. I. Stegeman, “Spatial modulation instability in periodically patterned semiconductor optical amplifiers,” J. Opt. Soc. Am. B 23, 341–346 (2006).
[CrossRef]

A. Parini, G. Bellanca, S. Trillo, M. Conforti, A. Locatelli, and C. De Angelis, “Self-pulsing and bistability in nonlinear Bragg gratings,” J. Opt. Soc. Am. B 24, 2229–2237 (2007).
[CrossRef]

X. Dai, Y. Xiang, S. Wen, and D. Fan, “Modulation instability of copropagating light beams in nonlinear metamaterials,” J. Opt. Soc. Am. B 26, 564–571 (2009).
[CrossRef]

P. Tchofo 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]

C. R. Phillips and M. M. Fejer, “Stability of the singly resonant optical parametric oscillator,” J. Opt. Soc. Am. B 27, 2687–2699(2010).
[CrossRef]

Opt. Commun. (4)

S. C. Tsang, K. S. Chiang, and K. W. Chow, “Soliton interaction in a two-core optical fiber,” Opt. Commun. 229, 431–439 (2004).
[CrossRef]

K. S. Chiang, Y. T. Chow, D. J. Richardson, D. Taverner, L. Dong, L. Reekie, and K. M. Lo, “Experimental demonstration of intermodal dispersion in a two-core optical fiber,” Opt. Commun. 143, 189–192 (1997).
[CrossRef]

J. Wang, L. Li, Z. Li, G. Zhou, D. Mihalache, and B. A. Malomed, “Generation, compression, and propagation of pulse trains under higher order effects,” Opt. Commun. 263, 328–336 (2006).
[CrossRef]

W. C. Xu, S. M. Zhang, W. C. Chen, A. P. Luo, and S. H. Liu, “Modulation instability of femtosecond pulses in dispersion-decreasing fibers,” Opt. Commun. 199, 355–360 (2001).
[CrossRef]

Opt. Express (4)

Opt. Fiber Technol. (1)

G. Millot, P. Tchofo Dinda, E. Seve, and S. Wabnitz, “Modulational instability and stimulated Raman scattering in normally dispersive highly birefringent fibers,” Opt. Fiber Technol. 7, 170–205 (2001).
[CrossRef]

Opt. Lett. (4)

Opt. Quantum Electron. (1)

I. M. Uzunov, “Influence of intrapulse Raman scattering on the modulational instability in optical fibers,” Opt. Quantum Electron. 22, 529–533 (1990).
[CrossRef]

Phys. Lett. A (1)

V. Rastogi, K. S. Chiang, and N. N. Akhmediev, “Soliton states in a nonlinear directional coupler with intermodal dispersion,” Phys. Lett. A 301, 27–34 (2002).
[CrossRef]

Phys. Rev. A (1)

H. S. Chiu and K. W. Chow, “Effect of birefringence on the modulation instabilities of a system of coherently coupled nonlinear Schrödinger equations,” Phys. Rev. A 79, 065803 (2009).
[CrossRef]

Phys. Rev. E (1)

L. D. Carr, J. N. Kutz, and W. P. Reinhardt, “Stability of stationary states in the cubic nonlinear Schrodinger equation: applications to the Bose–Einstein condensate,” Phys. Rev. E 63, 066604 (2001).
[CrossRef]

Phys. Rev. Lett. (2)

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

T. Tanemura, Y. Ozeki, and K. Kikuchi, “Modulational instability and parametric amplification induced by loss dispersion in optical fibers,” Phys. Rev. Lett. 93, 163902 (2004).
[CrossRef] [PubMed]

Phys. Scr. (1)

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

Proc. SPIE (1)

P. Peterka, P. Honzatko, J. Kanka, V. Matejec, and I. Kasik, “Generation of high-repetition rate pulse trains in a fiber laser through a twin-core fiber,” Proc. SPIE 5036, 376–381 (2003).
[CrossRef]

Other (1)

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

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Figures (16)

Fig. 1
Fig. 1

(a) Three-dimensional (3D) and (b) two- dimensional (2D) plots showing the variation of the MI gain spectrum g ( Ω ) with the total power P, calculated for the anomalous dispersion regime with β 2 = 0.02 ps 2 / m , γ = 2.5 / ( kW · m ) , C = 200 / m , and C 1 = 0 .

Fig. 2
Fig. 2

(a) 3D and (b) 2D plots showing the variation of the MI gain spectrum g ( Ω ) with the coupling coefficient C, calculated for the anomalous dispersion regime with β 2 = 0.02 ps 2 / m , γ = 2.5 / ( kW · m ) , C 1 = 0 , and P = 200 kW .

Fig. 3
Fig. 3

(a) 3D and (b) 2D plots showing the variation of the MI gain spectrum g ( Ω ) with the coupling-coefficient param eter C 1 , calculated for the anomalous dispersion regime with β 2 = 0.02 ps 2 / m , γ = 2.5 / ( kW · m ) , C = 200 / m , and P = 170 kW .

Fig. 4
Fig. 4

(a) 3D and (b) 2D plots showing the variation of the MI gain spectrum g ( Ω ) with the coupling-coefficient dispersion parameter C 1 , calculated for the anomalous dispersion regime with β 2 = 0.02 ps 2 / m , γ = 2.5 / ( kW · m ) , C = 200 / m , and P = 400 kW .

Fig. 5
Fig. 5

Dependence of the critical value C 1 cr on (a) total input power P for β 2 = 0.02 ps 2 / m , γ = 2.5 / ( kW · m ) , and C = 200 / m ; (b) coupling coefficient C for β 2 = 0.02 ps 2 / m , γ = 2.5 / ( kW · m ) , and P = 200 kW ; (c) SPM parameter γ for β 2 = 0.02 ps 2 / m , C = 200 / m , and P = 200 kW ; and (d) magnitude of GVD | β 2 | for γ = 2.5 / ( kW · m ) , C = 200 / m , and P = 200 kW .

Fig. 6
Fig. 6

(a) 3D and (b) 2D plots showing the variation of the MI gain spectrum g ( Ω ) with the total power P, calculated for the normal dispersion regime with β 2 = 0.02 ps 2 / m , γ = 5.0 / ( kW · m ) , C = 200 / m , and C 1 = 0 .

Fig. 7
Fig. 7

(a) 3D and (b) 2D plots showing the variation of the MI gain spectrum g ( Ω ) with the coupling coefficient C, calculated for the normal dispersion regime with β 2 = 0.02 ps 2 / m , γ = 5.0 / ( kW · m ) , C 1 = 0 , and P = 100 kW .

Fig. 8
Fig. 8

(a) 3D and (b) 2D plots showing the variation of the MI gain spectrum g ( Ω ) with the coupling-coefficient dispersion parameter C 1 , calculated for the normal dispersion regime with β 2 = 0.02 ps 2 / m , γ = 5.0 / ( kW · m ) , C = 200 / m , and P = 100 kW .

Fig. 9
Fig. 9

(a) 3D and (b) 2D plots showing the variation of the MI gain spectrum g ( Ω ) with the coupling-coefficient dispersion parameter C 1 , calculated for the normal dispersion regime with β 2 = 0.02 ps 2 / m , γ = 5.0 / ( kW · m ) , C = 200 / m , and P = 600 kW .

Fig. 10
Fig. 10

Dependence of the critical value C 1 cr on (a) total input power P for β 2 = 0.02 ps 2 / m , γ = 5.0 / ( kW · m ) , and C = 200 / m ; (b) coupling coefficient C for β 2 = 0.02 ps 2 / m , γ = 5.0 / ( kW · m ) , and P = 100 kW ; (c) SPM parameter γ for β 2 = 0.02 ps 2 / m , C = 200 / m , and P = 100 kW ; and (d) magnitude of GVD | β 2 | for γ = 5.0 / ( kW · m ) , C = 200 / m , and P = 100 kW .

Fig. 11
Fig. 11

Variation of the MI gain spectrum g ( Ω ) with the total power P, calculated for the anomalous dispersion regime with β 2 = 0.02 ps 2 / m , γ = 2.5 / ( kW · m ) , λ = 1.5 μm , C = 200 / m , and C 1 = 1 ps / m without (solid curve) and with (dashed curve) SS.

Fig. 12
Fig. 12

Variation of the MI gain spectrum g ( Ω ) with the total power P, calculated for the normal dispersion regime with β 2 = 0.02 ps 2 / m , γ = 5.0 / ( kW · m ) , λ = 1.0 μm , C = 200 / m , and C 1 = 1 ps / m without (solid curve) and with (dashed curve) SS.

Fig. 13
Fig. 13

Evolution of MI from a cw input in the absence of CCD ( C 1 = 0 ps / m ), calculated for the anomalous dispersion regime with β 2 = 0.02 ps 2 / m , γ = 2.5 / ( kW · m ) , λ = 1.5 μm , C = 200 / m , P = 200 kW , and P 1 / P 2 = 4 .

Fig. 14
Fig. 14

Evolution of MI from a cw input in the presence of CCD ( C 1 = 1 ps / m ), calculated for the anomalous dispersion regime with β 2 = 0.02 ps 2 / m , γ = 2.5 / ( kW · m ) , λ = 1.5 μm , C = 200 / m , P = 200 kW , and P 1 / P 2 = 4 .

Fig. 15
Fig. 15

Evolution of MI from a cw input in the absence of CCD ( C 1 = 0 ps / m ), calculated for the normal dispersion regime with β 2 = 0.02 ps 2 / m , γ = 5.0 / ( kW · m ) , λ = 1.0 μm , C = 200 / m , P = 100 kW , and P 1 / P 2 = 4 .

Fig. 16
Fig. 16

Evolution of MI from a cw input in the pres ence of CCD ( C 1 = 1 ps / m ), calculated for the normal dispersion regime with β 2 = 0.02 ps 2 / m , γ = 5.0 / ( kW · m ) , λ = 1.0 μm , C = 200 / m , P = 100 kW , and P 1 / P 2 = 4 .

Equations (19)

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i a 1 z 1 2 β 2 2 a 1 t 2 + γ | a 1 | 2 a 1 + C a 2 + i C 1 a 2 t = 0 , i a 2 z 1 2 β 2 2 a 2 t 2 + γ | a 2 | 2 a 2 + C a 1 + i C 1 a 1 t = 0 ,
a 1 = P 0 exp ( i k z ) , a 2 = δ P 0 exp ( i k z ) ,
a 1 = ( P 0 + u ) exp ( i k z ) , a 2 = ( δ P 0 + v ) exp ( i k z ) ,
i u z 1 2 β 2 2 u t 2 + [ ( γ P 0 δ C ) u + γ P 0 u * ] + C v + i C 1 v t = 0 , i v z 1 2 β 2 2 v t 2 + [ ( γ P 0 δ C ) v + γ P 0 v * ] + C u + i C 1 u t = 0.
u = F 1 exp ( i K z i Ω t ) + G 1 exp ( i K z + i Ω t ) , v = F 2 exp ( i K z i Ω t ) + G 2 exp ( i K z + i Ω t ) ,
[ ( K δ C 1 Ω ) 2 r 1 ] [ ( K + δ C 1 Ω ) 2 r 2 ] = 0 ,
r 1 = 1 4 β 2 Ω 2 ( β 2 Ω 2 + 4 γ P 0 ) , r 2 = 1 4 ( β 2 Ω 2 4 δ C ) ( β 2 Ω 2 4 δ C + 4 γ P 0 ) .
r 1 < 0 or r 2 < 0.
a 1 = P 1 exp ( i k z ) , a 2 = P 2 exp ( i k z ) ,
( P 1 , P 2 ) = ( 1 2 P ± 1 2 P 2 P min 2 , 1 2 P 1 2 P 2 P min 2 ) .
[ ( K + 2 2 Ω C 1 ) 2 s 1 ] [ ( K 2 2 Ω C 1 ) 2 s 2 ] = s ,
s 1 = 1 2 γ 2 P 2 2 C 2 + 1 4 β 2 2 Ω 4 + ( 1 2 C 1 2 2 β 2 C ) Ω 2 ,
s 2 = 1 2 γ 2 P 2 2 C 2 + 1 4 β 2 2 Ω 4 + ( 1 2 C 1 2 + 2 β 2 C ) Ω 2 ,
s = 1 2 β 2 2 C 1 2 Ω 6 ( 5 β 2 2 C 2 + C 1 4 β 2 2 γ 2 P 2 ) Ω 4 ( γ 2 P 2 4 C 2 ) ( β 2 γ P + 2 C 1 2 ) Ω 2 + 1 4 ( γ 2 P 2 4 C 2 ) 2 .
g ( Ω ) = Im ( K ) .
i a 1 z 1 2 β 2 2 a 1 t 2 i 1 6 β 3 3 a 1 t 3 + γ | a 1 | 2 a 1 + i σ t ( | a 1 | 2 a 1 ) + C a 2 + i C 1 a 2 t = 0 , i a 2 z 1 2 β 2 2 a 2 t 2 i 1 6 β 3 3 a 2 t 3 + γ | a 2 | 2 a 2 + i σ t ( | a 2 | 2 a 2 ) + C a 1 + i C 1 a 1 t = 0 ,
[ ( K 1 + 2 2 Ω C 1 ) 2 s 1 ] [ ( K 1 2 2 Ω C 1 ) 2 s 2 ] = s σ Ω S ,
K 1 = K 1 6 β 3 Ω 3 σ Ω P ,
S = ( 10 C 2 γ 2 3 P 2 ) σ Ω K 1 2 + 2 ( 4 C 2 γ 2 P 2 ) ( P γ 2 σ 2 Ω 2 + 2 β 2 γ Ω 2 P ) K 1 + β 2 2 ( 3 C 2 2 γ 2 1 4 P 2 ) σ Ω 5 [ ( 4 C 2 γ 2 P 2 ) ( 2 C 1 2 γ 2 P β 2 γ ) + 2 C 1 2 C 2 γ 2 ] σ Ω 3 + C 2 ( 9 C 2 γ 4 2 P 2 γ 2 ) σ 3 Ω 3 ( 4 C 2 γ 2 P 2 ) 6 C 2 γ 2 σ Ω + ( 4 C 2 γ 2 P 2 ) 8 C C 1 γ Ω .

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