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Volumn 31, Issue 6, 2000, Pages 1351-1373

The mechanism of the polarizational mode instability in birefringent fiber optics

Author keywords

Dirichlet expansion; Evans function; Polarization mode instability; Traveling waves

Indexed keywords


EID: 0034347554     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141099349966     Document Type: Article
Times cited : (27)

References (38)
  • 2
    • 0029270874 scopus 로고
    • Phase-locked stationary soliton states in birefringent nonlinear optical fibers
    • N. AKHMEDIEV, A. BURYAK, J.M. SOTO-CRESPO, AND D. ANDERSON, Phase-locked stationary soliton states in birefringent nonlinear optical fibers, J. Opt. Soc. Amer. B, 12 (1995), pp. 434-439.
    • (1995) J. Opt. Soc. Amer. B , vol.12 , pp. 434-439
    • Akhmediev, N.1    Buryak, A.2    Soto-Crespo, J.M.3    Anderson, D.4
  • 3
    • 0002085123 scopus 로고
    • Steady state pulses in a birefringent nonlinear optical fiber: Soliton multiplication processes
    • N. AKHMEDIEV, V. ELEONSKII, E. KULAGIN, AND L. SHILNIKOV, Steady state pulses in a birefringent nonlinear optical fiber: Soliton multiplication processes, Sov. Tech. Phys. Lett, 15 (1989), pp. 587-588.
    • (1989) Sov. Tech. Phys. Lett , vol.15 , pp. 587-588
    • Akhmediev, N.1    Eleonskii, V.2    Kulagin, E.3    Shilnikov, L.4
  • 4
    • 0005235678 scopus 로고
    • A topological invariant arising in the stability analysis of travelling waves
    • J.C. ALEXANDER, R.A. GARDNER, AND C.K.R.T. JONES, A topological invariant arising in the stability analysis of travelling waves, J. Reine Angew. Math., 410 (1990), pp. 167-212.
    • (1990) J. Reine Angew. Math. , vol.410 , pp. 167-212
    • Alexander, J.C.1    Gardner, R.A.2    Jones, C.K.R.T.3
  • 6
    • 0023150231 scopus 로고
    • Polarization instabilities for solitons in birefringent fibers
    • K.J. BLOW, N.J. DORAN, AND D. WOOD, Polarization instabilities for solitons in birefringent fibers, Opt. Lett., 12 (1987), pp. 202-204.
    • (1987) Opt. Lett. , vol.12 , pp. 202-204
    • Blow, K.J.1    Doran, N.J.2    Wood, D.3
  • 7
    • 84975565210 scopus 로고
    • Vector solitons in birefringent nonlinear dispersive media
    • D.N. CHRISTODOULIDES AND R.I. JOSEPH, Vector solitons in birefringent nonlinear dispersive media, Opt. Lett. 13 (1988), pp. 53-55.
    • (1988) Opt. Lett. , vol.13 , pp. 53-55
    • Christodoulides, D.N.1    Joseph, R.I.2
  • 10
    • 0343676826 scopus 로고
    • Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion
    • A. HASEGAWA AND F. TAPPERT, Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion, Appl. Phys. Lett., 23 (1973), pp. 142-144.
    • (1973) Appl. Phys. Lett. , vol.23 , pp. 142-144
    • Hasegawa, A.1    Tappert, F.2
  • 11
    • 0040942605 scopus 로고    scopus 로고
    • The gap lemma and geometric critera for instability of viscous shock profiles
    • R.A. GARDNER AND K. ZUMBRUN, The gap lemma and geometric critera for instability of viscous shock profiles, Comm. Pure Appl. Math., 51 (1998), pp. 797-855.
    • (1998) Comm. Pure Appl. Math. , vol.51 , pp. 797-855
    • Gardner, R.A.1    Zumbrun, K.2
  • 12
    • 84990563336 scopus 로고
    • Analysis of the linearization around a critical point of an infinite dimensional Hamiltonian system
    • M. GRILLAKIS, Analysis of the linearization around a critical point of an infinite dimensional Hamiltonian system, Comm. Pure Appl. Math., 43 (1990), pp. 299-333.
    • (1990) Comm. Pure Appl. Math. , vol.43 , pp. 299-333
    • Grillakis, M.1
  • 13
    • 29444432472 scopus 로고
    • Stability theory of solitary waves in the presence of symmetry, II
    • M. GRILLAKIS, J. SHATAH, AND W. STRAUSS, Stability theory of solitary waves in the presence of symmetry, II, J. Funct. Anal., 94 (1990), pp. 308-348.
    • (1990) J. Funct. Anal. , vol.94 , pp. 308-348
    • Grillakis, M.1    Shatah, J.2    Strauss, W.3
  • 14
    • 0000670781 scopus 로고
    • Instability of standing waves for nonlinear Schrödinger type equations
    • C.R.T. JONES, Instability of standing waves for nonlinear Schrödinger type equations, Ergodic Theory Dynam. Systems, 8 (1988), pp. 119-138.
    • (1988) Ergodic Theory Dynam. Systems , vol.8 , pp. 119-138
    • Jones, C.R.T.1
  • 15
    • 84967743294 scopus 로고
    • Stability of travelling wave solutions of the Fitzhugh-Nagumo system
    • C.R.T. JONES, Stability of travelling wave solutions of the Fitzhugh-Nagumo system, Trans. Amer. Math. Soc., 286 (1984), pp. 431-469.
    • (1984) Trans. Amer. Math. Soc. , vol.286 , pp. 431-469
    • Jones, C.R.T.1
  • 16
    • 0032622893 scopus 로고    scopus 로고
    • The evans function and generalized Melnikov integrals
    • T. KAPITULA, The Evans function and generalized Melnikov integrals, SIAM J. Math. Anal., 30 (1999), pp. 273-297.
    • (1999) SIAM J. Math. Anal. , vol.30 , pp. 273-297
    • Kapitula, T.1
  • 17
    • 0033628312 scopus 로고    scopus 로고
    • Existence and stability of standing hole solutions to complex Ginzburg-Landau equations
    • T. KAPITULA AND J. RUBIN, Existence and stability of standing hole solutions to complex Ginzburg-Landau equations, Nonlinearity, 13 (2000), pp. 77-112.
    • (2000) Nonlinearity , vol.13 , pp. 77-112
    • Kapitula, T.1    Rubin, J.2
  • 18
    • 0002348145 scopus 로고    scopus 로고
    • Stability of bright solitary-wave solutions to perturbed nonlinear Schrödinger equations
    • T. KAPITULA AND B. SANDSTEDE, Stability of bright solitary-wave solutions to perturbed nonlinear Schrödinger equations, Phys. D, 124 (1998), pp. 58-103.
    • (1998) Phys. D , vol.124 , pp. 58-103
    • Kapitula, T.1    Sandstede, B.2
  • 19
    • 0001127339 scopus 로고
    • Second-order perturbations for solitons in optical fibers
    • D. KAUP, Second-order perturbations for solitons in optical fibers, Phys. Rev. A, 44 (1991), pp. 4582-4590.
    • (1991) Phys. Rev. A , vol.44 , pp. 4582-4590
    • Kaup, D.1
  • 20
    • 0001269503 scopus 로고    scopus 로고
    • Perturbation theory for the manakov soliton and its application to pulse propagation in randomly birefringent fibers
    • D. KAUP AND T. LAKOBA, Perturbation theory for the Manakov soliton and its application to pulse propagation in randomly birefringent fibers, Phys. Rev. E (3), 56 (1997), pp. 6147-6165.
    • (1997) Phys. Rev. E (3) , vol.56 , pp. 6147-6165
    • Kaup, D.1    Lakoba, T.2
  • 21
    • 0000452782 scopus 로고
    • Soliton trapping and daughter waves in the Manakov model
    • D. KAUP AND B.A. MALOMED, Soliton trapping and daughter waves in the Manakov model, Phys. Rev. A, 48 (1993), pp. 599-604.
    • (1993) Phys. Rev. A , vol.48 , pp. 599-604
    • Kaup, D.1    Malomed, B.A.2
  • 22
    • 11544364689 scopus 로고    scopus 로고
    • Structural stability of non-groundstate traveling waves of coupled nonlinear schrödinger systems
    • Y. LI AND K. PROMISLOW, Structural stability of non-groundstate traveling waves of coupled nonlinear Schrödinger systems, Phys. D, 124 (1998), pp. 137-165.
    • (1998) Phys. D , vol.124 , pp. 137-165
    • Li, Y.1    Promislow, K.2
  • 23
    • 0000763166 scopus 로고
    • On the theory of two-dimensional stationary self-focusing of electro-magnetic waves
    • S.V. MANAKOV, On the theory of two-dimensional stationary self-focusing of electro-magnetic waves, Soviet Physics JETP, 38 (1974), pp. 248-253.
    • (1974) Soviet Physics JETP , vol.38 , pp. 248-253
    • Manakov, S.V.1
  • 24
    • 84975605130 scopus 로고
    • Stability of solitons in birefringent optical fibers, I. Equal propagation amplitudes
    • C. MENYUK, Stability of solitons in birefringent optical fibers, I. Equal propagation amplitudes, Opt. Lett., 12 (1987), pp. 614-616.
    • (1987) Opt. Lett. , vol.12 , pp. 614-616
    • Menyuk, C.1
  • 25
    • 0024914687 scopus 로고
    • Pulse propagation in an elliptically birefringent optical Kerr medium
    • C. MENYUK, Pulse propagation in an elliptically birefringent optical Kerr medium, IEEE J. Quant. Electron., 25 (1989), pp. 2674-2682.
    • (1989) IEEE J. Quant. Electron. , vol.25 , pp. 2674-2682
    • Menyuk, C.1
  • 26
    • 0001332821 scopus 로고    scopus 로고
    • Stability of walking vector solitons
    • D. MIHALACHE, D. MAZILU, AND L. TORNER, Stability of walking vector solitons, Phys. Rev. Lett., 81 (1998), pp. 4353-4356.
    • (1998) Phys. Rev. Lett. , vol.81 , pp. 4353-4356
    • Mihalache, D.1    Mazilu, D.2    Torner, L.3
  • 27
    • 84975557382 scopus 로고
    • Polarization scattering by soliton-soliton collisions
    • L.F. MOLLENAUER, J.P. GORDON, AND F. HEISMANN, Polarization scattering by soliton-soliton collisions, Opt. Lett., 20 (1995), pp. 2060-2063.
    • (1995) Opt. Lett. , vol.20 , pp. 2060-2063
    • Mollenauer, L.F.1    Gordon, J.P.2    Heismann, F.3
  • 28
    • 0002106841 scopus 로고
    • Hamiltonian dynamics of solitons in optical fibers
    • D.J. MURAKI AND W.L. KATH, Hamiltonian dynamics of solitons in optical fibers, Phys. D, 48 (1991), pp. 53-64.
    • (1991) Phys. D , vol.48 , pp. 53-64
    • Muraki, D.J.1    Kath, W.L.2
  • 29
    • 0000301402 scopus 로고
    • Soliton solutions of multicomponent nonlinear Schrödinger equation
    • Y. NOGAMI AND C.S. WARKE, Soliton solutions of multicomponent nonlinear Schrödinger equation, Phys. Lett., 59 (1976), pp. 251-253.
    • (1976) Phys. Lett. , vol.59 , pp. 251-253
    • Nogami, Y.1    Warke, C.S.2
  • 31
    • 0001640976 scopus 로고
    • Stationary soliton-like pulses in birefringent optical fibers
    • J.M. SOTO-CRESPO, N.N. AKHMEDIEV, AND A. ANKIEWICZ, Stationary soliton-like pulses in birefringent optical fibers, Phys. Rev. E, 51 (1995), pp. 3547-3555.
    • (1995) Phys. Rev. E , vol.51 , pp. 3547-3555
    • Soto-Crespo, J.M.1    Akhmediev, N.N.2    Ankiewicz, A.3
  • 32
    • 0028550323 scopus 로고
    • Pulse collisions and polarization conversion for optical fibers
    • C. SOPHOCLEOUS AND D.F. PARKER, Pulse collisions and polarization conversion for optical fibers, Opt. Comm., 112 (1994), p. 214.
    • (1994) Opt. Comm. , vol.112 , pp. 214
    • Sophocleous, C.1    Parker, D.F.2
  • 33
    • 35949010580 scopus 로고
    • Bound solitary waves in birefringent optical fiber
    • M.W. TRATNIK AND J.E. SIPE, Bound solitary waves in birefringent optical fiber, Phys. Rev. A, 38 (1988), pp. 2011-2017.
    • (1988) Phys. Rev. A , vol.38 , pp. 2011-2017
    • Tratnik, M.W.1    Sipe, J.E.2
  • 34
    • 0001076665 scopus 로고
    • Dynamics of optical pulses in randomly birefringent fibers
    • T. UEDA AND W. KATH, Dynamics of optical pulses in randomly birefringent fibers, Phys. D, 55 (1992), pp. 166-181.
    • (1992) Phys. D , vol.55 , pp. 166-181
    • Ueda, T.1    Kath, W.2
  • 35
    • 0030083457 scopus 로고    scopus 로고
    • Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence
    • P.A. WAI AND C.R. MENYUK, Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence, J. Lightwave Tech., 14 (1996), pp. 148-157.
    • (1996) J. Lightwave Tech. , vol.14 , pp. 148-157
    • Wai, P.A.1    Menyuk, C.R.2
  • 36
    • 0000686130 scopus 로고
    • Modulational stability of ground states of nonlinear Schrödinger equations
    • M. WEINSTEIN, Modulational stability of ground states of nonlinear Schrödinger equations, SIAM J. Math. Anal, 16 (1985), pp. 472-491.
    • (1985) SIAM J. Math. Anal , vol.16 , pp. 472-491
    • Weinstein, M.1
  • 37
    • 84990553584 scopus 로고
    • Liapunov stability of ground states of nonlinear dispersive evolution equations
    • M. WEINSTEIN, Liapunov stability of ground states of nonlinear dispersive evolution equations, Comm. Pure Appl. Math., 39 (1986), pp. 51-68.
    • (1986) Comm. Pure Appl. Math. , vol.39 , pp. 51-68
    • Weinstein, M.1
  • 38
    • 0033074434 scopus 로고    scopus 로고
    • Multisoliton perturbation theory for the Manakov equations and its applications to nonlinear optics
    • J. YANG, Multisoliton perturbation theory for the Manakov equations and its applications to nonlinear optics, Phys. Rev. E (3), 59 (1999), pp. 2393-2405.
    • (1999) Phys. Rev. E (3) , vol.59 , pp. 2393-2405
    • Yang, J.1


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