New Types of Rogue Wave in an Erbium-Doped Fibre System

We report a novel and new types of rogue optical wave propagation in an erbium-doped fibre system governed by the nonlinear Schrodinger and the Maxwell–Bloch equation. The breather solutions of the three fields, namely field envelop, polarization and population inversion, are used to generate the rogue waves. For the first time, we report bright and, in particular, dark rogue waves in a coupled nonlinear optical systems. The distinction between bright and dark rogue waves are discussed in detail through figures. The rogue wave formation in our model can also be connected to the generation of supercontinuum generation in resonant optical fibre.

[1]  L. Ostrovsky,et al.  Modulation instability: The beginning , 2009 .

[2]  A. M. Kamchatnov,et al.  New approach to periodic solutions of integrable equations and nonlinear theory of modulational instability , 1997 .

[3]  P. Shukla,et al.  Surface plasma rogue waves , 2011 .

[4]  J. Soto-Crespo,et al.  How to excite a rogue wave , 2009 .

[5]  Lugiato,et al.  Exact linear stability analysis of the plane-wave Maxwell-Bloch equations for a ring laser. , 1986, Physical review. A, General physics.

[6]  Multi-soliton solutions of a coupled system of the nonlinear Schrödinger equation and the Maxwell-Bloch equations , 1994 .

[7]  C. K. Chui,et al.  A novel approach to solving the nonlinear Schrodinger equation by the coupled amplitude-phase formulation , 1995 .

[8]  Frédéric Dias,et al.  The Peregrine soliton in nonlinear fibre optics , 2010 .

[9]  Jingsong He,et al.  The Darboux transformation of the derivative nonlinear Schrödinger equation , 2011, 1109.0674.

[10]  A. M. Basharov,et al.  Present state of self-induced transparency theory , 1990 .

[11]  Akira Hasegawa,et al.  Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion , 1973 .

[12]  A. Hasegawa,et al.  Generation of a train of soliton pulses by induced modulational instability in optical fibers. , 1984, Optics letters.

[13]  A Montina,et al.  Granularity and inhomogeneity are the joint generators of optical rogue waves. , 2011, Physical review letters.

[14]  K. Porsezian,et al.  Modulational instability in optical fibers with arbitrary higher-order dispersion and delayed Raman response , 2006 .

[15]  A. Hasegawa.  OBSERVATION OF SELF-TRAPPING INSTABILITY OF A PLASMA CYCLOTRON WAVE IN A COMPUTER EXPERIMENT. , 1970 .

[16]  B. Jalali,et al.  Optical rogue waves , 2007, Nature.

[17]  S. Mccall,et al.  Self-Induced Transparency by Pulsed Coherent Light , 1967 .

[18]  Kharif Christian,et al.  Rogue Waves in the Ocean , 2009 .

[19]  Marc Haelterman,et al.  Observation of induced modulational polarization instabilities and pulse-train generation in the normal-dispersion regime of a birefringent optical fiber , 1998 .

[20]  Yamada,et al.  Coexistence of self-induced transparency soliton and nonlinear Schrödinger soliton. , 1991, Physical review letters.

[21]  R. Meinel,et al.  General N-soliton solution of the AKNS class on arbitrary background , 1984 .

[22]  About shape of giant breather , 2010 .

[23]  He Jingsong,et al.  The Darboux Transformation for NLS-MB Equations , 2002 .

[24]  Cavalcanti,et al.  Modulation instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[25]  Adrian Ankiewicz,et al.  Rogue waves and rational solutions of the Hirota equation. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Joseph H. Eberly,et al.  Analytic Study of Pulse Chirping in Self-Induced Transparency , 1972 .

[27]  K. Okamoto,et al.  Extended four‐photon mixing approach to modulational instability , 1988 .

[28]  Govind P. Agrawal,et al.  Nonlinear Fiber Optics , 1989 .

[29]  A. Hasegawa,et al.  Tunable coherent IR and FIR sources utilizing modulational instability , 1980 .

[30]  D. H. Peregrine,et al.  Water waves, nonlinear Schrödinger equations and their solutions , 1983, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[31]  Guy Millot,et al.  Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber , 2003 .

[32]  H. Haus.  Applications of Nonlinear Fiber Optics , 2002 .

[33]  Porsezian,et al.  Optical soliton propagation in an erbium doped nonlinear light guide with higher order dispersion. , 1995, Physical review letters.

[34]  N. Akhmediev,et al.  Modulation instability and periodic solutions of the nonlinear Schrödinger equation , 1986 .

[35]  S. John,et al.  SELF-INDUCED TRANSPARENCY SOLITARY WAVES IN A DOPED NONLINEAR PHOTONIC BAND GAP MATERIAL , 1998 .

[36]  F. Ito,et al.  Experimental verification of frequency level‐off of modulational instability in the minimum dispersion region , 1989 .

[37]  K. Porsezian,et al.  Modulational instability and generation of self-induced transparency solitons in resonant optical fibers , 2009 .