Observation of two soliton propagation in an erbium doped inhomogeneous lossy fiber with phase modulation M.S. Mani Rajan a,⇑ , A. Mahalingam a , A. Uthayakumar b , K. Porsezian c a Department of Physics, Anna University, Chennai, India b Department of Physics, Presidency College, Chennai, India c School of Physics, Pondicherry University, Puducherry, India article info Article history: Received 20 June 2012 Received in revised form 14 October 2012 Accepted 21 October 2012 Available online 1 November 2012 Keywords: Inhomogeneous fibers Optical soliton Nonlinear Schrödinger equation Lax pair Darboux transformation NLS–MB equation abstract We consider optical pulse propagation in an Erbium doped inhomogeneous lossy optical fiber with time dependent phase modulation, which is governed by a system of General- ized Inhomogeneous Nonlinear Schrödinger Maxwell–Bloch (GINLS–MB) equation. Multi- soliton propagation is studied analytically by means of deriving associated Lax pair and the soliton solutions are obtained using Darboux transformation. By suitably adjusting the group velocity dispersion and nonlinearity parameter, we discuss various soliton dynamics such as periodic distributed amplification, pulse compression etc. In each case, we demonstrate the influence of inhomogeneous parameter. Finally we investigate the pulse compression through nonlinear tunneling. Ó 2012 Elsevier B.V. All rights reserved. 1. Introduction Optical soliton is one of the most important innovations in the area of communication technology. The principle of sol- itons in an optical fiber which is commonly called as Nonlinear Schrödinger (NLS) soliton is based on the perfect balance between the group velocity dispersion (GVD) and the Kerr effect. The GVD causes the temporal broadening of the optical pulse, due to the frequency dependent refractive index and the Kerr effect is the change in refractive index due to pulse intensity. By proper choice of pulse width and power of the pulse, we can indeed cancel one effect with the other [1–3]. The optical solitons in fiber was first proposed by Hasegawa and Tappert [4,5] theoretically and experimental verifications have been carried out by Mollenauer et al. [6]. Even though solitons would travel infinite distance in a lossless fiber, in real fibers due to the effect of losses, they would be broadened and hence need amplification. To avoid the problems caused by the electronic amplifiers, all-optical communication systems involving Erbium-Doped Fiber Amplifiers (EDFA) are presently employed. When the core of the optical fiber is doped with Erbium, the wave propagation has both effects due to silica and Er impurities. The silica waveguide gives the NLS soliton effect where as Er impurities are responsible for the Self-Induced Transparency (SIT) effect to the optical pulse [7,8]. Erbium is selected because the energy difference between the two levels is nearly equal to the operating wavelength used nowadays. The coherent interaction effect is due to resonant absorption, which can balance the optical losses in the fiber medium and the medium becomes optically transparent to that particular wavelength. In Erbium-doped fibers, a soliton is collectively called as nonlinear Schrödinger–Maxwell–Bloch (NLS–MB) soliton. 1007-5704/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cnsns.2012.10.008 ⇑ Corresponding author. E-mail address: senthilmanirajanofc@gmail.com (M.S. Mani Rajan). Commun Nonlinear Sci Numer Simulat 18 (2013) 1410–1432 Contents lists available at SciVerse ScienceDirect Commun Nonlinear Sci Numer Simulat journal homepage: www.elsevier.com/locate/cnsns