Optical Soliton Propagation in an Erbium Doped Nonlinear Light Guide with Higher Order Dispersion

Abstract

We propose a coupled system of the Hirota equation and the Maxwell-Bloch equations to describe the wave propagation in an erbium doped nonlinear fiber with higher order dispersion.The Painleve property of the same is analyzed and the coupled system is found to be integrable. The Lax pair is also constructed and the single-soliton solution is explicitly shown. The coupled system is found to allow soliton-type propagation. PACS numbers: 42.SO.Rh, 02.30.Jr, 42.65. -k, 42.81.DpThe extraordinary growth of communication technology was made possible only because of the discovery of microwaves. Every day the amount of intelligence to be communicated becomes more and more, so communication using light wave technology has been developed. Optical communication gives the necessary bandwidth, which can handle numerous channels. Optical fibers made of silica are used for guiding the light waves.Still the entire efficiency of optical communication is not utilized. This is because of the undesired, natural problems of the fibers. The two major problems are the dispersion and the dissipation due to the frequency dependence of the index of refraction and the optical losses, respectively.The dispersion makes the optical pulse spread temporally so that the energy may fall on the next bit slot, so that cross talk or error detection may occur. The optical losses cause the vanishing of the pulse because of absorption and scattering. This also causes error detection.The other important natural phenomenon of optical fibers is the nonlinear effect. When the intensity of the optical pulses crosses a certain threshold value then the fiber behaves nonlinearly. The most important effect is self-phase modulation (SPM) due to Kerr nonlinearity.Kerr nonlinearity is defined as the intensity-dependent refractive index. SPM produces spectral broadening. The effect of SPM is in opposition to that of dispersion in the anomalous dispersion region (the wavelength at which the blueshifted frequency component travels faster than the redshifted frequency).So with the proper selection of the parametric conditions, the effect of dispersion can be exactly balanced with the help of SPM. With this principle the pulse will travel through a very long distance without any change in shape -this effect is called the soliton [1,2].In 1980, Mollenauer, Stolen, and Gordon [3] observed experimental solitons for the first time in low-loss fibers.Later in 1986 [4], the same group reported that the experimentally observed solitons did not have the same properties as theoretical ones. This is. because of higher order effects like higher order dispersion, self-steepening, and stimulated inelastic scattering. All these effects will give some additional perturbation to the soliton system.It is evident that if one analyzes any type of soliton in fibers, all the above important additional effects have to be included. Here in this Letter we mainly concentrate on this problem of our proposed system.The other important nonlinear effect is the coherent interaction of the optical fi...

Publisher's Note:N-order bright and dark rogue waves in a resonant erbium-doped fiber system [Phys. Rev. E86, 066603 (2012)]

“…Recent experiments by Nakazawa et al, have confirmed guided wave SIT soliton formation and propagation by employing a few meters of erbium doped fibre [8][9][10][11]. Recently, considering all higher order effects in the propagation of femtosecond pulses, the coupled Hirota and Maxwell-Bloch (CH-MB) equations have been proposed and analyzed for soliton solutions [12]. Some generalization of NLS-MB equations, for instance, the CH-MB equations and the NLS-MB equations with variable dispersion and nonlinear effects are discussed [13][14][15].…”

“…(24) into eqs. (11,12,13), we can get the first order rogue waves {Ē [1] ,p [1] ,η [1] } in the form of determinant. The dynamical evolution of |Ē [1] | 2 , |p [1] | 2 andη [1] for the parametric choice Theorem 2.…”

Characteristics of optical multi-peak solitons induced by higher-order effects in an erbium-doped fiber system

“…We consider ultrashort pulses propagating a resonant erbium-doped fiber system with the important higherorder effects above governed by a coupled system of the H-MB model [5] …”

“…In this case, nonlinear wave propagation could possess both the effects due to a mix of silica and erbium impurities. More specifically, the silica material gives the group velocity dispersion and self-phase modulation effects, which is governed by the nonlinear Schrödinger (NLS) equation; whereas Er impurities contribute to the self-induced transparency (SIT), which is described by the Maxwell-Bloch (MB) model [1][2][3][4][5][6][7][8][9]. As a result, the constraint to the NLS soliton namely the optical losses can be somewhat compensated with the effect of SIT.…”

“…Nonlinear waves propagating in an erbium-doped fiber system have attracted special attention, since the resonant absorption of the erbium-doped two levels system is a good solution to the optical losses [1][2][3][4][5][6][7][8][9]. One of the most well-known examples is the amplification and reshaping of optical soltion (bright soliton on a zero background) in a long-haul optical communication through fibers with an active region doped with erbium atoms.…”