Efficient soliton compression by fast adiabatic amplification

Exact Self-Similar Solutions of the Generalized Nonlinear Schrödinger Equation with Distributed Coefficients

“…Although self-similar solutions have been extensively studied in fields such as hydrodynamics and quantum field theory, their application in optics has not been widespread. Some important results have, however, been obtained, with previous theoretical studies considering self-similar behavior in radial pattern formation [2], stimulated Raman scattering [3], the evolution of self-written waveguides [4], the formation of Cantor set fractals in soliton systems [5], the nonlinear propagation of pulses with parabolic intensity profiles in optical fibers with normal dispersion [6], and nonlinear compression of chirped solitary waves [7,8].In this Letter we present the discovery of a broad class of exact self-similar solutions to the nonlinear Schrö -dinger equation with gain or loss (the generalized NLSE) where all parameters are functions of the distance variable. This class also encloses the set of solitary wave solutions which describes, for example, such physically important applications as the amplification and compression of pulses in optical fiber amplifiers [9].…”

“…Although self-similar solutions have been extensively studied in fields such as hydrodynamics and quantum field theory, their application in optics has not been widespread. Some important results have, however, been obtained, with previous theoretical studies considering self-similar behavior in radial pattern formation [2], stimulated Raman scattering [3], the evolution of self-written waveguides [4], the formation of Cantor set fractals in soliton systems [5], the nonlinear propagation of pulses with parabolic intensity profiles in optical fibers with normal dispersion [6], and nonlinear compression of chirped solitary waves [7,8].…”

Chirped Self-Similar Solutions of a Generalized Nonlinear Schrödinger Equation

“…Although self-similar solutions have been extensively studied in fields such as hydrodynamics and quantum field theory, their application in optics has not been widespread. Some important results have, however, been obtained, with previous theoretical studies considering self-similar behaviour in radial pattern formation [6], stimulated Raman scattering [7], the evolution of self-written waveguides [8], the formation 0932-0784 / 11 / 0100-0001 $ 06.00 c 2011 Verlag der Zeitschrift für Naturforschung, Tübingen · http://znaturforsch.com of Cantor set fractals in soliton systems [9], the nonlinear propagation of pulses with parabolic intensity profiles in optical fibers with normal dispersion [10], and nonlinear compression of chirped solitary waves [11,12]. In this paper we present the discovery of a broad class of exact self-similar solutions to the nonlinear Schrödinger equation with gain or loss (the generalized NLSE) where all parameters are functions of the distance variable.…”

Controlling pulse propagation in optical fibers through nonlinearity and dispersion management

“…Adiabatic soliton compression, through the decrease of dispersion along the length of the fiber has been shown to provide good pulse quality [8]. The possibility of amplification of soliton pulses using a rapidly increasing distributed amplification with scale lengths comparable to the characteristic dispersion length has been reported [9]. It has been numerically shown that, in the case where the gain due to * atre@prl.res.in † prasanta@prl.res.in the nonlinearity and the linear dispersion balance each other, equilibrium solitons are formed [10].…”