Engineering chirped Lambert W-kink signals in a nonlinear electrical transmission network with dissipative elements

Abstract

The dynamics of modulated waves in a nonlinear discrete transmission network with dissipative elements are investigated analytically. The generalized cubic-quintic Ginzburg-Landau (GCQ-GL) equation with intrapulse Raman scattering (IRS) terms governing spatially damped slowly modulated wave propagation is derived. Considering modulated Stokes wave propagating in the network, we investigate their baseband modulational instability (MI) and show that there are significant changes for the bandwidth frequency where the network may exhibit baseband MI. We show that the MI growth rate increases with the propagating frequency. The analytical chirped Lambert W-kink soliton-like solution of the derived GCQ-GL equation is presented and used to analyze the dissipative effects on chirped Lambert W-kink signals propagating through our network system. We show that the amplitude decreases both in space and time, while the width and the velocity remains constant when the Lambert W-kink signal propagates along the dissipative network. The effects of the cubic-Raman contributions on (i) the propagating frequency, (ii) the baseband MI, as well as (iii) the dynamics of Lambert W-kink signals are also investigated. In particular, our results reveal that a decrease in the cubic-Raman contributions enhances the baseband MI. The results of this paper may be useful for theoretical study of the propagation of ultrashort pulses in a single-mode optical fiber, as well as for experimental realization of undistorted transmission of optical pulses in optical fibers and further understanding their optical transmission properties.