Alternate backward and forward waves in a coupled nonlinear transmission line

In this work, we investigate backward and forward waves in a coupled nonlinear discrete electrical lattice. It is made of several of the well-known Noguchi electrical transmission line that are transversely coupled to one another by an inductor L2. Based on the linear dispersion law, we show that the behavior of this model depends on the wave frequency that it propagates. It can adopt purely right-handed, purely left-handed or composite right-/left-handed behaviors without changing its structure. It appears that for fixed line's parameters, the network is right-handed for low frequencies and becomes left-handed for high frequencies. It also appears that the increase of the coupling linear inductor induces a decrease of the width of the bandpass filter in the left-handed region while it increases its width in the right-handed region. By means of a method based on the semi-discrete limit and in suitably scaled coordinates, we derive a two-dimensional NLS equation governing the propagation of slowly modulated waves in the network. The exact transverse bright solitary solution is found. Using this solution, we investigate numerically both right-handed and left-handed behaviours of the system and show how to manipulate the coupling inductor to modify the width and the motion of the bright solitary voltage signals in the network.