Akhmediev-Peregrine rogue waves generation in a composite right/left handed transmission line

We analyze the right-handed behavior of a composite right/left-handed transmission line where electromagnetic wave is propagated. Cubic-nonlinearity, second-order dispersion and losses are taken into account. The left-handed behavior in such system which has been previously investigated in literature is compared to right-handed behavior presented here. Three frequency ranges have been outlined. The first one presents a distorted pulse which does not satisfy soliton conditions. We demonstrate that a weak nonlinearity strongly act on dispersion effect in order to induce modulational instability which leads to Akhmediev-Peregrine rogue waves generation. The second frequency range corresponds to intermediate frequencies which presents a collapsed soliton leading to a dispersive pulse. This situation is progressively improved and leads to a stable and robust soliton at the third frequency range when frequency increases. We also analyze in details the internal excitation leading to the external modification which provokes rogue waves generation in such system. It clearly appears that the number of rogue waves increases with frequency. The peak power and the form of rogue waves strongly dependant on the nonlinearity strength of distortion. The above results can allow the best comprehension of the rogue waves generation in composite transmission lines.