New Types of Rogue Wave in an Erbium-Doped Fibre System

We report a novel and new types of rogue optical wave propagation in an erbium-doped fibre system governed by the nonlinear Schrödinger and the Maxwell--Bloch equation. The breather solutions of the three fields, namely field envelop, polarization and population inversion, are used to generate the rogue waves. For the first time, we report bright and, in particular, dark rogue waves in a coupled nonlinear optical systems. The distinction between bright and dark rogue waves are discussed in detail through figures. The rogue wave formation in our model can also be connected to the generation of supercontinuum generation in resonant optical fibre.