  The rogue waves in a resonant erbium-doped fibre system governed by a coupled
system of the nonlinear Schr\"odinger equation and the Maxwell-Bloch equation
(NLS-MB equations) are given explicitly by a Taylor series expansion about the
breather solutions of the normalized slowly varying amplitude of the complex
field envelope $E$, polarization $p$ and population inversion $\eta$. The
n-order breather solutions of the three fields are constructed using Darboux
transformation (DT) by assuming periodic seed solutions. What is more, the
n-order rogue waves are given by determinant forms with $n+3$ free parameters.
Furthermore, the possible connection between our rouge waves and the generation
of supercontinuum generation is discussed.
