  This work concerns the analysis of electromagnetic dispersive media modelled
by generalized Lorentz models. More precisely, this paper is the second of two
articles dedicated to the long time behaviour of solutions of Maxwell's
equations in dissipative Lorentz media, via the long time decay rate of the
electromagnetic energy for the corresponding Cauchy problem. In opposition to
the frequency dependent Lyapunov functions approach used in [Cassier, Joly,
Rosas Mart\'inez, Z. Angew. Math. Phys. 74 (2023), 115], we develop a method
based on the spectral analysis of the underlying non-self-adjoint operator of
the model. Although more involved, this approach is closer to physics, as it
uses the dispersion relation of the model, and has the advantage to provide
more precise and more optimal results, leading to distinguish the notion of
weak and strong dissipation.
