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

Long time behaviour of the solution of Maxwell's equations in dissipative generalized Lorentz materials (II) A modal approach