  For the Maxwell's equations in a Havriliak-Negami (H-N) dispersive medium,
the associated energy dissipation law has not been settled at both continuous
level and discrete level. In this paper, we rigorously show that the energy of
the H-N model can be bounded by the initial energy and the model is well-posed.
We analyse a backward Euler-type semi-discrete scheme, and prove that the
modified discrete energy decays monotonically in time. Such a strong stability
ensures that the scheme is unconditionally stable. We also introduce a fast
temporal convolution algorithm to alleviate the burden of the history
dependence in the polarisation relation involving the singular kernel with the
Mittag-Leffler function with three parameters. We provide ample numerical
results to demonstrate the efficiency and accuracy of a full-discrete scheme
via a spectra-Galerkin method in two dimensions. Finally, we consider an
interesting application in the recovery of complex relative permittivity and
some related physical quantities.
