  A fresh approach to the full wave analysis of time evolution of the
polarization induced in the electromagnetic scattering from dispersive non
magnetic particles is presented. It is grounded on the combination of the
Hopfield model for the polarization field, the expansion of the polarization
field in terms of static longitudinal and transverse modes of the particle, the
expansion of the radiation field in terms of transverse wave modes of free
space, and the principle of least action. The polarization field is linearly
coupled to the electromagnetic field. The losses of the matter are provided
through a linear coupling of the polarization field to a bath of harmonic
oscillators with a continuous range of natural frequencies. The set of linear
ordinary differential integral equations of convolution type of the overall
system is reduced by eliminating both the radiation degrees of freedoms and the
bath degrees of freedom, and the reduced system of equations is studied. The
role played by the radiation field in the coupling between the longitudinal and
transverse mode amplitudes of the polarization is described. The principal
characteristics of the temporal evolution of the mode amplitudes are found as
the particle size varies, including the impulse response. Results are presented
for the analytically solvable spherical particle. The proposed approach leads
to a general method for the analysis of the temporal evolution of the
polarization field induced in dispersive particles of any shape, as well as for
the computation of transients and steady states.
