  A fresh approach to the full wave analysis of time evolution of the
polarization induced in the electromagnetic scattering from dispersive
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
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. The reduced system of equations, which governs the time
evolution of longitudinal and transverse mode amplitudes of the polarization,
is studied. 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, which are validated in the small size limit. The proposed approach
leads to a general method for the analysis of the temporal evolution of the
polarization field induced in dispersive particles with arbitrary shape, as
well as, for the computation of the transients and the steady states.
