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A fresh approach to the full wave analysis of time evolution of thepolarization induced in the electromagnetic scattering from dispersive nonmagnetic particles is presented. It is grounded on the combination of theHopfield model for the polarization field, the expansion of the polarizationfield in terms of static longitudinal and transverse modes of the particle, theexpansion of the radiation field in terms of transverse wave modes of freespace, and the principle of least action. The polarization field is linearlycoupled to the electromagnetic field. The losses of the matter are providedthrough a linear coupling of the polarization field to a bath of harmonicoscillators with a continuous range of natural frequencies. The set of linearordinary differential integral equations of convolution type of the overallsystem is reduced by eliminating both the radiation degrees of freedoms and thebath degrees of freedom, and the reduced system of equations is studied. Therole played by the radiation field in the coupling between the longitudinal andtransverse mode amplitudes of the polarization is described. The principalcharacteristics of the temporal evolution of the mode amplitudes are found asthe particle size varies, including the impulse response. Results are presentedfor the analytically solvable spherical particle. The proposed approach leadsto a general method for the analysis of the temporal evolution of thepolarization field induced in dispersive particles of any shape, as well as forthe computation of transients and steady states.

Time-Domain Formulation of Electromagnetic Scattering Based on a Polarization Mode Expansion and the Principle of Least Action