Time-domain calculation of forerunners in Drude dispersive media without collisions

The forerunners of the step-modulated sine pulse propagating in Drude dispersive media are calculated in the time domain. Two such problems are solved analytically. In the first problem, the plane source of the electric field is inside the medium. And the second problem considers the normal incidence of a linearly polarized wave from a vacuum upon a half-space medium. The obtained forerunners are identified as Sommerfeld precursors but the frequency of the oscillations and their amplitudes are closer to the exact solutions than the predictions of canonical Sommerfeld precursor. Moreover, the obtained periodicity of the forerunners is in perfect agreement with the exact solution. The developed analytics is an important contribution to the time-domain theory of the forerunners. The obtained data will be helpful for an experimental study of the forerunners and for the comparison with the forerunners in other dispersive media or with other waveforms of the incident pulse.