  A theory for excitation of molecular resonances by a train of precursors is
developed. Right at the vacuum-medium interface, a train of incident square
waves interacts with light electrons and is converted into a train of
precursors, which further excite molecular dipoles. Analytic calculations
indicate that these excited dipoles generate radiation, including secondary
precursors propagating in the backward direction. Encoded in this radiation are
proper frequencies of excited molecular dipoles allowing for spectroscopic
measurements. The frequency of the train of incident square pulses can be by
several orders of magnitude smaller than the proper frequencies of molecular
resonances.
