We study theoretically the optical response of the resonant medium on the few-cycle pulse-driven excitation for different types of the coupling strength to the field. It is demonstrated that the medium can exhibit a specific excitation response depending on the field coupling nonlinearity. Remarkably, the analysis of this response revealed the possibility of the controllable generation and shaping of unipolar optical pulses, which can be important in real-time observation and time-domain control of ultrafast processes in matter.