Coupling of broadband terahertz pulses into metal-metal terahertz quantum cascade lasers is presented. Mode matched terahertz transients are generated on the quantum cascade laser facet of subwavelength dimension. This method provides a full overlap of optical mode and active laser medium. A longitudinal optical-phonon depletion based active region design is investigated in a coupled cavity configuration. Modulation experiments reveal spectral gain and (broadband) losses. The observed gain shows high dynamic behavior when switching from loss to gain around threshold and is clamped at total laser losses.