Free induction decay (FID), optical nutation, and rapid passage induced signals in nitrous oxide, under both optically thin and optically thick conditions, have been observed using a rapid current pulse modulation, or chirp, applied to the slow current ramp of a quantum cascade (QC) laser. The variation in optical depth was achieved by increasing the pressure of nitrous oxide in a long path length multipass absorption cell. This allows the variation of optical depth to be achieved over a range of low gas pressures. Since, even at the highest gas pressure used in the cell, the chirp rate of the QC laser is faster than the collisional reorientation time of the molecules, there is minimal collisional damping, allowing a large macroscopic polarization of the molecular dipoles to develop. This is referred to as rapid passage induced polarization. The resultant FID signals are enhanced due to the constructive interference between the field within the gas generated by the slow ramp of the laser (pump), and that of the fast chirp of the laser (probe) signal generated by pulse modulation of the continuously operating QC laser. The FID signals obtained at large optical depth have not been observed previously in the mid-infrared regions, and unusual oscillatory signals have been observed at the highest gas pressures used.