We explore two parabolic quantum well (PQW) samples, with and without Bragg mirrors, in order to optimise the building blocks of a Bosonic Cascade Laser. The photoluminescence spectra of a PQW microcavity sample is compared against that of a conventional microcavity with embedded quantum wells (QWs) to demonstrate that the weak coupling lasing in a PQW sample can be achieved. The relaxation dynamics in a conventional QW microcavity and in the PQW microcavity was studied by a non-resonant pump-pump excitation method. Strong difference in the relaxation characteristics between the two samples was found. The semi-classical Boltzmann equations were adapted to reproduce the evolution of excitonic populations within the PQW as a function of the pump power and the output intensity evolution as a function of the pump-pump pulse delay. Fitting the PQW data confirms the anticipated cascade relaxation, paving the way for such a system to produce terahertz radiation.