Bosonic cascade lasers are terahertz (THz) lasers based on stimulated radiative transitions between bosonic condensates of excitons or exciton-polaritons confined in a trap. We study the interaction of an incoming THz pulse resonant in frequency with the transitions between neighboring energy levels of the cascade. We show that at certain optical pump conditions the cascade becomes transparent to the incident pulse: it neither absorbs nor amplifies it, in the mean field approximation. The populations of intermediate levels of the bosonic cascade change as the THz pulse passes, nevertheless. In comparison, a fermionic cascade laser does not reveal any of these properties.The concept of bosonic cascade lasers has been introduced a few years ago with the objective of generating THz frequency radiation in a compact semiconductor system [1]. The bosonic cascade is defined as a series of bosonic energy levels with equal THz range spacing in energy. A boson excited in the highest level can undergo a series of transitions down the cascade, generating multiple THz frequency photons in analogy to fermionic quantum cascade lasers [2,3], which were also developed in the THz regime [4][5][6][7]. The critical difference of a bosonic cascade is that bosonic final state stimulation enhances the scattering rates such that even in the limit of weak spontaneous scattering rate, particles can reach the ground level of the cascade. A variety of theoretical considerations of bosonic cascades have since been considered, including the quantum statistics of the cascade levels [8] and the interplay of double bosonic stimulation coming from a THz cavity and the bosonic particles themselves [9]. Physical implementations of bosonic cascades can be based on excitons or exciton-polaritons in parabolic traps [10]