Transient properties of modified reservoir-induced transparency

We investigate the transient response of a $\Lambda$-type system with one transition decaying to a modified radiation reservoir with an inverse square-root singular density of modes at threshold, under conditions of transparency. We calculate the time evolution of the linear susceptibility for the probe laser field and show that, depending on the strength of the coupling to the modified vacuum and the background decay, the probe transmission can exhibit behaviour ranging from underdamped to overdamped oscillations. Transient gain without population inversion is also possible depending on the system's parameters.