The primary goal of this study is to infer a time-domain (TD) counterpart of the frequency domain leaky wave. To reach this goal, a number of challenging problems will be tackled: (1) Develop adequate computational tools for performing detailed TD electromagnetic (EM) analyses via CST Studio simulations, the post-processing of the results included. (2) The TD study of the radiation from a gap-fed long slot at an air-dielectric interface. (3) The TD study of the radiation from a gap-fed long slot located just below an air-dielectric interface. The results of these explorations represent a first step towards establishing a causal counterpart of the leaky-wave radiation.