It is well-known that a transfer function method is useful to predict the profile of a pulse after it propagates through an intracavity fast-light medium. However, by using this technique, a behavior of the pulse inside the medium cannot be determined. In this paper, we describe a new theoretical approach to deal with this constraint. In the new method, we find an analytical solution for a monochromatic field of infinite spatial and temporal extents, and add the waves with the weighted amplitude and with the tailored phase to embody a Gaussian input pulse moving toward the cavity. At different time frames, the sum of these waves produces a spatial profile of the pulse before, inside and after the cavity. In particular, the pulse profile can be visualized during a superluminal propagation through the intracavity fast-light medium with zero group index. This model allows us to understand the physical process behind the superluminal propagation through a white light cavity, which is significant to realize a high bandwidth data buffer system overcoming conventional delay bandwidth product(DBP) problem.