Fast‐field programs (FFPs) have emerged as an important tool for predicting transmission loss in an ocean waveguide. Such models have been primarily used for time‐harmonic sources; however, pulses or other broadband sources may be treated by Fourier synthesis. A new technique is developed that provides adirectsolution by marching the solution forward in time. As an example of the method, a pulse incident on an interface between two homogeneous half‐spaces is considered. Snapshots of the pulse in time illustrate graphically the effects on the reflected and transmitted waves. Second, an interesting hyperbolic cosine profile is considered that leads to repeated focusing as the pulse propagates out in range.