We study the general wave phenomenon of diffractive focusing from a single slit for two types of waves and demonstrate several properties of this effect. Whereas in the first situation, the envelope of a surface gravity water wave is modulated in time by a rectangular function, leading to temporal focusing, in the second example, surface plasmon polariton waves are focused in space by a thin metal slit to a transverse width narrower than the slit itself. The observed evolution of the phase carrier of the water waves is measured for the first time and reveals a nearly flat phase as well as an 80% increase in the intensity at the focal point. We then utilize this flat phase with plasmonic beams in the spatial domain, and study the case of two successive slits, creating a tighter focusing of the waves by putting the second slit at the focal point of the first slit.