There are two designs for a laser beam expander:
The Keplerian design where two converging lenses create a focal point inside the device, mainly used with pulsed laser to prevent heating of the medium; and
The Galilean design, where one of the lenses is a diverging lens: there is no focus in the device, and the size of the expander also reduces.
Both designs have their advantages and disadvantages, depending on the applications. Read more