  We generate coherent ultraviolet radiation at 313 nm as the third harmonic of
an external-cavity diode laser. We use this radiation for laser cooling of
trapped beryllium atomic ions and sympathetic cooling of co-trapped
beryllium-hydride molecular ions. An LBO crystal in an enhancement cavity
generates the second harmonic, and a BBO crystal in a doubly resonant
enhancement cavity mixes this second harmonic with the fundamental to produce
the third harmonic. Each enhancement cavity is preceded by a tapered amplifier
to increase the fundamental light. The 36-mW output power of this
all-semiconductor-gain system will enable quantum control of the beryllium
ions' motion.
