  We demonstrate a compact and robust method for generating a 399-nm light
resonant on the $^{1}S_{0}-^{1}P_{1}$ transition in ytterbium using a
single-pass periodically poled LiNbO$_{3}$ waveguide for second harmonic
generation (SHG). The obtained output power at 399 nm was 25 mW when a 798-nm
fundamental power of 380 mW was coupled to the waveguide. We observed no
degradation of the SHG power for 13 hours with a low power of 6 mW. The
obtained SHG light has been used as a seed light for injection locking, which
provides sufficient power for laser cooling ytterbium.
