  Optical frequency conversion processes in nonlinear materials are limited in
wavelength by the accessible phase matching and the required high pump powers.
In this letter, we report a novel broadband phase matching (PM) technique in
high quality factor (Q) whispering gallery mode (WGM) resonators made of
birefringent crystalline materials. This technique relies on two interacting
WGMs, one with constant and the other with spatially oscillating phase
velocity. Thus, phase matching occurs cyclically. The technique can be
implemented with a WGM resonator with its disk plane parallel to the optic axis
of the crystal. With a single beta barium borate (BBO) resonator in that
configuration, we experimentally demonstrated efficient second harmonic
generation (SHG) to harmonic wavelengths from 780 nm in the near infrared to
317 nm in the ultraviolet (UV). The observed SHG conversion efficiency is as
high as 4.6% (mW)-1. This broadband PM technique opens a new way for nonlinear
optics applications in WGM resonators. This work is also the first reported
continuous wave UV generation by direct SHG in a WGM resonator
