  We demonstrate second harmonic generation (SHG) in an $x$-cut congruent
lithium niobate (LN) whispering gallery mode resonator. We first show
theoretically that independent control of the coupling of the pump and signal
modes is optimal for high conversion rates. A scheme based on our earlier work
in Ref. [1] is then implemented experimentally to verify this. Thereby we are
able to improve on the efficiency of SHG by more than an order of magnitude by
selectively out-coupling using a LN prism, utilizing the birefringence of it
and the resonator in kind. We report 5.28%/mW efficiency for SHG from 1555.4 nm
to 777.7 nm.
