  For some crystalline materials, a regime can be found where continuous
ductile cutting is feasible. Using precision diamond turning, such materials
can be cut into complex optical components with high surface quality and form
accuracy. In this work we use diamond-turning to machine a monolithic,
square-shaped, doubly-resonant $LiNbO_3$ cavity with two flat and two convex
facets. When additional mild polishing is implemented, the Q-factor of the
resonator is found to be limited only by the material absorption loss. We show
how our monolithic square resonator may be operated as an optical parametric
oscillator that is evanescently coupled to free-space beams via birefringent
prisms. The prism arrangement allows for independent and large tuning of the
fundamental and second harmonic coupling rates. We measure $2.6\pm0.5$ dB of
vacuum squeezing at 1064 nm using our system. Potential improvements to obtain
higher degrees of squeezing are discussed.
