  Microresonator-based platforms with $\chi^{(2)}$ nonlinearities have the
potential to perform frequency conversion at high efficiencies and ultralow
powers with small footprints. The standard doctrine for achieving high
conversion efficiency in cavity-based devices requires "perfect matching", that
is, zero phase mismatch while all relevant frequencies are precisely at a
cavity resonance, which is difficult to achieve in integrated platforms due to
fabrication errors and limited tunabilities. In this Letter, we show that the
violation of perfect matching does not necessitate a reduction in conversion
efficiency. On the contrary, in many cases, mismatches should be intentionally
introduced to improve the efficiency or tunability of conversion. We identify
the universal conditions for maximizing the efficiency of cavity-based
frequency conversion and show a straightforward approach to fully compensate
for parasitic processes such as thermorefractive and photorefractive effects
that, typically, can limit the conversion efficiency. We also show rigorously
that these high-efficiency states are stable.
