“…(A closely related case is that of sum-frequency generation in a cavity resonant at the two frequencies being summed [40].) Second-harmonic generation in a doubly resonant cavity, with a resonance at both the pump and harmonic frequencies, has most commonly been analyzed in the low-efficiency limit where nonlinear down-conversion can be neglected [4,5,6,7,8,9], but down-conversion has also been included by some au-thors [1,2,3]. Here, we show that not only is downconversion impossible to neglect at high conversion efficiencies (and is, in fact, necessary to conserve energy), but also that it leads to a critical power where harmonic conversion is maximized.…”