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We derive general conditions for 100 percent frequency conversion in anydoubly resonant nonlinear cavity, for both second- and third-harmonicgeneration via chi2 and chi3 nonlinearities. We find that conversion efficiencyis optimized for a certain critical power depending on the cavity parameters,and assuming reasonable parameters we predict 100 percent conversion usingmilliwatts of power or less. These results follow from a semi-analyticalcoupled-mode theory framework which is generalized from previous work toinclude both chi2 and chi3 media as well as inhomogeneous (fully vectorial)cavities, analyzed in the high-efficiency limit where down-conversion processeslead to a maximum efficiency at the critical power, and which is verified bydirect finite-difference time-domain (FDTD) simulations of the nonlinearMaxwell equations. Explicit formulas for the nonlinear coupling coefficientsare derived in terms of the linear cavity eigenmodes, which can be used todesign and evaluate cavities in arbitrary geometries.

Chi2 and chi3 harmonic generation at a critical power in inhomogeneous doubly resonant cavities