χ ( 2 ) and χ ( 3 ) harmonic generation at a critical power in inhomogeneous doubly resonant cavities

We derive general conditions for 100% frequency conversion in any doubly resonant nonlinear cavity, for both secondand third-harmonic generation via χ (2) and χ (3) nonlinearities. We find that conversion efficiency is optimized for a certain “critical” power depending on the cavity parameters, and assuming reasonable parameters we predict 100% conversion using milliwatts of power or less. These results follow from a semi-analytical coupled-mode theory framework which is generalized from previous work to include both χ (2) and χ (3) media as well as inhomogeneous (fully vectorial) cavities, analyzed in the high-efficiency limit where down-conversion processes lead to a maximum efficiency at the critical power, and which is verified by direct finite-difference time-domain (FDTD) simulations of the nonlinear Maxwell equations. 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