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This invention is a doubly-resonant cavity structure having a plurality of resonant modes. The invented cavity allows total frequency conversion for second or third-harmonic generation using χ(2) and χ(3) nonlinearities between the cavity structures. The total frequency conversion is efficiently optimized by determining a critical power for the process of the total frequency conversion, and this critical power depends only on parameters of the cavity structure. The invention can achieve 100% frequency conversion with milliwatts of power, and can have intense light in cavity, without the phase-matching problem.