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Third-harmonic generation can be realized via both $\chi^{(3)}$ and cascaded$\chi^{(2)}$ nonlinear processes in a triply-resonant microcavity. It is stillunknown how these processes interfere with each other and the optimization ofthe conversion efficiency still remains as a question. In this work, theinterplay between the direct third-harmonic generation and the cascaded processcombining of the second-harmonic generation and the sum-frequency generationare investigated. It is found that the interference effect between these twoprocesses can be used to improve the conversion efficiency. By optimizing thecavity resonance and the external coupling conditions, the saturation of thenonlinear conversion is mitigated and the third-harmonic conversion efficiencyis increased. A design rule is provided for achieving efficient third-harmonicgeneration in an optical microcavity, which can be generalized further to thehigh-order harmonic generations.

Optimal third-harmonic generation in an optical microcavity with $\chi^{(2)}$ and $\chi^{(3)}$ nonlinearities