**9. Conclusions**

For high-gain stimulus wave amplification via non-linear coupling in a micro-resonator, a high stored energy and a high polarization density is required. In order to maximize the intracavity energy and the polarization density, for a given resonance frequency (f0 ), the frequencies of the high-intensity ultrashort pulses that comprise the pump wave must be tuned accordingly. This can be accomplished via a computationally cost-efficient optimization algorithm such as the quasi-Newton BFGS algorithm. The optimization algorithm must be embedded in the numerical discretization method by choosing the stimulus wave magnitude as the cost function and by modifying it according to the problem constraints.

If the optimal frequencies of the high-intensity ultrashort pulses are set, it is possible to amplify a low-intensity stimulus wave with a very large gain coefficient even inside a micrometer-scale resonator.

**Author Contributions:** Conceptualization, Ö.E.A.; Methodology, Ö.E.A.; Software, Ö.E.A.; Validation, Ö.E.A, M.K.; Formal analysis, Ö.E.A.; Investigation, Ö.E.A.; Resources, Ö.E.A.; Data curation, Ö.E.A, M.K.; Writing—Original draft preparation, Ö.E.A.; Writing—Review and editing, Ö.E.A, M.K.; Visualization, Ö.E.A.; Supervision, M.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
