Optical amplification by nonlinear wave mixing offers wideband high-gain amplification that is desirable for a variety of applications. When the wave mixing process occurs in an interaction medium with sufficient length, the attained gain per excitation pulse is usually higher than that can be attained by lasers. Furthermore, the bandwidth of amplification via nonlinear wave mixing is much higher than the bandwidth allowed by laser transitions of laser gain media. However, optical amplification by nonlinear wave mixing offers negligible gain in the micrometer scale, due to a very limited length of the interaction medium. In micro-resonators, such a short interaction length does not offer sufficient small signal gain to compensate the round-trip loss. In this study, we present a Fletcher-Reeves algorithm-based nonlinear programming of the wave mixing process that tunes the frequencies of the excitation pulses of the source device in order to provide an ultra-high optical gain in the micro-scale via maximizing the electric energy density in a micro-resonator. Using this smart wave mixing approach, we obtained a micro-resonator gain of 4.7x107 for an input wave at 640 THz, and a gain of 1.5x108 at 100 THz. The results of our mathematical formulation are compared with well-known experimental results, and a mean accuracy of 99% is observed. The study aims to show that optical amplifiers that are based on the principle of nonlinear wave mixing can be used in the micro-scale for wideband ultra-high gain operation.
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