  Optical amplification of the input wave by mixing the pump wave within a
nonlinear interaction medium offers high gain for a variety of applications. In
real life studies, the interaction mediums which allow the optical
amplification of the input wave have many resonance frequencies. However, the
computational expense for tuning the pump frequency to yield the optical
amplification of the input wave increases with the number of resonance
frequencies within the interaction mediums. Here, we present a Fletcher-Reeves
based algorithm for parametric amplification in micro-resonators having
multiple resonance frequencies. Using our novel mathematical formulations, we
obtained a gain of 4.7x107 for the input wave at 640 THz and a gain of 1.5x108
for the input wave at 100 THz within the micro-resonators. Moreover, the
performance of our algorithm is verified by the well know mathematical
expression, and we achieved more than 99% accuracy in computation of optical
amplification. To our knowledge, this is the first study where Fletcher-Reeves
algorithm is used for the parametric amplification. Our methodology can be
accompanied to design optical parametric amplifiers for applications of
high-speed optical communications, photonic circuits, and ultrafast lasers.
