  The continuous advancements in ultrafast lasers, characterized by high pulse
energy, great average power, and ultrashort pulse duration, have opened up new
frontiers and applications in various fields such as high-energy-density
science. In this study, we investigated the implementation of non-Hermitian
nonlinear parametric amplification by introducing anti-parity-time (anti-PT)
symmetry to three-wave interaction processes. By exploring the parameter space
defined by the coupling coefficient, phase mismatch, and absorption, we
categorized the behavior of the non-Hermitian optical parametric system into
four distinct quadrants, representing unbroken/broken anti-PT symmetry and
amplification/attenuation, and amplification-attenuation boundaries and
exceptional lines can be observed in such parametric space. Through simulations
of the dynamical behavior of the interacting waves, we demonstrated the rich
evolutions of the signal and idler waves in systems belonging to the respective
quadrants and near exceptional points, revealed by the unique performance of
eigenmodes. Our findings provide insights into the evaluation of energy flow
direction in optical parametric amplification engineering by the directly
linked parameter space, which contribute to a deeper understanding of photonics
and laser science, potentially leading to new applications in these fields.
