  We illustrate that a Hermitian nonlinear optical system consisting of
hybridized parametric amplification and second harmonic generation mimics
non-Hermitian evolution dynamics. Oscillation damping, evolution to a static
steady state, and exceptional points arise from the use of second harmonic
generation as an irreversible loss mechanism. The investigated system can be
used to solve problems of inefficiency in parametric amplifier systems used
widely in laser science and industrial applications. More generally, these
findings suggest a new paradigm for the engineering of system dynamics where
energy recovery and system sustainability are of importance.
