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Non-Hermitian Dynamics Mimicked by a Hermitian Nonlinear System

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.