The cyclic exchange of energy between the pump, signal, and idler fields that characterizes optical parametric amplification (OPA) places a fundamental limitation on efficiency for Gaussian-shaped beam and pulse profiles typical of real laser sources. This is because the intensity dependent conversion period of OPA results in asynchronous conversion across the spatiotemporal intensity profiles of the mixing laser fields. We introduce a new method for achieving efficient OPA by using simultaneously phase-matched idler second harmonic generation (SHG) to act as an effective loss-channel for idler photons. The dynamics are characterized by damped conversion cycles, leading to asymptotic conversion of the pump and idler to the signal and idler second harmonic fields at all points in transverse space and time. We develop a damped Duffing oscillator model that unifies the description of conventional OPA with OPAs that use linear absorption \cite{Ma:15, El-Ganainy:15, Zhong:16, Li:17, Ma:17} or SHG \cite{Flemens:21} to remove idler photons and enhance efficiency. An experimental demonstration in a CdSiP\textsubscript{2}-based device enables 68% pump depletion with 44% pump to signal energy conversion efficiency--a several fold increase over conventional OPA efficiency. We then show that SHG can replace loss to induce non-Hermitian features such as regions of broken and unbroken PT-symmetric phase demarcated by an exceptional point in three-wave mixing nonlinear interactions. This enables a new paradigm where the behavior associated with the PT-symmetric phase of a non-Hermitian subsystem can be used to control the containing Hermitian system through the coherent couplings. These findings suggest a new approach for the engineering of dynamics where energy recovery and sustainability are of importance in photonics and laser science. Finally, we demonstrate self-dispersion managed adiabatic difference frequency generation (ADFG). While ADFG has been demonstrated to produce single-cycle pulses in the mid-IR \cite{Krogen:17}, this is not without the challenge of implementing a complicated dispersion management scheme to compensate for the complex dispersion imparted by the device. We engineer and characterize an aperiodically poled LiNbO\textsubscript{3} device that generates an octave-spanning bandwidth in the mid-IR (2-4 \textmu m) that imparts no net dispersion to the generated light.