Optimal pulse under efficient conversion and pump depletion

Determine the fate of the soliton optimum when conversion becomes efficient and pump depletion makes the pump equation nonlinear, including the resulting critical-power and nonlinear impedance-matching conditions.

Background

The closed-form soliton optimum is derived in the undepleted-pump regime, where the resonator dynamics remain linear with respect to the pump field. The paper notes that efficient conversion invalidates this assumption: pump depletion introduces nonlinear pump dynamics, and critical-power and nonlinear impedance-matching effects become relevant. The authors leave unresolved whether the soliton-shaped stored field remains optimal in that regime.