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Non-Hermitian quantum-like cascaded nonlinear optical frequency conversion and splitting in dissipative media

It is shown that cascaded nonlinear optical frequency conversion over an intermediate wavelength, subjected to dissipation, behaves similarly to population transfer via a decaying state in a three-state non-Hermitian quantum system. The intermediate dissipation leads to a fixed phase relationship between the input signal wave and the wave at the target frequency, what finally stabilizes both waves preventing any spatial oscillation of their powers. The cascaded conversion acts as a stable wave splitter between the input and target waves, the latter being nearly immune to power fluctuations of the pumps. A case of a simultaneous cascade of the sum frequency generation and the difference frequency generation processes is discussed as an example. A possible implementation, based on aperiodically engineered quasi-phase-matching in lithium niobate, is proposed.