Advantages of parametric amplifier over microwave amplifier?

Microwave and audio parametric amplifiers were used as low-noise amplifiers, to process low-level signals. Therefore their non-linearity probably never occurred in use.

In principle, Manley-Rowe theory holds for any frequency combination, and should apply also in optics. I am not aware about the application in optics but it is clearly possible.

In optical spectrum (frequencies above IR), however, quantum noise prevails above thermal noise, so low-noise amplification is usually not needed or not possible.