Closed-form analytic phase solutions of three-wave interactions are presented for the first time, to the best of my knowledge. Cases from simple second-harmonic generation to the most general three-wave interactions without any constraints are considered. The phase amplification or deamplification behavior in the phase-sensitive parametric process is illustrated using the results obtained here. The analytic solutions agree with the results from direct numerical integration. The validity range of an approximate phase solution is discussed.
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