Phase distortions in sum- and difference-frequency mixing in crystals

We show that if two waves are incident on a quadratically nonlinear crystal, with the third wave generated entirely within the crystal, a phase-velocity mismatch (Δk ≠ 0) leads to intensity-dependent phase shifts of the generated wave only if there is walk-off, linear absorption, or significant diffraction of at least one of the waves as well as significant energy exchange among the waves. The result is frequency broadening and wave-front distortion of the generated wave. Although the induced phase distortions are usually quite small, they may be significant in applications that require high spectral resolution or pointing accuracy.