Two-crystal second-harmonic interference ($I_{2\omega }=4{\alpha }^2{I}_0^2{L}^2{\cos }^2(\Delta k_{g}d/2)$)

Two identical phase-matched crystals generate coherent harmonic amplitudes. In a dispersive gap, the harmonic from the first crystal accumulates a different phase from twice the transmitted pump phase. Their interference gives the displayed undepleted-pump intensity in the stated equal-coupling amplitude normalization. Depletion changes the fringe shape; in the ideal lossless identical-crystal model, an opposite relative phase can coherently undo the first conversion.