If we have two laser beams with central wavelengths ${\lambda}_{1}$ and ${\lambda}_{2}$, (one with a spectral width of $\mathrm{\Delta}{\lambda}_{2}$ and one with negligible spectral width), interacting in a non-linear crystal, how would we calculate the spectral width of the difference-frequency-generated (DFG) output? I know it's a Lorentzian given by $\mathrm{\Delta}\lambda =\frac{4{\lambda}_{1}^{2}\mathrm{\Delta}{\lambda}_{2}}{4({\lambda}_{2}-{\lambda}_{1}{)}^{2}-\mathrm{\Delta}{\lambda}_{2}^{2}}$. But I don't know how to prove this.