In this paper, we present and discuss an extension and an improvement of the Figure of Merit (FoM) that we introduced in a previous paper. The FoM describes the effectiveness of the frequency doubling materials for ultrashort light pulse modulators via second-order cascaded effects. In the present work, as an input pulse we use a temporal Gaussian pulse so that our perturbative method allows an analytical expression even for the output pulse field after the second pass inside the crystal. For the first time together with the completely analytical expression for the second pass, we report also the exact numerical coefficients for the peak phase modulation. With the FoM it is possible to choose the more appropriate nonlinear material and the use of the cascaded interaction process. Finally, we present for the first time the FoM dependence from the wavelength in the interval 0.5–1 μm, and to a table already shown we added more nonlinear materials.