In this paper, we present and discuss an extension and an improvement of th
e Figure of Merit (FoM) that we introduced in a previous paper. The FoM des
cribes the effectiveness of the frequency doubling materials for ultrashort
light pulse modulators via second-order cascaded effects. In the present w
ork, as an input pulse we use a temporal Gaussian pulse so that our perturb
ative method allows an analytical expression even for the output pulse fiel
d after the second pass inside the crystal. For the first time together wit
h the completely analytical expression for the second pass, we report also
the exact numerical coefficients for the peak phase modulation. With the Fo
M 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 mu m, and
to a table already shown we added more nonlinear materials.