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.