\geq 1/16$, where $\Delta \hat{X}_{1}$ and $\Delta \hat{X}_{2}$ are the uncertainties in $\hat{X}_{1}$ and $\hat{X}_{2}$, respectively. A state is squeezed in $\hat{X}_{1} (\hat{X}_{2})$ if $\langle (\Delta \hat{X}_{1})^{2} \rangle <0.25\; \left( \langle (\Delta \hat{X}_{2})^{2}\rangle <0.25\right)$, or equivalently if $S_{X_{1(2)}}=4 \langle (\Delta \hat{X}_{1(2)})^{2} \rangle  -1$ satisfies the inequality $-1<S_{X_{1(2)}}<0$. The latter inequality implies that in order to exist squeezing, two-mode Glauber-Sudarshan $P$-function, $P(\alpha,\beta)= P(\alpha) P(\beta)$, requires to be nonpositive or singular in some regions of phase space [@knight]. Anyway, the two-mode squeezing parameters can be written as: $$\begin{aligned}
\label{vsqdx2}
 S_{X_{1}}&=&\mathrm{Re} \Big( \langle \hat{a}_{1}^{2} \rangle + \langle \hat{a}_{2}^{2} \rangle
 +2 \langle \hat{a}_{1}^{\dag}\hat{a}_{2}\rangle+2\langle \hat{a}_{1}\hat{a}_{2} \rangle \Big)
 +\langle \hat{a}_{1}^{\dag}\hat{a}_{1} \rangle  \nonumber\\
 &+& \langle \hat{a}_{2}^{\dag}\hat{a}_{2} \rangle - 2\Big[\mathrm{Re}\Big(\langle \hat{a}_{1} \rangle+\langle \hat{a}_{2} \rangle\Big)\Big]^{2}, \nonumber\\
 S_{X_{2}}&=&\mathrm{Re} \Big( 2\langle \hat{a}_{1}^{\dag}\hat{a}_{2} \rangle
 -2\langle \hat{a}_{1}\hat{a}_{2} \rangle
 -\langle \hat{a}_{1}^{2} \rangle - \langle \hat{a}_{2}^{2} \rangle\Big)
 +\langle \hat{a}_{1}^{\dag}\hat{a}_{1} \rangle  \nonumber \\
 &+& \langle \hat{a}_{2}^{\dag}\hat{a}_{2} \rangle - 2\Big[\mathrm{Im}\Big(\langle \hat{a}_{1} \rangle+\langle \hat{a}_{2} \rangle\Big)\Big]^{2}.
 \end{aligned}$$ Figure \[two-modesq\] shows the temporal behavior of two-mode squeezing in $X_{1}$ for some of the chosen parameters as considered in figure \[quant.ph-sq\]. Also, the upside (downside) plots concern with the absence (presence) of the intensity-dependent coupling. In the upside plot of figure \[two-modesq\](a), where the Kerr effect and intensity-dependent coupling are both 