  The exclusive vector meson production cross section is one of the most
promising observables to probe the high energy regime of the QCD dynamics. In
particular, the squared momentum transfer ($t$) distributions are an important
source of information about the spatial distribution of the gluons in the
hadron and about fluctuations of the color fields. In this paper we complement
previous studies on exclusive vector meson photoproduction in hadronic
collisions presenting a comprehensive analysis of the $t$ - spectrum measured
in exclusive $\rho$, $\phi$ and $J/\Psi$ photoproduction in $pp$ and $PbPb$
collisions at the LHC. We compute the differential cross sections taking into
account gluon saturation effects and compare the predictions with those
obtained in the linear regime of the QCD dynamics. Our results show that gluon
saturation suppresses the magnitude of the cross sections and shifts the
position of the dips towards smaller values of $t$.
