  In this work we estimate the differential cross section for the high energy
deeply virtual Compton scattering on a photon target within the QCD
dipole-dipole scattering formalism. For the phenomenology, a saturation model
for the dipole-dipole cross section for two photon scattering is considered.
Its robustness is supported by good description of current accelerator data. In
addition, we consider the related exclusive vector meson production processes.
This analysis is focused on the light $\rho$ and $\phi$ meson production, which
produce larger cross sections. The phenomenological results are compared with
the theoretical calculation using the CD BFKL approach.
