  We present a detailed study of vector meson photoproduction in
ultraperipheral heavy ion collisions (UPCs). Using the dipole model, we develop
a framework for the joint impact parameter and transverse momentum dependent
cross sections. We compute the unpolarized cross section and $\cos 2\phi$
azimuthal angular correlation for $\rho^0$ photoproduction with $\phi$ defined
as the angle between the $\rho^0$'s transverse momentum and its decay product
pion meson's transverse momentum. Our result on unpolarized coherent
differential cross section gives excellent description to the STAR experimental
data. A first comparison between theoretical calculation and experimental
measurement on the $\cos 2\phi$ azimuthal asymmetry, which results from the
linearly polarized photons, is performed and reasonable agreement is reached.
We find out the characteristic diffractive patterns at both RHIC and LHC
energies and predict the impact parameter dependent $\cos 2\phi$ azimuthal
asymmetries for $\rho^0$ photoproduction by considering UPCs and peripheral
collisions. The future experimental measurements at RHIC and LHC relevant to
our calculations will provide a tool to rigorously investigate the coherent and
incoherent production of vector meson in UPCs, as well as to probe the nuclear
structure in heavy ion collisions.
