  We study diffractive vector meson production in ultra-peripheral collisions
(UPCs) of heavy nuclei, utilizing a theoretical framework based on the Color
Glass Condensate (CGC) formalism. We focus on Au+Au, U+U, Ru+Ru, Zr+Zr, and
Pb+Pb collisions, examining the transverse momentum dependence of vector meson
production cross-sections and ${\rm cos(2\Delta\Phi)}$ asymmetries in the decay
product distributions to explore the role of nuclear geometry. The angular
modulation is due to the linear polarization of the incoming photons and
quantum interference effects. We extract nuclear radii and find them to be
consistent with experimental data from the STAR collaboration. The amplitudes
of the ${\rm cos(2\Delta\Phi)}$ modulation in the cross-section and the
extracted radii depend on the nuclear geometry. This dependence is dominated by
the geometry-dependent variation of the minimum impact parameter required for
ultra-peripheral collisions.
