The propagation of a vector meson (rho and omega) in dense asymmetric
nuclear matter (with the number density of protons and neutrons differ
ent) is studied. Of particular interest is the density dependence of t
he vector meson masses, as also their variation with the asymmetry par
ameter, mass splitting among the rho isospin multiplets and the change
of the form of the rho meson self-energy or the polarization tenser (
Pi(mu nu)) when the p<->n symmetry is broken, Contributions of both th
e Fermi sea and Dirac vacuum have been considered. It is shown that wh
ile the density dependent dressing of the vector meson propagator lift
s the dispersion characteristics into the region of instability, the D
irac vacuum on the other hand contributes with opposite sign, thereby
enhancing the possibility of stable collective modes even for higher v
alues of vector meson momenta. The role of tenser coupling on the disp
ersion characteristics is also presented.