  It is known that a five-dimensional free vector field $A_{M}$ cannot be
localized on Randall-Sundrum (RS)-like thick branes, namely, the thick branes
embedded in asymptotic Anti-de Sitter (AdS) spacetime. In order to localize a
vector field on the RS-like thick brane, an extra coupling term should be
introduced. In this paper, we generalize the geometrical coupling mechanism by
adding two mass terms ($\alpha Rg^{MN}A_{M}A_{N}+\beta R^{MN}A_{M}A_{N}$) into
the action. We decompose the fundamental vector field $A_{M}$ into three parts:
transverse vector part $\hat{A}_{\mu}$, scalar parts $\phi$ and $A_{5}$. Then,
we find that the transverse vector part $\hat{A}_{\mu}$ decouples from the
scalar parts. In order to eliminate the tachyonic modes of $\hat{A}_{\mu}$, the
two coupling parameters $\alpha$ and $\beta$ should satisfy a relation.
Combining the restricted condition, we can get a combination parameter as
$\gamma=\frac{3}{2}\pm\sqrt{1+12\alpha}$. Only if $\gamma>1/2$, the zero mode
of $\hat{A}_{\mu}$ can be localized on the RS-like thick brane. We also
investigate the resonant character of the vector part $\hat{A}_{\mu}$ for the
general RS-like thick brane with the warp factor $A(z)=-\ln(1+k^2z^2)/2$ by
choosing the relative probability method. The result shows that, only for
$\gamma>3$, the massive resonant Kaluza-Klein modes can exist. The number of
resonant Kaluza-Klein states increases with the combination parameter $\gamma$,
and the lifetime of the first resonant state can be long enough as the age of
our universe. This indicates that the vector resonances might be considered as
one of the candidates of dark matter.
