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It is known that a five-dimensional free vector field $A_{M}$ cannot belocalized on Randall-Sundrum (RS)-like thick branes, namely, the thick branesembedded in asymptotic Anti-de Sitter (AdS) spacetime. In order to localize avector field on the RS-like thick brane, an extra coupling term should beintroduced. In this paper, we generalize the geometrical coupling mechanism byadding two mass terms ($\alpha Rg^{MN}A_{M}A_{N}+\beta R^{MN}A_{M}A_{N}$) intothe 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 thescalar parts. In order to eliminate the tachyonic modes of $\hat{A}_{\mu}$, thetwo 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 modeof $\hat{A}_{\mu}$ can be localized on the RS-like thick brane. We alsoinvestigate the resonant character of the vector part $\hat{A}_{\mu}$ for thegeneral RS-like thick brane with the warp factor $A(z)=-\ln(1+k^2z^2)/2$ bychoosing the relative probability method. The result shows that, only for$\gamma>3$, the massive resonant Kaluza-Klein modes can exist. The number ofresonant Kaluza-Klein states increases with the combination parameter $\gamma$,and the lifetime of the first resonant state can be long enough as the age ofour universe. This indicates that the vector resonances might be considered asone of the candidates of dark matter.

Generalized geometrical coupling for vector field localization on thick brane in asymptotic Anti-de Sitter spacetime