  In this paper, we investigate the localization of the $U(1)$ gauge field on
Randall-Sundrum-like braneworld models. The localization of the $U(1)$ gauge
field is important because it plays a fundamental role in the branworld
theories. To achieve the localization, we propose a novel action with a
non-minimal coupling between the $U(1)$ gauge field and gravity. We find that
the mass spectrum of the gauge field is continuous, without any gap between the
zero-mass mode and the massive modes, and except for the zero-mass mode all the
massive modes are not localized on the brane. Furthermore, the massive modes
have negative squared masses, indicating they are tachyonic. Our analysis can
be applied to a wide range of thin and thick braneworld scenarios, provided
that the five-dimensional spacetime is asymptotically anti-de Sitter.
