  The application of optical lattices allows a tuning of the geometry of
Bose-Einstein condensates to effectively reduced dimensions. In the context of
solid state physics the consideration of the low-dimensional Fr\"ohlich polaron
results in an extension of the polaronic strong coupling regime. With this
motivation we apply the Jensen-Feynman variational principle to calculate the
ground state properties of the polaron consisting of an impurity in a
Bose-Einstein condensate in reduced dimensions. Also the response of this
system to Bragg scattering is calculated. We show that reducing the dimension
leads to a larger amplitude of the polaronic features and is expected to
facilitate the experimental observation of polaronic properties. In optical
lattices not only Feshbach resonances but also confinement-induced resonances
can be used to tune the polaronic coupling strength. This opens up the
possibility to experimentally reveal the intermediate and strong polaronic
coupling regimes and resolve outstanding theoretical questions regarding
polaron theory.
