  We theoretically study the transport of exciton polaritons under different
applied photon potentials. The relation between the photon potentials and the
thickness of the cavity layer is calculated by the finite element simulation.
The theoretical analysis and numerical calculation indicate that the cavity
photon potential is proportional to the thickness of the cavity layer with the
coefficient being about $1.8$ meV/nm. Further, the periodic and linear photon
potentials are considered to control the transport of the exciton polaritons in
weak- and strong-field pump situations. In both situations the periodic
potential cannot by itself effectively suppress the scatterings of the disorder
potentials of the cavity photons and excitons and the nonlinear exciton-exciton
interaction. When the linear potential is added to the cavity photons, the
polariton transport exhibits the Bloch oscillation behavior. Importantly, the
polariton Bloch oscillation can strongly suppress the space broadening due to
the disorder potentials and nonlinear exciton-exciton interaction, which is
beneficial for designing the polariton circuits.
