The growing interest in exciton-polaritons has driven the need to manipulate their motion and engineer their band structures to the forefront of contemporary research. In this study, we explore the band structures that emerge from a spatially modulated potential, realized through the use of an optical conveyor belt. By leveraging Bloch theory and conducting a meticulous analysis of the time evolution of polariton intensity in Fourier space, we have derived the energy dispersion relations both analytically and numerically within the context of a static lattice model. For time-dependent potentials, we employ the Lagrange variational method to elucidate the dynamics of polariton motion. Our results reveal that polaritons exhibit linear dispersion and follow linear trajectories with minor oscillations superimposed. In this investigation, we not only deepen our fundamental understanding of exciton-polaritons but also provide a robust tool for advancing photonic devices and exerting precise control over current transport in quantum computing. Our findings pave the way for future innovations in high-speed and high-performance technologies.

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• Exciton polariton
• 2-dimensional systems
• Atomic Properties
• Variational wave functional methods