A transfer matrix method for analyzing quantum transport in harmonically driven systems with spatiotemporal coherence has been developed. In such systems, the energy conservation law is violated, and transport occurs through an infinite number of sideband states. This transfer matrix method enables us to compute transmission and reflection probabilities of such dynamical mesoscopic systems without consuming a large amount of computing time and memory space. We apply this technique to photon-assisted tunneling (PAT) in a dual-gate field-effect transistor, and demonstrate the possibility of observing resonant level splittings due to the dynamical Stark effect in dual-gate PAT devices.