  Space-time modulated metasurfaces (STMMs) are a recently proposed
generalization of reconfigurable intelligent surfaces, which include a proper
time-varying phase at the metasurface elements, enabling higher flexibility and
control of the reflected signals. The spatial component can be designed to
control the direction of reflection, while the temporal one can be adjusted to
change the frequency of the reflected signal or to convey information. However,
the coupling between the spatial and temporal phases at the STMM can adversely
affect its performance. Therefore, this paper analyzes the system parameters
that affect the space-time coupling. Furthermore, two methods for space-time
decoupling are investigated. Numerical results highlight the effectiveness of
the proposed decoupling methods and reveal that the space-time phase coupling
increases with the bandwidth of the temporal phase, the size of the STMM, and
with grazing angles of incidence onto the STMM.
