Nonreciprocal wave propagation in a time-space modulated metasurface using the modified plane wave expansion method

The present work focuses on the impact of including the time-space modulation features on the band structure. This study introduces a modified plane wave expansion method for dealing with the out-of-plane wave propagation in a two-dimensional periodic metasurface. The proposed method, which is applied to structures with modulated properties, tackles the constraints of the conventional plane wave method. The characteristics of uncommon systems with space-time-variant properties are explored by analyzing the produced dispersion curves by modified plane wave method. This approach can also resolve the inconsistencies and drawbacks of other similar approaches. Three scenarios are employed to extract the patterns of bandgap regions and discover the impact of time-traveling material features on the creation of bandgap in periodic metasurfaces. The integrity of the introduced method has been established by comparison with data obtained from COMSOL finite element software as well as the reported results in the literature. The secondary objective of this study is to manipulate the location of the bandgap to achieve complete control over the propagation of waves. The effectiveness of the proposed approach becomes more apparent when applied to metamaterials that incorporate piezoelectric materials with discrete structures. This relates primarily to enhanced precision and speed, particularly in higher modes and sheds light on a potential application of extending this scenario to the more complex structures.