Metamaterials possess high freedom on structural design, yet their ability to modulate electromagnetic waves is subject to intrinsic constraints that are independent of specific meta-atom geometries. The constraints are revealed by analyzing the statistical amplitudes and phases of transmission and reflection wave in some representative metamaterials. Based on scattering theory, a reconstructed and more general description of the electromagnetic modulation process in metamaterials is established. Two explicit and geometry-independent corollaries concerning the coupling between transmission and reflection waves are further obtained and verified. The results provide a new perspective on the fundamental modulation mechanism of metamaterials on electromagnetic waves.
Xu et al. (2026) studied this question.