Matching Magneto-Inductive Waves at Discontinuities in One- and Two-Dimensional Structures

Magneto-inductive (MI) waves, propagating through near-field magnetic coupling in resonant loop arrays, are crucial for energy transfer, sensing, and communication within low-frequency magnetic metamaterials and metasurfaces. Reflection at discontinuities in MI arrays affects device performance, yet matching conditions, especially in two-dimensional (2-D) structures, are inadequately characterized. Here, we present an analytical approach to derive matching impedances at the junction of two dissimilar 1-D MI waveguides and at 2-D array edges, incorporating frequency and propagation direction dependencies. Validated by circuit-based and full-wave simulations, the proposed conditions significantly suppress reflected waves and enable effective energy absorption at array boundaries. These results offer valuable insights and practical guidelines for designing matched MI structures, potentially improving performance in wireless power transfer systems, sensing devices, and magnetic metasurface technologies.