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

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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 structures, are inadequately characterized. Here we present an analytical approach to derive matching impedances at the junction of two dissimilar one-dimensional MI waveguide and at two-dimensional 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.