Characterizing the dispersion behavior of poly-atomic magnetic metamaterials

The propagation of magnetoinductive (MI) waves across magnetic metamaterials known as magnetoinductive waveguides (MIWs) has been an area of interest for many applications due to the flexible design and low-loss performance in challenging radio-frequency (RF) environments. Thus far, the dispersion behavior of MIWs has been limited to mono- and diatomic geometries. In this work, we present a recursive method to generate the dispersion equation for a general poly-atomic MIW. This recursive method greatly simplifies the ability to create closed-form dispersion equations for unique poly-atomic MIW geometries versus the previous method. To demonstrate, four MIW geometries that have been selected for their unique symmetries are analyzed using the recursive method. Using applicable simplifications brought on by the geometric symmetries, a closed-form dispersion equation is reported for each case. The equations are then validated numerically and show excellent agreement in all four cases. This work simultaneously aids in the further development of MIW theory and offers new avenues for MIW design in the presented dispersion equations.