  The propagation characteristics of magneto-quasistatic waves, more commonly,
known as magnetostatic waves in a long, metallic rectangular waveguide filled
with a metamaterial slab are comprehensively investigated. The metamaterial
slab consists of split-ring resonators as an anisotropic uniaxial medium with
transversal negative effective permeability. Some analytical relations and
numerical validations on the characteristics of these waves are presented. The
results include the dispersion relations, mode patterns (field distributions)
that can be supported by such media and their corresponding cutoff frequencies,
group velocities, power flows, and storage energies of magnetostatic waves. The
findings from the present research study can be advantageous to advance the
synthesis and development of negative permeability materials with peculiar
features in guiding structures.
