Materials with hyperbolic dispersion have recently garnered much attention in the optical and quantum communities due to their potential for controlling large- $k$ waves over a broad wavelength range. Their rarity has motivated many fundamental studies at microwave frequencies to improve their applications with full utilization of large- $k$ waves. Here, we report that hyperbolic dispersion can be mimicked by exploiting the structural dispersion of electromagnetic modes in waveguides filled with anisotropic dielectric materials. As demonstrated, the material parameters in the waveguide are subtly designed, and effective hyperbolic dispersion is achieved, which can reduce the dielectric loss and nonlocal effects related to the finite thickness of the discrete constituent elements of metamaterials at microwave frequencies. Numerical simulations are performed, including negative and anomalous refractions, negative reflection, and directional hyperbolic polaritons to validate the analytical results. The present method paves the way for the development of hyperbolic metamaterials at microwave frequencies.
