Linear guided waves in hyperbolic slab waveguide. Dispersion relations

Guided waves modes in a slab waveguide formed from the isotropic dielectric layer embedded by hyperbolic materials are investigated. Optical axis is normal to the slab plane. The dispersion relations for TE and TM waves are found. The differences between hyperbolic waveguide and conventional one are demonstrated. In particular, for each TM mode of hyperbolic waveguide there are two cut-off frequencies and the number of modes is limited. For the TE and TM modes Poynting vector component along the wave's propagation axis could be equal to zero.