Nonlinear guided wave modes in an asymmetric slab waveguide formed by an isotropic dielectric layer placed on a linear or nonlinear substrate and covered by a hyperbolic material are investigated. Optical axis is normal to the slab plane. The dispersion relations for TM waves are found. It is shown that there are additional cut-off frequencies for each TM mode. The effects of the nonlinearity on the dispersion relations are investigated and discussed. There are the modes, which are corresponded with situation where the peak of electric field is localized in the nonlinear substrate. These modes are absent in the linear waveguide. To excite these modes the power must exceed certain threshold value.

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.

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