  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.
