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sion systems is associated with the creation of complete optical photon networks and optical com-
munication lines. In such systems, the transmission, reception and processing of signals without the
use of electronic devices and electronic processes will occur at the full level of photons. It is known
that in anisotropic media, electromagnetic waves propagate differently than in isotropic media [4].
In an anisotropic medium, the optical properties depend on the direction of light propagation, and
therefore, the orientation of the optical axis of the waveguide should affect the propagation condi-
tions of natural waves. New optical solutions require the creation of media with special optical prop-
erties. As you know, integrated optical components are manufactured in very complex processes, for
example, in the process of ion implantation. In order for the devices to be created to function as
designed by the developer, a detailed analysis of the waveguide propagation characteristics is neces-
sary, as well as the development of a simple set of calculation tools for production. This requires an
adequate mathematical model of the interaction of electromagnetic waves with matter, built on
Maxwell's equations. 
In this work, we obtained a mathematical model for calculating the eigen modes of a planar
anisotropic waveguide for an arbitrary tilt of the optical axis in the plane of incidence. New mathe-
matical models of the dispersion equations of a waveguide with an anisotropic medium for TE- and
TM-waves are obtained in this article. The asymptotic behavior of dispersion curves for a TM-wave
is studied as a function of the angle of orientation of the optical axis in the wave propagation
plane.The mathematical model of the interaction of an electromagnetic field with anisotropic mate-