Wave reflection from a triangular layer

The reflection of waves from layers with a parabolic and triangular profile is of interest when investigating the ionospheric propagation of radio waves. Although the properties of a parabolic layer are fairly well known, the problem of the reflection of waves from a triangular layer has not been considered in the literature. In this paper, using the accurate solutions of the Helmholtz equation for a linear layer, we obtain analytical expressions for the complex reflection and transmission coefficient of a triangular layer which are expressed in terms of cylindrical functions of order 1/3. For frequencies considerably greater or less than the critical frequency these expressions give quantitative agreement with the well - known equations, but differ considerably from these relations at frequencies close to the critical frequency.