The method of multiply reflected waves in the problem of the propagation of electromagnetic waves in regular waveguides /Review/

The paper examines various aspects of the method of multiply reflected waves, with particular reference to the study of long and ultralong wave propagation in the earth-ionosphere waveguide. A detailed analysis is presented of exact field representations: in the form of the sum of boundary integrals, in the form of a modified series of zonal harmonics, and in the form of a plane-wave expansion. Attention is also given to approximate field representations, associated with the method of path integrals, the geometric-optics approximation, and the quasi-geometric-optics approximation, including the White diffraction corrections. Two model problems are used to illustrate the application of the rigorous approach to the problem of field representation in a waveguide in the form of a series of multiply reflected waves. Finally, studies relating to the method of multiply reflected waves are briefly surveyed.