The analytical model of the processes accompanying dispersion of electromagnetic waves by heterogeneity of a semi-infinite plasma waveguide has been considered. The electromagnetic field extending along a plasma waveguide was led to a system of the pair equations integrated which was transformed to a boundary problem for functions, analytical in planes of the complex variable. Results of the simulation performed have shown a possibility of the account of the contribution of various types of waves in a resultant absent-minded field. Dispersive characteristics for different types of waves were calculated. The expressions were obtained, allowing to estimate a radiation field in a distant zone on the basis of a stationary phase method.