Representation of the radiation field of semi-infinite circular dielectric waveguide as an expansion of the Gauss-Laguerre basis form

In the millimeter-wave interferometers, designed to study fast processes, the end-open dielectric waveguides, open and shielded, are used as a probing systems. The calculation of the radiation field is a rather complicated electrodynamics problem, which requires the inclusion of exciter of waveguide devices. The problem of radiation from the end of a semi-infinite waveguide gives an approximate solution.

Article substantiates the suggestion of using radiation field decomposition in the Gauss-Laguerre basis modes for the free-space. The results of the decomposition of the electric fields of H01 and HE11 waves in this basis are presented, A problem of radiation from an open end of semi-infinite waveguide has been solved for the lower approximation (a reflected waves were not considered). The results of amplitude and phase distributions calculation for radiation wave in cylindrical coordinates are presented. The calculations were performed for various distances from the end of the waveguide. A comparison with results obtained using the method of the Huygens-Kirchhoff is performed.