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An approximation algorithm to the sourcewise Green's function in the D'Alembert equation for the circular waveguide

The approximation algorithm to the tensor Green's function calculation in the D'Alembert equation for the polarization potential in the circular waveguide is proposed. The tensor Green's function is presented in the sourcewise form as the sum of the Green's function for free space and the regular part caused by reflections from the waveguide walls. The circular waveguide is a circular cylinder with a directrix in the form of a circle. The directrix in the form of a circle is approximated by a broken line in the form of an inscribed rectilinear polygon. This approximation allows one to use the method of specular reflections and get the tensor Green's function as an infinite sum of tensor divergent spherical waves with a delta-shaped front. The resulting representation of the Green's function can be used to solve the nonstationary intrinsic boundary-value problems of electrodynamics in the case of a circular waveguide with consideration for the reflections from the walls.