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.