Abstract
A wave splitting method is proposed to solve the problem of propagation of microwaves in a circular waveguide bend of circular cross section. The splitting method, applied to the vector Helmholtz equation, gives a stable solution in terms of waves propagating to the right and to the left in the bend. The formulation is particularly transparent for analyzing the scattering properties of toroidal bends. The basis for the transparency of the method is that the wave splitting is formally exact as the exponential of the square root of a differential operator. The modal functions of the straight cylindrical waveguide are chosen as basis functions in the transverse quasi‐toroidal variables.
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