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Solving the Wave Equation in Waveguides of Varying Cross Sections Using Spherical Coordinates

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When the boundaries of a waveguide are closer in shape to a cone than to a cylinder, a modal decomposition in spherical coordinates, as carried out here, is more efficient than one carried out in cartesian or cylindrical coordinates. For the case of a waveguide varying only slightly from a cone, a degenerate one-dimensional equation analogous to the horn equation is presented.

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