A system of differential equations to optimize the shape of the deformations is derived. These formulas also can be applied for the design of any system containing two reflectors. We present numerical results for practical designs of launchers for rotating higher order volume modes.
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A. Möbius, "Avoidance of edge diffraction effects of WGM-fed quasi-optical antennas by feed waveguide deformation," Proc. SPIE 1576, 16th International Conference on Infrared and Millimeter Waves, 15767I (4 December 2017);