Mode transformation due to curvature and diameter variations in smooth-wall circular waveguides

With development of waveguide technique the interest in creation of mode transformers, i.e. the devices which transform propagating modes in an overmoded waveguide, has appeared. Nowadays one of the basic methods for calculation of waveguide transformers is the method of cross-sections. It has a number of advantages in comparison with other methods. In particular, it allows effective calculation of the waveguide transformers containing smooth transitions which length is large compared to the waveguide transverse dimensions. Such transformers have small internal reflections, and also have a large bandwidth. Though the theory of a method of cross-sections is well enough developed, a very few papers containing complete results of calculation and optimization of mode converters and their geometries are known. In the present work, calculation and optimization of the geometries of waveguide transformers for mode pairs in a smooth-wall circular waveguide are given. On the basis of a method of cross-sections, electromagnetic fields in any cross-section of a nonuniform waveguide are represented as a superposition of the waves of both, forward and backward, directions which exist in a uniform waveguide of the same cross-section.