Theory of the helical waveguide of rectangular cross-section

The helical waveguide may be regarded as being formed by rotating a rectangle about a line, at the same time moving it parallel to the line. If the motion parallel to the line is omitted, the figure obtained is circular in form, but points which differ in azimuth by 2¿ are not equivalent, and infinite azimuthal angles become possible. This figure is called the infinite circular guide; it cannot exist physically, but for purposes of calculation may be taken as an approximation to the helical guide. An exact treatment of the infinite circular guide is given; this treatment is also relevant to the problem of the circular waveguide bend. Perturbation theory is then used to find the correction that must be made to the value of the propagation constant for the infinite circular guide to give the value appropriate to the helical guide. It is found, in fact, that the correction is zero.