Improved Relations Describing Directional Control In Electromagnetic Wave Guidance

It is useful to be able to characterize the direction-changing capability of electromagnetic waveguides without detailed knowledge of the waveguiding structure. The first work in this area was reported by Miller in 1964.1 A direction-determining parameter Rmin was defined Run* = a3 (1) in which Rmin is a bend radius, a is the full transverse width of the field distribution, and A is the wavelength in the medium in which the waveguide is embedded.* For bend radii longer than Rm)n, Ref. 1 indicates that wave propagation is virtually as in a straight guide; at radii less than Rmin something drastic happens. Just what changes * Notice that we have redefined a here; in Ref. 1 the full transverse width of the field distribution was 2a. 2161 2162 T H E BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1969 occur in a straight guide depends on the nature of the medium in detail; for hollow conducting guides the change is large mode conversion and for beam transmission in a sequence of infinitely wide lenses the change is also mode conversion appearing as a wide oscillation of the beam about the nominal axis of propagation. Following similar lines of thought, a parameter 5TM = £ a (2)