Theory of Curved Circular Waveguide Containing an Inhomogeneous Dielectric

It has been recognized for several years that a major problem in the transmission of circular electric waves through multimode round waveguides is the question of negotiating bends. Theoretical studies 1,2 " 3 have shown that a gentle bend couples the TE 0i mode to the T E U , T E 1 2 , TE13, · · · modes and to the T M n mode. The T M n mode presents the most serious problem, since it has the same phase velocity as TE 0 i in a perfectly conducting straight guide. It follows that power introduced in the TEoi mode at the beginning of a gradual bend will be essentially completely transferred to the TMn mode at odd multiples of a certain critical bending angle t?c. The angle is proportional to the ratio of wavelength to guide radius but independent of bending radius; in other words, power transfer cannot be avoided merely by using a sufficiently gentle bend. S. E. Miller4 has discussed a number of methods for transmitting the circular electric wave around bends with small net power loss to T M n . These methods are of two general types. 1209