HELIX WAVEGUIDE 1357 



It may be of interest to compare the attenuation constants given by 

 (9) with the results obtained by calculating the power dissipated in the 

 walls of a pipe' which has different resistances in the circumferential and 

 longitudinal directions. If the wall resistance for circumferential currents 

 is represented by Re and for longitudinal currents by Rz , the expressions 

 for a are 



TM nm modes 



Rz 



a 



TE„TO modes 



a = 



{(xo/eoY'-aa - I'V 



Rev' + Rz{n/v)\l - v') p' 



(Mo/€o)^/-a(l - i/'Y'^ p2 _ ^2 



The results for ordinary metallic pipe are obtained by setting 



Re = Rz — R = (co^o/2cr) 



[f Re = 0, the expressions above agree with (9), inasmuch as 

 I = R(eo/ixo) '" when the jacket conductivity is large. 



4/ — tan~^ n(l — v')^''/vv, n ^ 



For this value of rp the circularly polarized TE„^ mode which varies as 

 exp(—in9) has low attenuation. (We assume 7i 9^ 0, since the case 

 n = has been treated above.) One of the properties of helix waveguide 

 is the difference in propagation between right and left circularly polarized 

 TE„m modes. By properly designing the helix angle for the frequency, 

 mode, and size of guide, the loss to one of the polarizations can be made 

 very low. If the jacket is lossy enough the attenuation of the other 

 polarization should be quite high. Thus only one of the circularly polar- 

 ized modes should be propagated through a long pipe. Such a helix has 

 features analogous to the optical properties of levulose and dextrose 

 solutions, which distinguish between left and right circularly polarized 

 light. 



Let an be the attenuation constant of the mode which varies as 

 exp{ — i7i9), and a_„ the attenuation constant of the mode which varies 



^ S. A. Schelkunoff, Electromagnetic Waves, van Nostrand, New York, 1943, 

 pp. 385-387. 



