CURVED WAVE GUIDES 21 



p = VO.S + 0.5-y/i + I K |4 = cosh .V 

 (/ = \/-0.5 + O.SvTTlTf* = sinh x 



II' = I tanh - 



P 2 



In analogy to Case 1 of Section 3, tlie condition of j k i = 1 may be called 

 critical coupling. It occurs at the critical radius of curvature 



1.366-10' o'V"' ^ ,,., 



Rocr = r^ ^\ — meters 4-10 



For subcritical coupling {Ro » -^n) H' approaches 



' ' subcr. 



^0 



4 



For supercritical coupling {Rn « R„), 



V2 



1 



From the above results, it is possible to predict the behavior of waves 

 originating either as TEm or as TMn modes, in any given wave guide 

 configuration. This is done for some typical cases in the following sections. 



5. Propa'g.\tion IX Long Wavkguides with Constant Curvature 



It has been shown in Section 3 that for each curvature there exist two 

 modes of propagation. 



In one, 



and the attenuation 



In the other, 



and the attenuation 



Wa = ^' < 1 5-1 



-f TEOl 



aa < ;i ^-'^ 



Wb = ^ > 1 5-3 



. OTE + TM z a 



«& > r -^-* 



