634 thp: bell system technical journal, may 1954 



1.0 



ft' 



Fig. 13(e) — See Fig. 13. 



with Fiijr,) = - 1 and TEn ^ ^i ; TMn -^ ij^ ; TEjo -^ y, , etc. 



for p > 0, (To < (T < 1 and p < 0, —I < a < — ao, 



there are no solutions. 



These formulae are valid for any p which is not itself so small as to be of 

 order 1/ro^. If they are applied to modes varying as e'"^, where n = ± 1 

 and a, p are positive, they indicate the following results: for a > I, 

 V 



n = ±1, ^--^ 1 + 



(J 



< (T < (70 , n = ±l,i3' 



-; for (To < 0- < 1, no w = ±1 modes; for 



p 

 1 + , \. These, in turn, may be classified 



in the following way. For cr > 1, /i = — 1, and for < cr < ao , " = +1 

 which correspond to /x and k both positive, the propagation constant 

 tends to the value for a plane wave whose direction of circular polariza- 

 tion coincides with that of the wave guide pattern. For o-o < o- < 1, 



