24 BELL SYSTEM TECHNICAL JOURNAL 



The length of one complete interference cycle is 



'"' ~ (pi- gm - ^i) 



If both components had equal attenuation, the beats superimposed on the 

 decaying envelope of the TEoi wave would correspond to an amplitude ratio 



eo max 1 + W ^ , 



^ ^ 1 nr ^ P '^ ^1 



eo mm 1 — Ir 



However, during the progress of the mixed wave through the curved section, 

 the intensity of the fluctuations is reduced by the greater attenuation 

 constant of the faster and weaker "6" component. In one complete inter- 

 ference cycle, the dififerential attenuation reduces the weaker component to 



A^w -(a.,-ai)so^ -(2wlp + q) 



Approximation for Weak Coupling 



For I K I « 1 



/36 - /3a = (/32 - /3i)(l + 0.5 I . \') 

 From 3-15 and 3-19 



at] 



1.2 X 10' 



at] 



/(I v%u (J + 0.5 i /c 1^) radian/m 



V ^og 



a 

 For intermediate coupling, 6-1 may be transformed into 



^6 - |Sa = k^lf{K) 



.,. , ±±± _ Vl + Vf+W^ + V- 1+ Vl+l^' 

 with /(«) = /T, I I — ■ — i — i — 



Approximation for Strong Coupling 

 For 1 K I » 1 



/u, = 1 + 0.125 1 K \-' ^b - i^a = k^iU + 0.125 1 K \-') 

 Substituting the value of k from 4-13 and transforming, 



/?6 - i8a = ,-p /(«. = ^^ (1 + 0-12^^ \k\ ) 6-2 



The phase difference between the two components is 



2.32a5 , 2.32ad r ,^„ /: ^ 



AoAq Ao 



