CURVED WAVE GUIDES 19 



and 



' ' 3.83277 



Substituting the values of 4-2, 4-3 and 4-4 into 1.2-4 one finds for the 

 coupling coefficient between the two groups of plane waves traveling at a 

 slant to the wave guide axis 



, c\/2 Vl - v"" 0.369a r- 



Kg = = 'V 1 — V^ 



3.83 Ro 



The coupling coefficient k between the TEoi and TMu modes which are 

 the resultants of their slant wave groups is greater than ^3 according to the 

 following reasoning: 



From 1.2-10 



/3 = /?o(l ± 0.5 ks) 

 This makes the cutoff factors of the coupled modes 



_ 5 Vq 



" ~ /3 ~ 1 ± O.Syfe, 

 and the coupled propagation constants 



r = iSVl - v^ = /3o\/(l ± 0.5ksY - pI 

 For k.. « 1 



r = ^o\/r^^§ (1 ± iTr^2 ] = Tod - 0. 



5k) 



Hence, in view of eq. 1.2-10, the effective coupHng coefficient of the wave 

 guide modes is 



_ ^» _ 0.369a 



From equations 3-15 and 3-19 



Ti - Ts = -^-^ RiVr^^^ 

 at} 



VrTTa . ii8o . -27r77a 



Ti - r2 Ti - r, (1 _ j)Ri\oVl^^' 

 From 1.2-3, 4-5 and 4-7 one obtains the coupling discriminant 



- 0.369 •2t- 377a' 



4-6 

 4-7 



Since 



* Loc cit. 



RoRM^ - 7)(1 - "') 

 i?v = 0.00452 X^'-'-p,* 4-8 



