GUIDED-WAVE I'KOl' \( ; AllO.N TllliorciJl (i V1{()MA(; X i;'lM( ' MIODIA .")!)? 



boundary value problem may be put into the form, of which (20) is a 

 special case, 



V'/i + XI fi = 0, 



and 



V% + X2f2 = 0, 



Ao dX Ai dNj ^{pE + Ph) 



P_H^ 

 VeVh 



+ Pe{1 — Ph") 





where d/dN and d/dS are normal and tangential derivatives at the guide 

 surface, where, in addition, /i = /2 . 



4. DISCUSSIOX OF THE PKOPAGATION CONSTANTS 



At this point we specialize the characteristic eciuation (26) to one or 

 other of the two media. 



4.1. Thcferrite (pe = 0, ve = 1) 



4.11. After some rearrangement the characteristic equation becomes 



1 



FniXlTo) 



Xl' L Xl 



where X2,i = ^ Ai,2 and the X satisfy 



1 



'Fnix^ro) 



(1 — j^h) ( 1 — — ) + Vhp/ 

 X1.2' - ^^ '-^ Xm - ^^ = 0. 



PH 



The x's are given by 



Xl,2 = ( 1 — — ) — PffXl,2 . 



From Polder's equations for pn and uh , (28) may be written 

 Xi.2' - [p + <r(l - iS')]Xi.2 - /3' = 0, 



or 



X1X2 = -I3\ 



Xi + X2 = /9 + a(l - /?'), 



= 7? + (T + (7X1X2 . 



(27) 

 (28) 



(29) 



(30) 

 (31a) 

 (31b) 



If /3^ be eliminated between equations (28) and (29), xi,2' may be ex- 



