GUIDED WAVE PROPAGATION THROUGH GYROMAGNETIC MEDIA. Ill 1175 



Approximate foniuiltu; for all antisymmetric modes at small p, 

 a ^ 1: 



TM modes: /3' = fi^j ^^^ , (41) 



1 — 0-^ 

 TE modes: /S' = /3„,>' M - 7-^. ) ' (42) 



where 



2 2 

 ^2 -, n TT 

 iSn.i = 1 - -^ n = 1. 2. 



and 



iSn/ = 1 - ^ zf^~ n = 0,1, 2, 



TEMmode: 



= 1 - 



1 - a 



^^ = l-r^. (43) 



TEM mode for large a: 



= 1 + ^ + 0(^1. (44) 



.2 . . P , ^/l 



<r 



TEM mode for very small a: 



for sufficiently small a, the /3^ for the TEjVI mode is independent 

 of a. For general a, p, except a- = 1, 



f = l-^' + ^t (45) 



1 — ap — 0-2 



Reference to the expression for n and k in terms of tr, p will show that 

 the wa\'e progresses as though the medium had a scalar permeability 

 /Xeff given by 



1 1/1+1 



3. FIELD PATTERNS IN" THE FILLED CIRCULAR GUIDE 



In Part I we discussed propagation in a circular guide filled with 

 ferrite and longitudinally magnetized. Formulae or the field com- 



