GUIDED WAVE PROPAGATION THROUGH GYROMAGNETIC MKIMA. Ill 1171 



A TE mode with antisymmetric H, and a Tj\l mode with symmetric 

 E;: have the same propagation constant 



TT / ,1 



^" = 1 - -U+^i (n = 0,1,2 •••). 



A TE mode with symmetric Hz and a T]\I mode ^^^th antisymmetric 

 Ez have the same propagation constant 



= 1-^' (n = l,2,-..). 



Since appUcation of a very small magnetization will not destroy the 

 symmetr}^ properties, it follows that the solution of equation (34), and 

 the solution of equation (33), which in the limit p = reduce to 



correspond to a TE-limit and a TM-limit mode respectively. Likewise, 

 the solutions of equation (33) and the solution of equation (34) which 

 in the limit p = reduce to 



correspond to a TE-limit and a TM-limit mode respectively. When 

 p ^ 0, the new 13' are thus given by different equations, so that the 

 magnetization is seen to have removed the degeneracy of the isotropic 

 case. 



In the special case of the TEM limit mode (/3^ = 1 when p = 0) only 

 one of equations (33) and (34) has real roots. For, when p = 0, the 

 Polder relation gives 



1 - Xi' 1 - X2' 



1 - crX, 1 - 0X2 (36) 



= 0, 



if /3^ is to equal unity. But equation (3G) satisfies equation (34) only 

 [equation (33) would demand Xi = X2 which is impossible for real /3]. 

 Thus the TEM mode exists as the limit of an antisymmetric mode only. 



In fact it is easily shown that for a value of a too small ( less than k) ^^ 



admit any except the TEM mode in the isotropic medium, the only solu- 

 tions of equation (33) for general a, p describe incipient modes. 



