GUIDED WAVE PROPAGATION THROUGH GYROMAGNETIC MEDIA. Ill 11()7 



whose solutions for the transmitted and reflected amplitude are 



and 



P = J -^- 8z. 



Thus, to first order, the transmitted wave only undergoes a phase change, 

 of amount 



5^+ = ( /3„ - ^^-— — ? j 8z. 



A similar result applies to a left circular wave; the only difference arises 

 in the contribution 



0) 



f KHtn*-H,.dS 



to ~ which v,i\\ merely change sign. The remainder of I a , and also Ib 



are unchanged. Thus the Faraday rotation of a plane polarized wave, 

 which is one half the difference of the phase change for right and left 

 circular waves, is equal to 



= -7^ J / KHtn*Gtn 



^/\n ''area of disc 



The integral on the right is real, and, when the disc is circular of radius 

 Ti , is of exactly the type that has already been encountered in the case 

 of the ferrite embedded in a material \nth the same dielectric constant 

 (Section 1.2). Here, however, k need not be small, so long as bz is suffi- 

 ciently small. In using the results of Section 1.2 it must be remembered 

 that the mode functions there related to a dielectric, while here they 

 relate to air-filled guide. When this is taken into account, one obtains 

 for the specific rotation of a TE-mode: 



bip 





bz (Unm^ — l)./n(Wnm) L MO \ To 



a TM-mode: 



b<p _ CO jUoeo nK j2 I ' ^i 



(31a) 



(31b) 



