948 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



significant features of transmission in this medium. Since no direction 

 in the x-z plane can be a preferred one, the plane wave may be assumed 

 to travel in the 2-direction ^ith variation, e~ . Then, from equations 

 (4) and (5) 



and 



/3^ = W^Mefif , 



"^ — n. 2^ -^2" 



^y — n 2\-^«' 



Since Meg is negative between | o- | = 1 — | p | and | cr | = \/l + pV4 

 — I p 1/2, the medium is cut off for plane waves in this range of magnetic 

 field (at a fixed signal frequency). H is elhptically polarized when the 

 medium is magnetized and \Hz\/\Hx\ = | k |/| ju | = \ ph \- We may 

 also put 



m - jH. = 



0}{fl — k) 



But I Hx + jHz I and | Hx — jH^ | are proportional to the amphtudes of 

 the left-handed and right-handed circularly polarized components of 

 the magnetic field. The medium may thus be considered to exhibit the 

 permeabiUty, 



for left-handed components and the permeability, 

 M+K' = Mo(l+ j^) 



for right-handed components. The effective permeabiUty is essentially 

 a parallel combination of these two permeabihties and the medium may 

 propagate (jueff > 0) even when n — k is negative, as ^dll happen for 

 Vl + pV4 - \p\/2 < (7 < 1. 



Since the medium itself has no non-reciprocal properties it is clear 

 that if the latter are to arise they must do so as a result of interaction 

 between the medium and its surroundings. The boundaries of the ferrite 



