942 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



about a cylinder coaxial with the ferrite. Thus, the internal and external 

 impedances of such a system at any coaxial cylinder can only com- 

 pensate accidentally (perhaps at a single frequency) and non-reciprocity 

 is the rule. 



It is freciuently asserted without ciualification that for non-reciprocity 

 a further condition upon the relevant rf field is that its projection upon a 

 plane normal to the magnetizing field be elliptically or circularly polar- 

 ized in the limit of vanishing magnetization. The argument is based on 

 the consideration, in itself correct, that the effective material constants 

 are different for right- and left-circularly polarized field vectors. Suppose 

 that the magnetization direction is y. Then the tensor relating B to H 

 is (see Part I, Section 2.1): 



Jii 







Mo 







■JK 



For right- and left-circular fields with H^ = ij/Zx , therefore, the medium 

 is isotropic in the plane transverse to the dc field with permeabilities 

 Iji -\- K, iJL — K respectively. Since opposite circular polarizations accom- 

 pany opposite propagation directions, (see for example. Fig. 2) the per- 

 meabilities, and hence the propagation constants, are different for oppo- 

 site propagation directions. It is then argued that the field must already 

 be circularly, or at least elliptically polarized to start with, if non- 

 reciprocal effects are to result from application of the magnetization. 

 However, the argument is true only for effects of first order in the mag- 

 netization. For general values of magnetization, the rf field, even if 

 linearly polarized to begin with, will become elliptically polarized, and 



■////////////////////////////////////// ////////////////////////////////////, 



l;l; { " ^ \\\\ 



III C"~^~"~^ ' ! l! 



I M I V /' I M I 



/Ml ■• /III 



III 



I M 



III 

 I I I I 

 ' I I ' 



^///'/■///'A^//// 



I I I I 

 I I I I 



I 

 I I ' I 



nil 

 III', 



1 I I ( 



I II I 

 III 



ImI 



Ml, 



■/ --//// ^ // - 



'/■■' ■■///-. ^//////^/. ^r^ 



Fig. 2 - 

 waveguide. 



Magnetic lines of force parallel to the broad side of a rectangular 



