940 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



By contrast, Part II of this paper deals with devices whose non- 

 reciprocal operation depends in principle as well as in numerical detail 

 on the disposition of the boundary, or, more generally, on geometrical 

 configuration. These devices employ magnetizing fields transverse to 

 the propagation direction. Some electromagnetic field configurations are 

 unaffected by such a dc field, but, whenever the rf magnetic field in the 

 case of a ferrite (or the rf electric field for a plasma) has a component 

 normal to the dc magnetic field, this is no longer the case. For, now, the 

 magnetization (or the charges) will be caused to precess about the dc 

 field, giving extra terms in Maxwell's equations and a resultant change 

 in the propagation. This change may be simply an alteration in phase 

 velocity, the propagation remaining reciprocal. This is the case, for 

 example, for the propagation of plane waves in an infinitely extended 

 medium [Cotton-Mouton effect]. Here, since every direction of propaga- 

 tion normal to the dc field is physically equivalent to any other and, in 

 particular, to the opposite direction, no non-reciprocity can arise. 



For reciprocity to be preserved in the presence of the dc magnetic 

 field is, however, exceptional and requires a certain amount of geo- 

 metrical symmetry in the system. That non-reciprocity may be expected 

 in asymmetrical systems may be foreseen if we consider a system, typical 

 of those to be treated in this paper, in which all the rf fields are inde- 

 pendent of the coordinate along which the dc magnetic field is pointing. 

 The relevant conducting boundaries and any interfaces between ferrite 

 (plasma) and air are all surfaces parallel to the direction of propagation 

 and lying in the dc magnetic field direction. Suppose the system to be 

 divided into two parts by another surface of a similar kind and examine 

 the surface impedance of one of the parts (which should contain some 

 gyromagnetic material). If the propagation direction be reversed it is 

 necessary to reverse the magnetic field to retrieve a situation in the 

 part considered geometrically equivalent to the original. But, since the 

 precession of the magnetization (or charges) about the dc magnetic 

 field has a definite sense, the magnetic or electric current associated 

 with this precession will be reversed when the dc field is reversed. Thus, 

 the properties of the medium are altered and the surface impedance will 

 be different for the two directions of propagation. In general, the surface 

 impedance of the other part of the system will not compensate for this 

 distinction between the two directions and we shall find different propa- 

 gation constants for opposing directions. An exception will occur if the 

 system contains a surface about which it has geometrical symmetry, for, 

 then, compensation clearly takes place about this surface and the system 

 is reciprocal. 



