10 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1952 



Equations (8) are easily interpreted in terms of the spinning gyroscope 

 model of Fig. 3. If magnetic losses had been ignored (i.e. a = 0) then 

 both fjL and K would have been real. Under this condition, it is seen that 

 if an alternating field, hy , is applied along the y axis, then an alternating 

 flux, hy , is created along the y axis which is in phase with hy , and an 

 alternating flux, hx , is created which is 90° out of phase with hy . Reci- 

 procity between the x and y directions would demand that both terms 

 containing jK should have the same sign. Thus, Equations (8) give a 

 quantitative expression for the results which were previously qualita- 

 tively deduced by means of the electronic model illustrated in Figs. 2 

 and 3. 



If a waveguide is filled with a ferromagnetic material such as a ferrite 

 and if then a steady magnetic field is applied along the axis of the 

 waveguide, it is necessary in order to describe this wave to find a solu- 

 tion to Maxwell's equations which is consistent with Equations (8) 

 and in which b, h, E and D are all proportional to exp [jut — Vb\. This 

 problem is not solved exactly. However, in the appendix a solution is 

 obtained for an infinite plane wave. It is found that the ferromagnetic 

 medium can support only a positive or a negative* circularly polarized 

 wave or a combination of both. It is also shown in the appendix that the 

 propagation constants for these two circularly polarized waves are dif- 

 ferent and are given by the following expressions: 



and 



\ = -^ V(m + K)[z] (11) 



r- =^~y/{n-K)[z] (12) 



where 



V± — Propagation constant 



CO = Angular frequency of wave 



c = Velocity of light in unbounded space (3 X 10 cm/sec) 



e = Complex dielectric constant of medium 



In Equations (11) and (12) it is apparent that the effective perme- 

 ability of the medium to a positive circularly polarized wave, for in- 



* The usual notation is used here, where the positive component is the com- 

 ponent which is rotating in the direction of the positive electric current which 

 creates the steady longitudinal field. 



