FERRITES IN MICROWAVE APPLICATIONS 1339 



this particular case it can easily be shown that at every point in the 

 material this field is given by* 



rtix 



and by definition 



Ox = Mo(^z + nix) = 



In one sense this wave is no longer a plane wave as it has a com- 

 ponent of h in the direction of propagation. However, the electric field, 

 Ej and the magnetic flux density, b, are unchanged and remain the same 

 as in a normal plane wave. 



The solution to the wave equation for the foregoing case yields a 

 propagation constant 



1/ 



<•■ =^ (10) 



in which the effective relative permeability of the medium is 



2 2 



Me£E = (11) 



The real and imaginary parts of this expression are plotted in Fig. 4 for 

 three frequencies. 



These curves have the same general shape as those for the positive 

 circular component of the wave propagated along the dc field direction, 

 but here they apply to the entire linearly polarized wave. Again we have 

 the possibility of zero or negative permeabiHty. In the region just above 

 resonance the real part of the permeability takes on large values and 

 maintains these even after the absorption curve is nearly zero. This 

 suggests that it is possible to adjust the permeability to equal the 

 dielectric constant of the material so that the medium matches free 

 space perfectly. The medium then can be used as a switch by changing 

 the field from the point where Mes = to the point where ^^s = €-t 



In the region between zero applied field and saturation where the curve 

 levels off, the effective permeability changes almost linearly. In the 



* We follow Stratton in making M an ^-like quantity rather than B-like. 

 t In a waveguide /tefif must be adjusted to satisfy the condition that 



f^eS 



