1336 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1953 



From these curves we may calculate the rotation per unit path length, 

 the absorption of the positive component, the net insertion loss and the 

 ellipticity of the resultant wave. 



The rotation per unit length is given by 



; = i(^_ - ^+) (5) 



where ^± are the imaginary parts of the propagation constants, T^. Let 

 us consider the special case in which the dielectric loss is zero. For con- 

 venience we define the complex effective permeabilities seen by the 

 circularly polarized waves as follows: 



M+ = M — K = /x+ — j/+ 

 t . // 



/X_ = /X + K = M- — iM- 



The propagation constants may then be Avritten: 



(6) 



r+ = oiVmo \/\ [VI M+ 1 - m; + y Vi M+ 1 + m;] 



r ^'^ 



r_ = coViil^o y I [Vl M- I - Mi - iVi M- I + Mil . 



It is of particular interest to consider what happens to /3+ when /x^. 

 becomes zero or negative. If we rewrite the expression for j8+: 



^+ = ^ l/| ^^i4 + Mf) + m; 



(8) 



we see that, when ju+' is zero or negative, /?+ depends primarily on the 

 magnitude of \i'\ for wherever ii" is negligible, /3+ is zero. Furthermore, 

 we see that the attenuation constant, a+, given by: 



"^ = ! Vf ^^4 + Mf - m; 



(9) 



becomes dependent primarily upon /x/ when /x+' becomes negative so 

 that we observe a significant attenuation long before \i^" becomes large. 

 In Fig. 2 are shown the rotation of the plane of polarization of the linearly 

 polarized wave and the absorption of the positive circularly polarized 

 component of the wave. The dielectric constant of the ferrite was as- 

 sumed to be 9.0, a typical value for many ferrites. 



From these curves it is evident that the wave will be elliptically po- 

 larized whenever the effective field is large enough to make /x+' zero or 



