THE MICROWAVE GYRATOR 13 



of the frequency of the wave for a fixed magnetic field, a similar set of 

 curves would have resulted. This set would indicate the frequency 

 dependence of the Faraday rotation. If the frequency of the wave is far 

 removed from the resonance frequency, the difference between the 

 indices of refraction of the positive and negative component is not 

 frequency dependent. However, near resonance, this difference is a 

 very rapidly varying function of the frequency. It is to be remembered 

 that these equations were derived for an infinite plane wave. However, 

 it would be expected that these equations would describe quite accurately 

 the propagation of the dominant mode in a waveguide. The approxima- 

 tion would, of course, be better when the cut-off wavelength was much 

 greater than the unbounded wavelength. This condition is met when 

 the waveguide is filled with ferrite and for these cases quantitative 

 agreement is obtained. 



The above analysis shows that if a dominant mode wave (plane 

 polarized) is incident upon a ferromagnetic material which is magnetized 

 along the length of the waveguide, the wave will split into positive and 

 negative circularly polarized waves whose phase constants are given by 

 Equation (14).) Since the two circular components travel with different 

 velocities in the medium, they will upon emerging from it unite to form 

 a plane polarized wave whose plane of polarization has been rotated with 

 respect to the incident polarization. The angle of rotation of the polariza- 

 tion is given by: 



= ^ [^_ - /3+] (15) 



where : 



I = path length through ferromagnetic material (cm) 



In order to evaluate Equation (15), it must be combined with Equation 

 (14). However, a few approximations are valid in Equation (14) which 

 make it much simpler. In particular many ferrites exist for which the 

 magnetic losses are extremely small as long as the internal field within 

 the body is kept small so that the frequency of the wave does not ap- 

 proach the ferromagnetic resonance frequency. This field can be kept 

 small if the magnetic field is not raised above the point necessary to 

 saturate the ferrite. Kittel has shown that for a finite body the effective 

 internal magnetic field that determines the resonant frequency is given 

 by: 



Hi = [Ha -h (iVx - N.)M.][Ha + (Ny - N.)M.] 



