FERRITES IN MICROWAVE APPLICATIONS 1357 



BANDWIDTH OF THE FARADAY ROTATION 



Some consideration has been given to means of increasing the band- 

 width over which the Faraday Rotation is relatively constant. Two 

 possible ways of broadbanding the effect can be suggested on the basis 

 of measurements and theory. 



In the infinite medium-plane wave theory the Faraday Rotation is 

 shown to be totally independent of frequency every\vhere far above the 

 ferromagnetic resonance frequency. One way of explaining this lack of 

 dependence upon frequency is to observe that the rotation per unit 

 wavelength decreases with increasing frequency while the number of 

 wavelengths per unit length increases at the same rate so that the rota- 

 tion per unit length remains constant. In a waveguide there are two 

 effects which cause the rotation to be frequency dependent. In the first 

 place the guide wavelength is not linearly related to frequency and sec- 

 ondly, where thin pencils of ferrite are used, the radial distribution of 

 field varies with frequency in such a way as to add to the frequency 

 dependence. 



By surrounding the ferrite element with a material of the same dielec- 

 tric constant as that of the ferrite the guide wavelength will be reduced 

 to approximately one-fifth the cut-off wavelength and will be almost 

 linearly related to the frequency in this region. Furthermore, the radial 

 distribution will not change appreciably with frequency because, neglec- 

 ting the difference in permeabilities, the waveguide is now filled with a 

 uniform dielectric. On this same basis there should be no tendency for 

 the structure to set up higher order modes, so that if care is taken in the 

 design of the transitions from circular to rectangular waveguide, the 

 higher order modes can be avoided. 



While the above approach would give very good bandwidth a lack of 

 very low-loss dielectrics having the proper values of dielectric constant 

 limits its usefulness. One of the best dielectrics in this range is Micalex K, 

 and it has a loss tangent of approximately 0.001 which would produce a 

 total loss of several tenths of a db in a length of two or three inches. 



The bandwidth can be increased in another way which requires no 

 special dielectric materials. Suhl has shown that when the forrite element 

 is not perfectly matched to the waveguide the resulting multiple reflec- 

 tions can enhance or detract from the inherent rotation. When the 

 element is an integral number of half wavelengths long the resulting 

 rotation is maximum and when the element is an odd number of quarter- 

 wavelengths long the rotation is minimum. Since the lotati.Hi «.t a per- 

 fectly matched cylinder increases with increasing frequent y we mu.st 

 choose a length for the unmatched element such that it is an integral 



