WAVEGUIDE MODES IN GYROMAGNETIC MEDIA 



411 



substantially dependent on the birefringent character of the medium for 

 large width to height aspect ratios of the waveguide. We shall find, 

 further, that propagation occurs with entirely real values of kx and k^ . 

 It will be shown that the proper wave equation for one of the two 

 birefringent rays is satisfied in the small waveguide limit by the rela- 

 tionship 



A-/ + kV + A-Z/m = 0. 



In the region of ^ > 0, and /.-, real, we confirm somewhat more rigorously 

 the recjuirement stated earlier that either kx or ky be imaginaiy. However, 

 kx and ky may both be real over a range of negative values of /x, permitting 

 boundary conditions to be satisfied, approximately, in waveguides 

 having aspect ratios of the type discussed earlier, by just one class of 

 rays in the small size wa^'eguide. 



Propagation in small size circular guide employing the essential charac- 

 ter of birefringence, occurs o^'er the entire range of | ^ | < | k |. This 

 range is di^'ided into that of m > and that of /x < 0. Transmission 

 occurs in one sense of circular polarization in each of these regions and 

 for both senses for n < 0. Thompson has suggested that propagation in 

 a small circular wa\'eguide might be attributed to the negative permea- 

 bility of one preferred polarization; it appears, however, that propaga- 

 tion is possible over a considerably wider range of conditions and 

 for somewhat different reasons. 



In the case shown in Fig. 2, higher propagating modes occur in a 

 rectangular waveguide when one half or more sinusoids of field varia- 

 tion occurs in the z direction. These simply produce the result of stronger 



RESULTANT^ 

 X VARIATION 



Fig. 2 — Mode in ferrite filled rectangular guide. 



