WAVEGUIDE MODES IN GYROMAGNETIC MEDIA 



413 



T = 2.80 Mc/sec/oersted 



coo = 7-^0 



Hq = Internal dc magnetic field 



4-7ril/s = Saturation magnetization 



Maxwell's equations are given as: 



Curl H = io^eE (3a) 



CurlE = -ic^(jioT-H (3b) 



Assuming a plane wave of dependence £»(»'-*'■'*>, and appropriately 

 combining (3a) and (3b), we have, 



[kk - k'l + o:'£iJLoT]-H = (4) 



The operator in square brackets is a dyadic which may be repre- 

 sented in matrix form. The quantity / is the idemf actor, having a unit 

 diagonal representation. If we are to require that a non-trivial field H 

 exist, the determinant of the operator in (4) must vanish. Since all rays 

 traveling perpendicularly to the magnetizing axis are equivalent the 

 medium is degenerate in the transverse plane, and some simplification 

 is achieved in causing k to lie in the yz plane and letting k^ = 0. Some 

 further simplification is achieved in normalizing the Polder tensor such 

 that 



fig 0\ 



^ ^ -ig f 



T 



W£)UO 



(5) 



h 



The following secular equation is then formed. 

 -/v-+/ ig 



-ig 

 



h/yKz 



ICyK 



yi^z 



-A-/ -f h 



= 



(6) 



Introducing the substitution p = k^~/k , and recognizing that 



Ky Kz 



m 



we have upon expanding (C), 



pW - g')h + /'/(f - Jh - g')] 



+ V[{h - f)h' - k'if ^ fh - g')] + kjf = 0. 



(7) 



