GUIDED-WAVE PKOPAGATION THROUGH GYROMAGNETIC MEDIA 583 



equations subject to the appropriate boundary conditions. Their sohition 

 will determine the propagation constant (3 of a wave as a function of a 

 and b, no matter what their interrelation. On the other hand, in a given 

 experiment jS is generally determined as a function of one parameter 

 only: the magnetizing field II o . Comparison of the family of calculated 

 results 13 = /3(o, 6), with the results /3 = ^{Ho), found experimentally 

 will, of course, determine a and h as functions of Ho . 



If, however, we have a prior knowledge of a and b in terms of Ho , 

 either through postulating the correct dynamical model for the medium, 

 or through independent experiments, we can utilize the functional form 

 of a and b in our analysis of /3, and thus arrive directly at /3 as a function 

 of Ho . The distinction between the two methods is by no means aca- 

 demic; early introduction of such a functional form of a and b into the 

 waveguide problem actually simplifies the analysis. Aside from this prag- 

 matic consideration the latter method seems to us more appropriate for 

 another reason: it is hardly the task of analysis of technical devices to 

 check on the physical theories that give a and b as functions of Hq ; such 

 checks are made by experiments specifically designed to avoid the ana- 

 lytic complexities attending the solutions for most of the technically 

 important structures. 



Accordingly we adopt the more direct approach of expressing a and 6 

 in terais of Ho (and, of course, in terms of the magnetic or electric carrier 

 density of a given sample) throughout these papers, even in those few 

 cases in which /3 can be expressed analytically as a function of a and b. 



2.1 Ferrites 



Most ferrites used in microwave applications are fully saturated in do 

 magnetic fields that are small compared with the dc field with which they 

 are biased in operation. We shall therefore always postulate a fully 

 saturated sample. Accordingly the magnetization vector Af at a point in 

 the sample will always be of constant magnitude, although its orienta- 

 tion will change in the ac field. 



One equation of motion for M that takes this into account is 



^ = y[M X IJr] - r^ [M X [M X IJr]] (2) 



at \ M \ 



where Ht is a total effective magnetic field seen by the spins that make 

 up M, t is the time and 7 is the gyromagnetic ratio appropriate to elec- 

 tron spins, whose ^-factor is close to 2. The expression on the right hand 

 side of (2) is in the nature of a torque; the force on M is always at right 

 angles to M, thus leaving its magnitude unchanged. The first term on 



