GUIDED-WAVE PKOrAUATlON THKOUGH GYUOMAGNKTIC MEDIA G37 



where n is negative, n — ±1, no modes exist for large enough guide. 

 For < 0- < (To , n = — 1 and a > 1, ?i = +1, the propagation constant 

 tends to that for a plane wave whose polarization is in the opposite 

 sense to that of the field pattern and here m is positi^'e, but k is negative. 

 An examination of the field pattern in this last case shows that most of 

 the field energy is indeed associated with a circular polarization opposite 

 to that of the pattern as a whole. 



The discussion of the preceding sections shows that the complete 

 structure of the mode spectrum for a guide filled with lossless ferrite is 

 very complex. It is also clear that for some combinations of guide size 

 and magnetic parameters the course of an individual mode in the 13" — a 

 plane may be quite involved. In particular, two values of /3" associated 

 with the same mode often occur at a given a. The extent to which the 

 complexity of the spectrum will be observed in practice will depend 

 principally upon the loss of the real ferrite and upon the guide radius. 

 The effect of loss near a = 1, where the incipient modes are crowded 

 will be to cause simultaneous excitation of many of these and conse- 

 quently^ a confused z dependence of the guide excitation. For values of 

 ro just below jn , the point of escape of the TE modes, the latter exist 

 over considerable ranges of a, see Fig. 12(a), and would probably be 

 observable. The TE modes near Un also persist over a wide range, but 

 are double-valued. Concerning such double-valued waves it may be ob- 

 ser\'ed that from the results of the subsequent treatment of losses, it is 



., dl3- . . 



clear that if y-j — ; > 0, it is necessary to put the source of power at the 



opposite end of the guide. 



4.15. Losses, Faraday rotation and merit figure. So far the analysis has 

 been concerned with the loss-free medium. It is of some interest to 

 determine the attenuation constant (the imaginary part of jS) that 

 arises when losses are taken into account. As long as these are small, 

 this can be done rather easily; in fact, sufficiently far from resonance 

 (o- = 1), for each formula giving /3 , we can establish one giving the 

 attenuation constant. 



If the losses are of magnetic origin we utilize the fact (already demon- 

 strated in section 2) that to first order in a, the permeabilities n, k are 

 functions of o- + ja sgn p, and of no other combination of o", a. Since 

 0", (X enter ^Maxwell's equations only through /u and k, /3 , which is derived 

 from them, must likewise depend on a through o- + ja sgn p. Any formula 

 for |8" derived for the loss-free medium can, therefore, be generalized to 

 the lossy case by replacing a with o- -F ja sgn p, to first order in a. To 

 this order, then, we find 



