GUIDED WAVE PROPAGATION THROUGH GYROMAGXETIC MEDIA. Ill 1135 



turbed system is a wave guide containing a medium whose permeability 

 and dielectric tensors are diagonal and isotropic, but ma}' \ary o\-er the 

 cross section of the guide, although not in the 2-direction along tlie guide. 

 For this system it will be assumed that a complete set of normal modes 

 exists for which appropriate orthogonality relations are known. The 

 perturbation of the system will then consist of changes in the permea- 

 bility and dielectric tensors of the medium, including the addition of 

 non-diagonal terms. If these changes are to be genuine perturbations, 

 they must be of one of two kinds. Either, the variation in the properties 

 of the medium is confined to a limited region, small in volume in some 

 appropriate sense, in which case its magnitude may be large, or, we may 

 have a small fractional change in the material properties exteiuUng over 

 a considerable volume. The fields in the guide may be expanded in the 

 normal modes and a system of equations is developed for the z-de- 

 pendence of the amplitudes of these modes. These equations are then 

 solved approximately, making use of the smallness of the perturbing 

 terms. The results may then be specialized to the various situations of 

 mterest. 



Let us suppose that the unperturbed permeability and dielectric con- 

 stant are niix, y) and ti{x^ y) respectively and that the system is now 

 altered so that it possesses a permeability tensor 



ii-iix, y) -jk{x, y) 



jii{x, y) 

 

 and a dielectric tensor 



t2{x, y) 



M2(a;, y) 

 







MsCa;, y) 



-jvix, y) 



j-n{x, y) eoCr, ?/) 



e^{x, y) 



Maxwell's equations for the perturbed system may be written, using 

 the notation of Parts I and II, f in the form: 



dHt* 





dz 

 dEt* 

 dz 



— jC0€2Et — 0)7] Et* = 0, 



-f jwniHt + o^kHi* = 0, 



V-^,* - 3^€^E, = 0, 

 V-Et*-^ jcofisH, = 0. 



(1) 



t We omit the vector signs from all transverse vectors, which are sufficiently 

 labelled by the subscript "t." 



