THE MICIIOWAVIO GYRATOH 29 



and: 



, , ^ [YHl{\ + a') .- co-][47r.y .7'//a(l + «')] + SirM^Va'Ha 

 n = I -\ 



K' = 



K" = 

 // 



M = 



47ril/,7c<j[7^//a(l + a^) — co^] 



[y'Hld + a^) - coY + 4coV«^^^ 



47rilf27Q!co[7 i!/a(l -'r ol) -{- 0}] 

 [y'Hld + a^) - coT + 4coV^a^//! 



In order to find the behavior of a wave being propagated in this 

 medium, it is necessary to find a solution to Maxwell's equations which 

 are consistent with the above set of equations and in which, h, h, E, 

 and D are of the following form : 



h = bo exp [jut — Vin-r)] 



h = ho exp [j(at — T{n-r)] 



_ _ . . (5) 



E = Eoexp [jut - r(n-r)] 



3 = Do exp [jut - r(n-r)] 



where Eo , and ho are complex vector functions of the coordinates and 

 which satisfy the boundary conditions imposed by the waveguide. 

 Further: 



n = unit vector in the direction of propagation 



r = propagation constant 



Maxwell's equations are: 



c ot 

 c at 



(6) 



Inserting the values given in Equations (5), these become: 



VXEo-TinX Eo) = =^^ (7) 



c 



VXho-TinX ho) = ^^^ (8) 



