DIELECTRIC-COATED WAVEGUIDE 



1255 



FEom waves. In Section V we shall calfulate the power hvc] in the TE„,i 

 waves resulting from this conversion. 



II. THE NOltMAL MODES OF THE DIELECTKIC-COATED WAVEGUIDE 



The waveguide structure under consideration is shown in Fig. 1. To 

 find the various normal modes existing in this structure, Maxwell's 

 equations have to be solved in circular cylindrical coordinates in the air- 

 filled region 1 and dielectric-filled region 2. The boundary conditions 

 are: equal tangential components of the electric and magnetic field 

 intensities at the boundary (r = h) between regions 1 and 2 and, assum- 

 ing infinite conductivity of the walls, zero tangential component of the 

 electric field at the walls (r = a). Upon introducing the general solutions 

 into these boundary conditions, we get a homogeneous system of four lin- 

 ear equations in the amplitude factors. Non-trivial solutions of this sys- 

 tem reciuire the coefficient determinant to be zero. This condition is 

 called the characteristic ecjuation. Solutions of the characteristic equa- 

 tion represent the propagation constants of the various modes. These 

 calculations have been carried out elsewhere, ' and the characteristic 

 equation arrived at there has the following form : 



11 



1 



1 



2 -^'2 



Xl 



X2 



exi 



1_ Jn'jpXi) e_ Wn{X2, pxd 



_ Xi Jn (pXi) pX2^ U„{X2 , PX2)_ 



1 Jn'ipXi) _J_ Vnjx-l, pX-2) 



_Xi Jn{pXi) pX2^ ZniXo , pXo). 



(1) 



= 0. 



v///////.^ 



Fig. 1 — The dielectric-coated waveguide; p = b/a, 5 = 1 — p= (a — b)/a. 



