LAMIXATIOD TRANSMISSION' LINKS. I 887 



II. WAVE PROPAGATION BETWEEN PLANE AND CYLINDRICAL IMPEDANCE 

 SHEETS 



We shall consider waves in a homogeneous, isotropic medium of 

 dielectric constant e, permeability n, and conductivity g (rationajized 

 MKS units). When convenient we shall also describe the medium in 

 terms of the secondary electromagnetic constants a and tj, defined by 



(T — ■\/i(jijx{g + ^coe) , 7? = \/i(,}n/(g + iue) . (1) 



The ([uantity a is called the intrinsic propagation constant and t? (lui 

 intrinsic impedance of the medium. 



We begin by considering structures bounded by infinite planes parallel 

 to the x-z coordinate plane, and we confine our attention to transverse 

 magnetic waves propagating in the ^-direction. We assume that the 

 only non-vanishing component of magnetic field is Hj , and that all the 

 fields are independent of x. Then the non-zero field components, written 

 to indicate their dependence on the spatial coordinates, are Hx(y, z), 

 Ey{y, z) and Ez(y, z), the time dependence e*"' being understood through- 

 out. The field components are shown in Fig. 1. 



The field vectors are connected by Maxwell's two curl ec^uations, which 

 reduce in the present case to 



dHJdz = {g + ioit)E,j , 



(2) 



dHx/diJ =—({/ + io:e)E, , 



and 



dEy/dz - dEJdy = 2co/x/^x . (3) 



If we eliminate Ey and E^ we get 



d'HJdy' + d'H./dz' = a'H, , (4) 



where a is the intrinsic propagation constant defined above. It is easy 

 to sec that (4) is satisfied by a wave function of exponential form, say 



//. = e~'" ~'\ (5) 



pr()\-ided that the constants k and 7 are such that 



k' + 7" = 0-". (0) 



We may regard k and 7 as the (possibly complex) propagation constants 

 in the y- and ^-directions respectively. Either may be chosen at will and 

 the other is then determined by the condition (6). The electric field com- 



