114 BELL SYSTEM TECHNICAL JOURNAL 



where 



K = 2a/Xo = -iTooa/ir, c = (k'' - l)"^ = ak/b 



dl = ni" - I - c"" = m^ - k\ 5i = ic (5-2) 



Xo = free space wave length, w = 1, 2, 3 • • • 



and 



\fL^{v + id) l^xVa^ = 1 + g{v, 6). (5-3) 



Here /mod(w) pertains to the modified Fig. 1. Since the expression for 

 f'{w) given in Appendix I is proportional to b and since the modified trans- 

 formation contains a in place of b, it follows that g{v, 9) for the magnetic 

 corner is exactly the same function, given by (2-6), as for the electric corner. 

 It is again assumed that the incident wave coming down from the left 

 in the modified Fig. 1 is of unit amplitude and of the dominant mode. 

 At large distances from the corner 



P = [,-"' -f i?He'"] sin 0, v-^-cc 



(o-4) 

 P = TbC "" sin d, V ^ -\-x 



which serve to define the coefiicients of reflection and transmission. The 

 subscript H on the reflection and transmission coefficients indicate that 

 here we are dealing with a magnetic corner. 



The conversion of the differential equation into the integral equation now 

 employs the Green's function 



G = 2 Z 5-' sin me, sin w^^-'^-'""-" (5-5) 



which corresponds to 



V = at = and = TT 

 The integral equation for P is found to be 

 P(vo , ^o) = e"""" sin 9o 



+ ^ [ dv I dd g(v,e)Piv,e) J^28Z' sinmdosmmde'^" ""'*" 

 2ir J— 00 •'0 "'=-1 



(5-6) 



where the parameters are given by (5-2). This is a general equation. 

 For the corner of the modified Fig. 1 g{v, 6) is given by (2-6). 



