2.. . /! ., .2.. _. ' '^^'^' = ^ 2 



i (1 + e) (l + ikJl) -(1-e) (l-ik£) 1 + e 



k Ji , 

 1 + i -4- (S-if + n^3 



2e 



+ OCk£)^ C30) 



2n 



in which equations (13) and (18) have been introduced. 

 Similarly, equation (23) may be simplified to read 



i o (S-if-n ) , , ,^ 2 



-=^B_ o(k.)2 = -^:i|:^^.o(k.)2 . (31) 



t , . o ,„ .J, 2. S-if+n -1 ^i — T- 



1 + 1^5 — (S-if+n ) k i 



2n o 



Finally, the simplified expression for the horizontal velocity 

 amplitude within the structure is obtained from equation (21) as 



1 + ink (l-x) 

 ^= FT-^ + O(kiL)^ . (32) 







To obtain the simplified formulas for the transmission and reflec- 

 tion coefficients from equations (30) and (31) the absolute value is 

 obtained under the assumption that k£ and k i << 1. From equation (30) 

 it is seen that the transmission coefficient to the adopted degree of 

 accuracy is given by 



I I 



'tT-^- kV^ 0(k£)2 . (33) 



2n 

 Introducing 



k if 

 A = ~r (34) 



25 



