44 BELL SYSTEM TECHNICAL JOURNAL 



The reflection and the transmission coefificients are then obtained from 

 (22) in terms of the impedance ratio 



, r? sec ?? 7} cos ^l/ ,-_. 



f] sec ^ t] cos ?? 



Thus, we have 



H — -■, — ; — r , 1 E — 



These coefficients refer to the tangential components of the field. 



In a similar way we can deal with the case in which the magnetic 

 vector of the incident wave is parallel to the boundary. The parts 

 played by E and // are interchanged and the impedance ratio becomes 



k=^l^. (26) 



7] COS yf/ 



The cosine factors have changed their places. 



The general case, in which neither E nor II is parallel to the bound- 

 ary, cannot be treated in the above manner. In this case the com- 

 ponents of E and // which are parallel to the boundary are not per- 

 pendicular to each other, the impedances Z^y and Zyx are not equal 

 to each other and the unique impedance Z^ — Z^y = Zyx, upon which 

 the results of Part II are based, does not exist. In accordance with 

 a suggestion made in Part I, the incident wave must be resolved into 

 components possessing unique impedances in the direction normal to 

 the boundary. It is well known that such a decomposition is possible 

 for ordinary plane waves; the latter can always be decomposed into 

 two components, in one of which E is parallel to the boundary and 

 in the other H is so disposed. 



It is not surprising that reflection of arbitrarily oriented waves 

 cannot be treated directly. The impedance ratios (25) and (26) for 

 two basic orientations are in general different and the polarization of 

 the reflected wave will be changed. An exceptional case arises when 

 the intrinsic propagation constants of the media are equal. In this case 

 \p = ^, as seen from (24), and the impedance ratio is independent of the 

 angle of incidence and of the particular orientation of the wave. Con- 

 sequently, the reflection and the transmission coefficients depend solely 

 upon the ratio of the intrinsic impedances of the media. 



Frequently the permeabilities of the media are assumed to be the 

 same, in which case the ratio of the intrinsic impedances is equal to 



