24 BELL SYSTEM TECHNICAL JOURNAL 



Electromagnetic Waves 



The transmission equations of uniform linearly polarized ^ plane 

 waves are : 



dE . ^, dH , , • s-n. 



d^=- ^"^^' ^ = - ^^ + ^"^^^' 



where : E is the electric intensity, H the magnetic intensity, and g, e, n 

 are, respectively, the conductivity, the dielectric constant and per- 

 meability of the medium. These equations are of the same form as 

 (2). Even the physical meanings of E and H are closely related to 

 those of V and /; thus £ is F per unit length and H is / per unit 

 length. 



The propagation constant and the characteristic impedance of an 

 unbounded medium to linearly polarized plane waves are : 



0- = -yjicofiig -f icoe), "^ ~ \ 



tcofi a to3fx 



g + i<jj€ g + tcioe cr 



These constants are so directly related to the fundamental electro- 

 magnetic constants of the medium that they themselves may be re- 

 garded as fundamental constants. On this account, we call o- and rj, 

 respectively, the intrinsic propagation constant and the intrinsic im- 

 pedance of the medium. The intrinsic impedance will frequently occur 

 as a multiplier in the expressions for the impedances of various types 

 of waves. 



The intrinsic impedance of a non-dissipative medium is simply 

 r? = -^JJife; in air, this is equal to 1207r or approximately 377 ohms.* 

 Thus in the uniform linearly polarized plane wave traveling in free 

 space, the relation between E and H is 



E = UOtH or E = 377H, 



provided the positive directions of E and H are properly chosen. 



An electromagnetic field of general character can be described by 

 means of three electric components Ex, Ey, E^, and three magnetic 

 components Hx, Hy, Hz. We can form the following matrix whose 

 components can be regarded as impedances : 



^ In this connection the word "uniform" is used to mean that equiphase planes 

 are also equi-amplitude planes. 



* See the letter from G. A. Campbell to Dean Harold Pender reproduced at the 

 end of this paper. 



