582 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



propagation between infinite parallel planes filled with ferrite in a longi- 

 tudinal magnetic field. The effect upon Faraday rotation of multiple 

 reflections is considered. 



2. THE PHYSICAL PROPERTIES 



The propagation of electromagnetic waves in a medium is governed 

 by Maxwell's equations which connect the space variations of E and H, 

 the electric and magnetic intensities with the time \'ariations of D and B, 

 the electric displacement and magnetic induction. To characterize the 

 particular medium relations may be given of the form D = \\ e\\E and 

 B = 1 1 M 1 1 ^ where 1 1 e 1 1 and 1 1 ju 1 1 are the dielectric and permeability ten- 

 sors. For disturbances whose amplitude is in some appropriate sense 

 small, the elements of these tensors will be independent of rf ampli- 

 tude, but will depend upon the dc state of the medium, upon the fre- 

 quency of the signal and in unfavorable cases upon the wavelength of 

 the latter. With the assumptions made in this paper the dependence 

 upon wavelength will not arise. 



The form of || e || and || m || may be known experimentally or it ma}^ be 

 deduced from some molecular model of the medium. If the e(iuations of 

 motion of the parts of the medium are known under applied electric and 

 magnetic fields, the displacement and magnetic induction resulting from 

 this motion may be found explicitly. In isotropic media and in the ab- 

 sence of applied dc fields, each component of the displacement or of 

 induction depends in the same way upon the associated component of 

 E or H. The tensors then become diagonal with equal elements. The ap- 

 plication of a dc magnetic field, say in the 2-direction, causes ions to circle 

 about this field or magnetic dipoles to precess about it. It follows that a 

 rf electric field in the ionic case or magnetic field in the ferrite, normal to 

 the dc magnetic field, will produce a component of motion at right angles 

 to itself and in time quadrature with it. From symmetry and from the 

 equations of motion in a magnetic field the tensors may be expected to 

 be now of the form 



(1) 



where a is an even function of magnetic field and h an odd function, c, in 

 general, will be independent of the magnetic field. 



That a and 6 at a given frequency and for a given sample of the mediinii 

 are not independent but are related through the magnetizing dc field, Hq , 

 is a fact of which we need not take cognizance when solving Maxwell's 



