412 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 



transverse cutoff. Therefore, by demonstrating the existence of the 

 lowest order mode we show that an infinite number of these anomalous 

 modes may propagate simultaneously. These modes are, however, 

 bound A'ery tightly as svu'face waves to the side walls of the guide because 

 of their strong transverse cutoff. The medium is therefore used in a 

 verj'' inefficient manner and high loss results, the loss increasing with 

 mode number. 



The higher propagating rectangular wa^'eguide modes have an ana- 

 logue in the higher propagating modes in a ferrite filled circular wave- 

 guide. This analogue occurs in terms of the integral number of peripheral 

 \'ariations. "We find, similarly, an infinite number of such propagating 

 modes each one corresponding to a given polarization sense and having 

 a given number of peripheral variations. The reservations on practical 

 transmission still hold in the same manner as in the rectangular case. 



In the course of preparing this publication it was brought to the 

 author's attention that ^Mikaelj'an employed an anah^sis similar, in part, 

 to that developed here. It is felt, in the present analj^sis, that the physical 

 results are made more readily evident by a consideration of the limiting 

 case of small guides, with large ratios of width to height in the case of 

 rectangular wa^•eguides. The choice of such large ratios is made to 

 simplify analyses invohdng imaginary values of Avi and /.■;r2 , wherein 

 the wave is considered to be bound to one wall of the guide and reflec- 

 tions from the opposite wall are of negligible amplitudes. 



II. ANALYSIS OF TRANSVERSELY MAGNETIZED FERRITE IN RECTANGULAR 

 GUIDE 



The character of the ferrite medium is introduced through the Polder 

 permeability tensor : 



r = I -k M I (1) 



1, 



The quantities m and k relate to the self and inducti^'e permeabilities 

 transverse to the z axis. The relative permeability' along the z axis is 

 given as unit3\ These permeabilities may be expressed as follows in 

 gaussian units.^ 



, = 1 + «^ (2a) 



COO" — CO" 



, = i![^ (2b) 



coo" — CO" 



