1246 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



It should be noted that a moderate amount of loss in the spurious 

 modes may be worse than none, so far as the effect on TEm is concerned. 

 Miller^ has shown that the total power dissipated in the system goes 

 through a maximum when (ai — ao)/K ^ 2. It appears that ai — ao must 

 exceed k by a couple of orders of magnitude before the loss in the driven 

 line (i.e., TEoi) becomes really small, if we are counting on dissipation to 

 counteract the coupling to spurious modes. 



Since by use of the compensator we are attempting to make the 

 TEoi - TM)i coupling coefficient zero, we may expect that this co- 

 efficient, if not exactly zero, will at least be small compared to the cou- 

 pling coefficients of spurious modes such as TE12 . Because K(ii) is very 

 small, it may be that a practicable amount of loss in the TMn mode would 

 improve the performance of the bend. But in view of the preceding para- 

 graph we must be careful, when introducing loss into TMu , not to 

 introduce the wrong amount of loss into some spurious mode which has 

 a larger coupling coefficient to TEoi • 



ACKNOWLEDGMENTS 



I am indebted to S. E. Miller, A. P. King, and J. A. Young for stimu- 

 lating discussions and several helpful suggestions relating to this work. 



APPENDIX 



Compensation of a Gradual Bend by a Dielectric Insert in the Adjacent 

 Straight Pipe 



We shall discuss briefly three different ways of transmitting the TEoi 

 mode around a plain (i.e., air-filled) bend with the aid of dielectric mode 

 transducers inserted into the straight sections of guide on one or both 

 sides of the bend. The first two methods involve converting the TEoi 

 mode to a normal mode of the bend and reconverting to TEm on the 

 other side.** In the third method, the input to the bend is pure TEqi , 

 and the output mixture of TEoi and TMn , whatever it may be, is re- 

 converted to TEoi by a dielectric transducer. 



A.i The TMn Normal Mode Solution 



One of the normal modes of the bend is a pure TMu mode (TMi/) 

 which is polarized at right angles to the TMu mode (TMu") that the 

 bend couples to TEoi • Clearly if one has a transducer in a straight guide 

 which converts TEoi entirely to TMu , it is a mere matter of rotating the 



