CIRCULAR WAVEGUIDE WITH INHOMOGENEOUS DIELECTRIC 



1237 



Fig. 2 — Various bend compensators, 



in Fig. 2(a). One could approximate the continuous variation with a 

 laminated .structure con.si.sting of a number of layers of different permit- 

 tivities, the permittivity varying slightly from one layer to the next. 



Although the geometrical optics approach provides a very good theo- 

 retical solution to the bend problem, it does not lead to a perfect compen- 

 sator. It is .shown at the end of this section that a perfect compensator, 

 in the sense of one which does not couple TEoi to any other mode at any 

 frequency, does not exi.st. The geometrical optics compensator couples 

 the same modes to TEoi that are coupled by the curvature of the bend 

 itself, namely TMu and the TEi,„ family; but the coupling coefficients of 

 the various modes are not in exactly the same ratios. Thus if 8 is given 

 by (98), the net coupling between TEoi and TMu in the compensated 

 bend is zero, but there will be a small residual coupling between TEoi 

 and each of the TEi„ modes. 



The curvature coupling coefficients are given by (49). Table I contains 

 numerical values which have been worked out for /3a = 12.9.30 and 

 jSa = 29.554, corresponding re.spectively to guide diameters of | inch and 

 2 inches at an operating wavelength of 5.4 mm. 



Dielectric coupling coefficients can be worked out without much dif- 



Table I — Coupling Coefficients and Power Transfer 

 IN Geometrical Optics Compensator 



