13-48 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956 



.. r 2 / / • //\ 7 2il/2 



§2 L<^ Mo€o(.e — te ) — ll \ 



Xo Free-space wavelength 



Xc = 2-Kaf'p Cutoff wavelength 



juo Permeability of interior and exterior media 



V = Xo/Xc = p\o/2ira Cutoff ratio 



[e - I + V - te ) 



^ + IT] 



e' - ie" 



n Electric Hertz vector 



n* Magnetic Hertz vector 



0" Conductivity of exterior medium 



rj/ Pitch angle of helix 



CO Angular frequency 



e" Harmonic time dependence assumed throughout 



J nix) Bessel function of the first kind 



Jn(x) dJn{x)/dx 



Hn'^ix) Hankel function of the second kind 



Hn^'^'ix) dHS-\x)/dx 



MKS rationalized units are employed throughout. Superscripts i and e 

 are used to indicate the interior and exterior regions. 



I. INTRODUCTION AND SUMMARY 



Propagation of the lowest circular electric mode (TEoi) in cylindrical 

 pipe waveguide holds great promise for low-loss long distance communi- 

 cation.^' ^ For example, the TEoi mode has a theoretical heat loss of 2 

 db/mile in waveguide of diameter 6 inches at a frequency of 5.5 kmc/s, 

 and the loss decreases with increasing frequency. Increased transmission 

 bandwidth, reduced delay distortion, and reduced waveguide size for a 

 given attenuation are factors favoring use of the highest practical fre- 

 quency of operation. An increased number of freely propagating modes 

 and smaller mechanical tolerances are the associated penalties. Any 

 deviation of the waveguide from a straight circular cylinder gives rise to 

 signal distortions because of mode conversion-reconversion effects. 



One solution to mode conversion-reconversion problems is to obtain a 

 waveguide having the desired low attenuation properties of the TEoi 

 mode in metallic cylindrical waveguide and very large attenuation for 

 all other modes, the unwanted modes.^' ^ The low loss of the circular 

 electric modes in ordinary round guide is the result of having only cir- 



1 S. E. Miller, B.S.T.J., 33, pp. 1209-1265, 1954. 



2 S. E. Miller and A. C. Beck, Proc. I.R.E., 41, pp. 348-358, 1953. 



3 S. E. Miller, Proc. I.R.E., 40, pp. 1104-1113, 1952. 



