METALLIC DELAY LENSES 77 



lobes are not very well suppressed because the illumination is only slightly 

 tapered. However, for repeater work, lobes in the vertical plane are not as 

 objectionable as lobes in the horizontal plane because interfering signals 

 generally originate from other stations lying in the horizon plane. 



The impedance match of the shielded lens antenna is affected by the 

 discontinuity of the wave guide at the expanding horn throat and by what- 

 ever energy is reflected back into the feed line from the lens. By tuning 

 means, the throat mismatch can be held to less than 0.2 db SWR (1.02 

 V.S.W.R.) over the 500 mc band and by a combination of lens tilt and 

 quarter-wave step in the lens the SWR due to the energy reflected from the 

 lens was also held to less than 0.2 db over the band. 



PART II— THEORETICAL CONSIDERATIONS 



We turn now to a consideration of the electromagnetic theory underlying 

 the operation of artificial dielectrics. If the polarizability of the individual 

 conducting element employed is known, equation (2) will permit a calcula- 

 tion of the effective dielectric constant. Before proceeding to this, however, 

 a brief review of dipole moment, dipole potential, and dielectric polarization 

 will be given (MKS units). 



Dipole Moment, Potential and Polarization 



Two charges, +9 and —q, displaced a small distance from one another, 

 constitute an electric dipole. If the vector joining them is called ds, the 

 dipole moment is defined as 



m = q ds. (5) 



The potential V, at any point, due to a point-charge q is defined as 



V = g/47r€r, . (6) 



where r is the distance from the point in question to the charge q. The 

 potential V due to a dipole of moment m is 



r=i^,cos(», (7) 



where 6 is the angle between r and m. 



A conducting object becomes polarized when placed in an electric field. 

 Its dipole moment m depends upon the field strength E and upon its own 

 polarizability a: 



m = aE. (8) 



If there are .V elements per unit volume, the polarization P of the artificial 

 dielectric is 



P = NoE, (9) 



