60 BELL SYSTEM TECHNICAL JOURNAL 



in the molecules of a true dielectric which produce the observed delay of 

 electromagnetic waves in such dielectrics. This involved arranging metallic 

 elements in a three-dimensional array or lattice structure to simulate the 

 crystalline lattices of the dielectric material. Such an array responds to 

 radio waves just as a molecular lattice responds to Ught waves; the free 

 electrons in the metal elements flow back and forth under the action of the 

 alternating electric field, causing the elements to become oscillating dipoles 

 similar to the oscillating molecular dipoles of the dielectric. In both cases, 

 the relation between the effective dielectric constant e of the medium, the 

 density of the elements N (number per unit volume) and the dipole strength 

 (polarizability a of each element) is approximately given by 



€ = €0 + iVa (2) 



where €o is the dielectric constant of free space. 



There are two requirements which are imposed on the lattice structure. 

 First, the spacing of the elements must be somewhat less than one wave- 

 length of the shortest radio wave length to be transmitted, otherwise dif- 

 fraction effects will occur as in ordinary dielectrics when the wavelength is 

 shorter than the lattice spacing (X-ray diffraction by crystalline substances). 

 Secondly, the size of the elements must be small relative to the minimum 

 wavelength so that resonance effects are avoided. The first resonance 

 occurs when the element size is approximately one half wavelength, and for 

 frequencies in the vicinity of this resonance frequency the polarizability a of 

 the element is not independent of frequency. If the element size is made 

 equal to or less than one quarter wavelength at the smallest operating 

 wavelength, it is found that a and hence e in equation 2 is substantially 

 constant for all longer wavelengths. 



Since lenses of this type will effect an equal amount of wave delay at all 

 wavelengths which are long compared to the size and spacing of the objects, 

 they can be designed to operate over any desired wavelength band. For 

 large operating bandwidths, the stepping process^ is to be avoided, since the 

 step design is correct only at one particular wavelength. Such unstepped 

 lenses are thicker, but the diffraction at the steps is eliminated and a some- 

 what higher gain and superior pattern compared to a stepped lens is achieved. 

 By tilting the lens a small amount, energy reflected from it is prevented from 

 entering the feed line and a good impedance match between the antenna and 

 the line can be maintained over a large band of frequencies. 



Another way of looking at the wave delay produced by lattices of small 

 conductors is to consider them as capacitative elements which "load" free 



« The lens of Fig. 1 has 12 steps. 



