]74 



DIFFRACTION BY TERRAIN 



8.1.7 



Polarization. 



Large Angles 



It may be noticed that in the preceding equations 

 no reference is made to the state of polarization of 

 the diffraction field. The results of the approximate 

 Fresnel-Kirchhoff theory are independent of the 

 state of polarization in agreement with oljservation. 



360 



270 



ISO 



90 



12" 



-12" 

 -18° 



ABOVE LINE OF SIGHT 



Figure 5. Phase lag (ordinate) of relative field 

 strength (E/Ea) versus v (abscissa). 



If the angles of diffraction (ai and a^, Figure 2) 

 become large, larger than a few degrees, for instance, 

 the approximate theory no longer applies. The 

 deviations from the Fresnel formulas then go in 

 opposite directions for the two states of polarization. 

 If the electric vector is parallel to the diffracting 

 edge, the field in the shadow at large angles is 



slightlj' diminished as compared with that given by 

 the Fresnel formulas; if the electric field is per- 

 pendicular to the diffracting edge, the diffa-acted 

 field in the shadow at large angles can become appre- 

 ciably larger than the calculated one and, in the case 

 of vcr3^ large angles, the excess may reach the mag- 

 nitude of, say, 6 to 15 db. In the region above the 

 line of sight, the sign of the polarization effect is 

 reversed (slight increase for polarization parallel to 

 the edge, appreciable decrease for polarization 

 perpendicular to the edge). 



These effects are entirely analogous to those that 

 are observed when the cm-rents induced in the surface 

 of the obstacle caimot be neglected (Section 8.1.3), 

 and they have the same phj'sical origin. 



8^ DIGRESSION ON FRESNEL'S THEORY 



^^^ Fresnel Zones 



The concept of the Fresnel zone has played an 

 important role in the development of diffraction 

 theory. As it is frequently referred to in papers on 

 the subject, it may be useful to digress briefly on it. 

 Fresnel's original construction is based on the con- 

 ception that any small element of space in the path 

 of a wave may be considered as the source of a 

 secondary wavelet, and that the radiation field can 



Figure 6. Relations of Fresnel zones and diffracting 

 slots. 



be built up by the superposition of all these wave- 

 lets (Hu3'ghens' principle). In particular, consider 

 the field produced by the transmitter in the open 

 part of the plane containing the diffracting screen 

 {EAPBF in Figure 1) and let each element of this 

 plane be the source of a secondary w-avelet. This 

 may be achieved by distributing a suitable ficti- 



