COMMUNICATIONS 2i7 and with Fig. 5 ) .(16)
NUbfERICAL CALCUL.4TIOXSThe numerical calculations presented in this section clarify the difference of the scat.tering bet.ween t.he case of an incident beam wave and that of an incident plane wave. For simplicity, only one polarization of ihcidence and the case of t.he perfectly conducting cylinder is considered. The scat.tering coefficient. for the conducting cylinder i s given by (10). In the far region from t.he scatterer (kr >> l ) , the scattered field can be expressed by where 6 = ;b -a/2 and e is Neumann's const.ant. Numerical calculations of (17) have been performed for the case of ka = 1 and ka = 5 with t,hree different. ratios (a/wo = 1/2,1,2) as shown in Figs. 2 and 3, respect.ively. The plane wave case is also included for comparison in the figures.
CONCLUSIONSIt is clear from (9) that if 01 << 1, then the plane wave solutions are obbained from (10) and (12). Since 01 = I/ka(a/wa), the condit.ion a << 1 is satisfied ivhenever a/wo << ku, i.e., when the cylinder is much smder than the width size of the incident wave.On the other hand, as U / W O becomes of the order of or greater than ka, (10) and (12) deviate from the plane wave solut,ion as should be expected. When W D is of the order of or less than Q., most of the energy should be scattered in the illuminated region of the cylinder.our results however predict the strongest contribution in t,he forward scattering direct,ion, for all wo < a. It. follows therefore that (10) and (12) are limited in that t,hey predict. t.he scattered field accurately provided that w o 2 a,.The numerical calculat.ionS presented in Figs. 2 and 3 are based on relation (io). It is. clearly shown that when a/wo << 1 the plane wave solution is obta.ined, whereas as u/wo increases (10) deviates strongly from the plane wave solution.
REFERENCESpp. 143-151, Feb. !,963. 131 P. L. E. Uslenghi, Scattering by radially inhomogeneous cylinders." AZta Freq., v01. 35; pp. 911-912, 1966. 141 J. R.. Wait. "Scat.tering of a @ane wave from a circular dielectric cylinder at otrlique incidence, Can. J. Phys.. vol. 35, pp. 89-95, 151 M. A. Plonus, "Backscattering from conduct,ing cylinder with a 1955. surroundlng shell, Can. Abstracf-The equations for the transformation of the tangential electric and magnetic fields through a series of uniform cylindrical layers of arbitrary properties are transformed from their generally ManuscriDt received Juiv 16. 197i. This work was sumorted in Dart by the U. 9. i i r Force h d e r Contract F04701-C-0166 and br-the