ON THE RADIATION-PATTERN RELATED TO CYLINDRICAL OBJECTS BURIED IN A SLAB AND SOME OF ITS APPLICATIONS

It is well known that radiation pattern A(($) over cap x, ($) over cap e) related to the scalar wave u(s)(x, ($) over cap e) scattered by a bounded body D, located in an infinite simple (homogeneous, isotropic, linear, local, time-invariant) space and illuminated by a monochromat ic plane wave propagating in the direction of the unit vector ($) over cap e, satisfies the reciprocity relation A(($) over cap e', ($) over cap e) = A(-($) over cap e, -($) over cap e') and interrelates the ou tgoing and incoming wave solutions through a functional equation of th e form u(x, ($) over cap e, omega) = integral[delta(($) over cap e - ( $) over cap e') - (2 pi i)(-1)A(($) over cap e, ($) over cap e')]u(x, ($) over cap e', -omega)d ($) over cap e'. These concepts and relation s play very important roles in investigations of direct as well as inv erse scattering problems in simple spaces. In connection with some rat her complicated configurations related to buried objects one has to kn ow if these concepts and relations can be extended to the cases where the infinite region outside D is not homogeneous. The answer seems, in general, to be negative. In this paper it is shown that if D is a cyl indrical body buried in a simple slab and A(($) over cap x, ($) over c ap e) is properly normalized, then the pattern concept and reciprocity relation are still valid in a certain wedge-shaped region W-delta whi le a generalization of the relation u(x, ($) over cap e, omega) = Su(x , ($) over cap e', -omega) can be made in all the space. The half spac es above and below the slab are supposed to be filled with different s imple materials. This configuration involves also the case of bodies b uried in a half space as a particular case where the material of the s lab and that of the region below it are identical.