L. B Felsen.

Relation between a class of two-dimensional and three-dimensional diffraction problems online

. (page 2 of 3)
Online LibraryL. B FelsenRelation between a class of two-dimensional and three-dimensional diffraction problems → online text (page 2 of 3)
Font size function t = V-e + V-E - V- 6. , with e given in (l9)-(2l), is a scalar wave
â€” â€” â€” mc â€”

function which is outgoing at infinity. This follows from the fact that the
Cartesian components of the vector (ÂŁ + E - ^. ), and therefore their deriva-
tives as well, possess these properties. Furthermore, we know that i|f vanishes
on the screen. [in fact VÂ»e = on the screen by (15)^ V-E vanishes there be-
cause of (^), while V. â‚¬. =0 at the screen since the sources do not extend
' â€” mc

to the screen.^ These properties of f ensure that it will vanish identically
provided that it vanishes as the edge is approached radially. We shall there-
fore examine the behavior of ^ near the edge; as we shall see, the divergence
\ri.ll vanish there provided the functions F^ and Fp are suitably chosen.

First, as mentioned above, V'ÂŁ. =0 near the edge. Next we ob-
' ' â€” mc

serve from (12), that the singular part of the expansion of V-E is given by

the form\ila (note: Ty^WP sin /2) = - -SyWP cos

2

Online LibraryL. B FelsenRelation between a class of two-dimensional and three-dimensional diffraction problems → online text (page 2 of 3)