A perfectly conducting flat screen occupies half of the x-y plane (i.e., x 0 and wave number
Question:
A perfectly conducting flat screen occupies half of the x-y plane (i.e., x 0 and wave number ? is incident along the z axis from the region z 0. Let the coordinates of the observation point be (X, 0, Z).
(a) Show that, for the usual scalar Kirchhoff approximation and in the limit Z >> X and ?kZ >> 1, the diffracted field is
Where x = (k/2Z)1/2X.
?(b) Show that the intensity can be written
I = |?|2 = I0/2[(C (x) + ?)2 + (S (x) + ?)2]
Where C(x) and S(x) are the so-called Fresnel integrals. Determine the asymptotic behavior of I for x large and positive (illuminated region) and x large and negative (shadow region). What is the value of I at X = 0? Make a sketch of I as a function of X for fixed Z.
(c) Use the vector formula (10.101) to obtain a result equivalent to that of part a. Compare the two expressions.
Step by Step Answer:
a b 1 k 2i ro eikrp Io Aperture p dA To is the observation point and rp xX y Y 2 Z ...View the full answer
