Question

Q3) An incident wave travels in free-space along the z-direction and impinges upon a cube of dielectric material with a constant permittivity of ε. The faces of the dielectric cube are parallel to the x-y. y-z, x-z planes. The length of each side of the cube is d. The polarization of the incident electric field is along the x-axis. Use the Born approximation to calculate the scattered electric and magnetic fields in the far-field zone along the ks-R, =+x and k = +y directions.

Answer 1

In Born Approximation for zone scattering field (1) E^- 1_s = exp (- j k r)/r Q_1 (k^^_s, k^^_i) (2) Q_1 (k^^_s, k^^_i) = {E_0 integral_v exp [j (k_s - k_i) r] delta epsilon_p (r) dv} [e^^_i - (e^^_i k^^_s) k^^_s} where k_i = k_z^^, e^^= x^^, delta epsilon (r') = epsilon - epsilon_0 within this approximation no wave is scattered along k^^_s = plusminus x^^i.e along a direction parallel to the polarization of incident plane. Along k^^_s = plusminus z^^, k^^_s = plusminus y^^the scattered wave is polarized along x^^= e^^_i as e^^_i k^^_s = 0 integral of equation (2) gives k^^_s = plusminus y^^(epsilon - epsilon_0) exp [j n(I k y^^- k z^^) r] dv = (epsilon - epsilon_0) integral_v exp (plusminus j k y - j k z) dv = 4 a (epsilon - epsilon_0)/k^2 sin^2 (ka/2) \r\n in case of k^^_s = plusminus z^^(epsilon - epsilon_0) integral_v exp [j (plusminus k z^^- k z^^) r] dv = { (epsilon - epsilon_0) a^3, k^^_s = + z^^(epsilon - epsilon_0) a^2/k sin (k a), k^^_s = -z^^(epsilon - epsilon_0) a^2/k sin (k a), k^^s = -z^^