ELECTRODYNAMICS PROBLEM SET 9 due April 13 th , before class I. REFLECTION WITH DISPERSION A plane wave of frequency ω is incident normally from vacuum on a semi-inﬁnite slab of material with a complex n ( ω ). a) Show that the ratio of reﬂected power to incident power is R = ± ± ± ± 1-n ( ω ) 1 + n ( ω ) ± ± ± ± 2 . (1) II. ANISOTROPIC MEDIUM Plane waves propagate in a homogeneous, nonpermeable ( μ = 1) but anisotropic dielectric medium. The dielectric is characterized by a tensor ± ij such that D i = ± ij E j . ± ij is symmetric so it can be diagonalized by choosing an appropriate orthogonal coordinate system. . a) Show that plane waves with frequency ω and wave vector k must satisfy k × ( k × E ) + ω 2 c 2 D = 0 . (2) b) Show that for a given wave vector k = k n there are two distinct modes of propagation with diﬀerent phase velocities v = ω/k which satisfy the Fresnel equation : 3 X i =1 n 2 i v 2-v 2 i = 0 , (3) where v i = c/ √ ± i and n i is the i th component of k / | k | . III. ORDERS OF MAGNITUDE
This is the end of the preview. Sign up
access the rest of the document.
This note was uploaded on 12/29/2011 for the course PHYSICS 606 taught by Professor Bedaque during the Spring '11 term at Maryland.