A plane wave E 0 exp[i(k 0 r t)] scatters from a dielectric cube with
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A plane wave E0 exp[i(k0 · r − ωt)] scatters from a dielectric cube with volume V = a3 and electric susceptibility χ << 1. Two cube edges align with k0 and E0.
(a) Calculate the differential scattering cross section in the Born approximation.
(b) Show that σBorn ≈ 1/4 k2a4χ2 when ka >> 1. The near-forward direction dominates the scattering when ka >> 1.
(c) The weak scattering assumed by the Born approximation implies that|Erad|/|E0|<<1 for all q, even when r ≈ a. Deduce from this that the ka. >> 1 result of part (b) is valid only when σBorn << χa2.
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