Interference structure of the Mie extinction cross section

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Abstract
It is shown that, in the large-size-parameter region (x ≫ n2/2) the Re(an + bn) is independent of the summation index n. For real refractive indices m < 2.5 the dominating term of Re (an + bn) has an x dependence of the form sin2[(m − 1)x] leading to the periodicity of Re(an + bn) and of the extinction curve QEXT(x) given by Δx = π/(m − 1). The derived periodicity is the same as the periodicity of interference structure derived by using the anomalous diffraction approximation; however, our derivation is not limited by the anomalous diffraction condition m − 1 ≪ 1. At refractive indices m > 2.5 the extinction curve does not have a simple periodic structure, since several terms of approximately equal magnitudes and different x dependences contribute to the Re(an + bn).