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Mie Theory and the Discrete Dipole Approximation. Calculating Radiative Properties of Particulate Media, with Application to Nanostructured Materials

Abstract : Radiative transfer in a semi-transparent medium can be described by a spacetime dependent directional monochromatic specific intensity field L λ (r, n,t), where λ is the wavelength, r the field point, n the unit direction vector, and t the time. This field L λ (r, n,t) obeys an integro-differential equation called the radiative transfer equation (RTE) which has the general form [1]: 1 c λ ∂ L λ (r, n,t) ∂t + n · ∇ r L λ (r, n,t) = −(κ λ + σ λ)L λ (r, n,t) + κ λ n 2 λ L 0 λ T (r,t) + σ λ 4π 4π Φ λ (n , n)L λ (r, n ,t)dΩ. (7.1) In this formulation, c λ is the speed of energy propagation in the semi-transparent medium, while ∇ r is the gradient with respect to position r, n λ is the refractive index, i.e., the real part of the complex optical index m λ of the medium, T (r,t) is the temperature field in the medium, and L 0 λ (T) is the specific intensity of the equilibrium radiation at temperature T. Finally, κ λ , σ λ , and Φ λ (n , n) are the bulk radiative properties of the medium, viz., its absorption coefficient, scattering coefficient , and scattering phase function, respectively. Introducing the extinction coefficient β λ = κ λ + σ λ and scattering albedo ω λ = σ λ /β λ , the steady-state version of the RTE (7.1) (valid on time scales such that the propagation of radiation can be assumed instantaneous) can be written in the form 1 β λ n · ∇ r L λ (r, n,t) = −L λ (r, n,t) + (1 − ω λ)n
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Franck Enguehard. Mie Theory and the Discrete Dipole Approximation. Calculating Radiative Properties of Particulate Media, with Application to Nanostructured Materials. Thermal Nanosystems and Nanomaterials, 118, pp.151-212, 2009, Topics in applied physics, ⟨10.1007/978-3-642-04258-4⟩. ⟨hal-01287434⟩

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