Superposition T-matrix method

For a system of Af particles with o = f3i = 7 = 0, I = 1,2,. ..,AA, the transformations of the vector spherical vector wave functions involve only the addition theorem under coordinate translations, i.e., 

The precedent equations can be written in explicit form by indicating the vector and matrix indices 

The expansions of the incident and scattered fields in each particle coordinate system. 

The representation of the field exciting a particle by a single-field expansion (which includes the incident field and the scattered fields from all other particles). 

The solution of the transmission boundary-value problem for each particle. 

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Liu L, Mishchenko MI, Amott WP A smdy of radiative properties of fractal soot aggregates using the superposition t-matrix method, J Quant Spectrosc Radiat Transf 109(15) ... 

The interaction effect is taken into account in steps 2 and 3, where the scattered fields from other particles are transformed and included in the incident field on each particle, while the interference effect is taken into account in steps 1 and 4 that address the incident and scattered path differences, respectively. For a system of TV spheres, the individual component T matrices are diagonal with the standard Lorenz Mie coefficients along their main diagonal, and in this case, the superposition T-matrix method is also known as the multisphere separation of variables technique or the multisphere superposition method [21,24,29,72,150]. Solution of (2.144) have been obtained using direct matrix inversion, method of successive orders of scattering, conjugate... 

In the following analysis, we derive (2.144) and (2.145) by using the superposition T-matrix method. The field exciting the /th particle can be expressed as... 

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