T-matrix method

The T-matrix method is a computational technique of light scattering by nonspherical particles originally formulated by P. C. Waterman (1928-2012) in 1965. The technique is also known as null field method and extended boundary technique method (EBCM). In the method, matrix elements are obtained by matching boundary conditions for solutions of Maxwell equations.

The incident and scattered electric field are expanded into spherical vector wave functions (SVWF), which are also encountered in Mie scattering. They are the fundamental solutions of the vector Helmholtz equation and can be generated from the scalar fundamental solutions in spherical coordinates, the spherical Bessel functions of the first kind and the spherical Hankel Functions. Accordingly, there are two linearly independent sets of solutions denoted as ${\displaystyle \mathbf {M} ^{1},\mathbf {N} ^{1}}$ and ${\displaystyle \mathbf {M} ^{3},\mathbf {N} ^{3}}$, respectively. They are also called regular and propagating SVWFs, respectively. With this, we can write the incident field as

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