The general formulation of the problem of light scattering (diffraction)
is rather simple.
The field is incident on a scatterer of the volume ,
and creates the field
inside the scatterer and
an additional (diffraction) field
outside it.
Thus, from Maxwell's equations one should find the total field
equal to
inside and to
outside and satisfying the boundary conditions on .
Despite the simplicity of the scheme, a concrete solution
of the problem essentially depends on the geometry of the
scatterer and its structure.
For instance, even for spherical scatterer with an anisotropic
tensor of the refractive index, a general solution
cannot be obtained in a closed form
[7].
Therefore, in the theory of light scattering by small particles
one has developed various methods whose applicability regions and
efficiency depend on the concrete conditions.
In this part we discuss the exact methods which include both
the analytical and numerical approaches, since from a contemporary point
of view
an efficient numerical algorithm realized at a computer is
equivalent to an analytical solution which as a rule also needs
non-trivial calculations.
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