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Introduction

The general formulation of the problem of light scattering (diffraction) is rather simple. The field $\vec{E}_0$ is incident on a scatterer of the volume $V$, and creates the field $\vec{E}_{\rm i}$ inside the scatterer and an additional (diffraction) field $\vec{E}_{\rm s}$ outside it. Thus, from Maxwell's equations one should find the total field $\vec{E}$ equal to $\vec{E}_{\rm i}$ inside $V$ and to $\vec{E}_0 + \vec{E}_{\rm s}$ outside $V$ and satisfying the boundary conditions on $V$. 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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