Multiple Scattering of Waves in 3D Crystals (Natural or Photonic) Formed by Anisotropically Scattering Centers

This paper considers the refraction and diffraction of waves in three-dimensional crystals formed by anisotropically scattering centers. The partial wave expansion method is used to consider the effect of multiple rescattering of waves by centers composing a crystal. The expression for the refractive index of a crystal is derived. It is shown that instead of the diagonal elements of the scattering matrix $\mathbf{T}$, appearing in the expression for the refractive index of a chaotic medium, the derived expression includes the diagonal elements of the reaction matrix $\mathbf{K}$. This fact is taken into account in writing the equations describing the dynamical diffraction of waves in a crystal. The results can be of interest for research into, e.g., diffraction of cold neutrons and photons in crystals, nanocrystalline materials, as well as for the description of parametric and diffraction radiation in electromagnetic crystals formed by anisotropically scattering centers.