Beam wakes for canonical chambers with anisotropic surface impedance

We consider analytical expressions for beam impedance of round, rectangular and $\Pi$-shaped waveguides with anisotropic surface impedance of arbitrary nature. The formulas are given for relativistic and non-relativistic cases when the surface impedance matrix has only diagonal elements. For round pipe and the relativistic limit a result for arbitrary impedance matrix is presented. The field matching technique for layered structures with layers of uniaxial anisotropy and anisotropic impedance boundary condition at the last layer is described. The analytical techniques are applied to the real structure examples with corrugations, dielectrics and anomalous skin effects