Orthogonality relations for the eigenmodes of lossy anisotropic waveguides (fibres)

The system of the eigenmodes propagating along an anisotropic fibre is constructed by the S-operator method. The fields of the radiation modes are shown to be unbounded at infinity in cross-section. For these modes the orthogonality relations are derived with the help of regularisation of divergent integrals. The normalising factor is demonstrated to be expressed in terms of the eigenvectors of the Sˆ-operator. The results obtained are applied to an excitation problem. The structure of the far-zone fields is analysed