Orthogonal and non-orthogonal devices in polarization optics

Unlike the homogeneous basic ("canonical") polarization devices, many inhomogeneous (multilayer) polarization devices have non-orthogonal eigenvectors. They may be called non-orthogonal devices. Their operators pertain to a class of operators unusual in physics and somewhat peripheral even in the linear operator theory - the non-normal operators. Moreover, the operators of some multilayer polarization devices are of a very pathological kind: singular and defective (with the eigenvectors collapsed onto one and the corresponding eigenvalue equal to zero). In this paper we give a comparative analysis of some of the most widespread orthogonal and non-orthogonal multilayer polarization devices - to which correspond normal and non-normal operators, respectively -on the basis of the spectral theorem of linear algebra in a pure operatorial (non-matrix) Dirac-dyadic language.