Complex Waves in Lossless Dielectric Waveguides

The rebuttal of the existing theory of complex waves is given and new approach is proposed. Unlike the existing one, the new theory, basing on the investigation of the properties generalized symmetric eigenvalue problem, is mathematically sound, provides a number of useful orthogonality relations and allows one to predict which structures and which modes are liable to create complex waves when perturbed with an even slight dielectric inhomogeneity. Moreover, it clearly explains the relation between complex and backward waves.