The continuous spectrum of open waveguides of nonseparable cross section

The authors introduce and obtain in principle the continuous spectrum of a large class of open waveguides of nonseparable cross section in full hybrid form. From the formal statement of completeness, they derive the field components of the continuum in the terms of E _x, E_z. Continuity at the interface yields an eigenvalue equation for the transverse admittance, whose solution determines the whole field. The particular case of vanishing eigenvalue constitutes the standard transverse resonance for the discrete modes. A variational solution of the eigenvalue problem is outlined, although further detailed work is required for any specific guide geometry