CONTINUOUS-SPECTRUM, CHARACTERISTIC MODES, AND LEAKY WAVES OF OPEN WAVE-GUIDES

The modes of open waveguides with nonseparable cross sections are deri ved by means of an extension of the resonance equation for the electro magnetic field. Such modes, forming a continuous spectrum, allow us to apply to discontinuity problems in open environments the techniques o riginally developed for closed waveguides. In this paper, the resonanc e equation is generalized according to functional analysis considerati ons. By this approach, it is possible to derive the modal spectrum fro m the simultaneous diagonalization of the real and imaginary parts of the admittance of the structure. A variational interpretation of the s olution of the generalized resonance equation gives additional insight into the modes of open waveguides. The generalized resonance equation , when applied to three-dimensional objects, provides the well-known c haracteristic modes of these structures. The relationship between cont inuous spectrum, characteristic modes, and leaky waves is also discuss ed.