Complex-Valued Functionals in Variational Analysis of Waveguides with Impedance Boundaries

摘要

Stationary complex-valued functionals are discussed and seen to have unique stationary points if they are analytic, which corresponds to analyticity of functions in complex-valued function theory. As an application, the problem of wave propagation in a circular waveguide with an impedance boundary, along with the corresponding two-dimensional resonator problem is considered. It is seen that the variational method for nonstandard eigenvalue problems, introduced a few years ago, can be generalized to complex-valued functionals if the functional is analytic. The method can be applied to result in simple analytic formulae for the waveguide with impedance boundaries.