Bounds on the Elements of the Equivalent Network for Scattering in Waveguides. II. Application to Dielectric Obstacles

Abstract

The theory developed in the companion article for obtaining rigorous bounds on cotη, where η the phase shift, is applied to scattering by dielectric obstacles in rectangular waveguides. For the obstacles considered here, bounds are also obtained on the phase shifts directly and on the elements of the equivalent T network. The exact solution for a dielectric slab of finite length, which extends to the conducting boundaries of the waveguide and completely encloses the obstacle, is introduced as a convenient trial function. The permittivity of the slab is retained as a parameter which is varied to improve the bounds. In the expressions for the bounds on cotηe and cotη0, the particular obstacle configuration appears only in certain integrals of relatively simple form. Numerical results are obtained for large and small obstacles of various shapes, including some truly three-dimensional cases. The upper and lower bounds on the phase shifts and on the elements of the equivalent circuit are found to be quite close to one another. In one case, the bounds obtained by using the simple trial function are compared with the bounds obtained by using the trial function which generates the Schwinger integral variational principle.