Construction of variational principles and variational bounds in waveguide scattering

Using projection operators, a variational-bound formulation is presented which, together with some previous work, can provide both upper and lower variational bounds on the phase shifts or equivalent network elements associated with obstacles located in waveguides. The scattering parameters for dielectric rectangular-parallelepiped obstacles in single and multimode waveguides serve as numerical examples to demonstrate the applicability of the method.