Transverse magnetic plane-wave scattering equations for infinite and semi-infinite rectangular grooves in a conducting plane

The transverse magnetic plane-wave scattering equations for infinite and semi-infinite rectangular grooves (RGs) in a conducting plane are proposed in terms of the overlapping T-block method and Floquet theorem. By utilising the Floquet theorem and taking the limit of multiple RGs as the number of RGs becomes infinity, the simultaneous solutions of infinite RG are then analytically obtained. Combining the analyses of infinite and large number of RGs yields approximate yet numerically efficient scattering equations for semi-infinite RG. Numerical computations are performed to verify that the solutions converge fast and agree with the mode-matching method.