Electromagnetic Wave Scattering at the Junction of Semi-Infinite 2-D Media With Forced Refraction

Three-dimensional and 2-D artificial media with forced refraction (MFR) are widely used for the design and fabrication of 3-D and 2-D planar microwave lenses with low optical aberrations and a wide field of view. An important aspect of their study is the electromagnetic analysis of wave interactions at the border of the artificial medium (external space) and at the border of two media with different parameters. In this article, we consider 2-D MFR on the base of a metal ribbon grating with an electrically small period placed inside a parallel plate waveguide (PPW). Approximate boundary conditions of anisotropic conductivity are used for the grating modeling. First, the junction of two semi-infinite media is studied. One is a medium with forced refraction, and the second is 2-D medium in the form of a semi-infinite PPW. The boundary problem is analytically solved using the Wiener–Hopf technique, and the solution is presented in the form of a generalized scattering matrix (GSM). Second, the junction of two MFR is analyzed with the GSM method. Finally, we analyze the obtained solutions and derive simple relations for the reflection coefficients of dominant modes in both junctions. Theoretical solutions are verified by the HFSS electromagnetic simulator.