Bloch Analysis of Lossy Metal-Only Interleaved Glide-Symmetric Mushrooms and Application to Wideband Reflecting Luneburg Lenses

We present a novel solution based on the multimodal transfer-matrix method for the Bloch analysis of general two-dimensional periodic (2D-periodic) structures to rigorously characterize finite conductivity and surface roughness losses, thereby overcoming limitations of commercial full-wave electromagnetic solvers. The approach reformulates the 2D Bloch analysis into a set of equivalent one-dimensional periodic problems defined along the main edges of the irreducible Brillouin zone associated with the unit cell under investigation. This dimensional reduction significantly suppresses numerical noise while also enhancing computational efficiency and improving the robustness of the extracted complex dispersion characteristics. Building on this framework, we propose and analyze a novel metal-only interleaved glide-symmetric mushroom unit cell implemented in a parallel-plate waveguide. The proposed topology is benchmarked against an interleaved glide-symmetric bed-of-nails configuration, demonstrating a higher achievable effective refractive index, reduced frequency dispersion, increased compactness, and comparable isotropy. These features make the unit cell well suited for the synthesis of wideband graded-index lenses requiring high refractive-index values and isotropic behavior. The simulations further show that the advantages of interleaving persist when compared with both non-interleaved glide-symmetric and conventional periodic structures. To optimize unit cell parameters and enhance operational bandwidth, we introduce a general design methodology based on the local frequency variation of the refractive index with respect to geometrical parameters. Finally, the capabilities of the proposed unit cell are demonstrated through the design of a wideband reflecting Luneburg lens operating in K-band.