Full-wave analysis of bound and leaky modes propagating along 2D periodic printed structures with arbitrary metallisation in the unit cell

A full-wave numerical approach for the analysis and design of two-dimensional printed periodic structures on a grounded dielectric slab is presented. Electromagnetic band-gap surfaces, metamaterials and leaky-wave antennas are important special cases of structures that can be analysed. The proposed technique permits the analysis of an arbitrary metallisation within the unit cell; it is based on a mixed-potential integral equation solved by the method of moments in the spatial domain. Two-dimensional periodic vector and scalar Green's functions are derived in the spectral domain and an appropriate choice of the spectral determination for each spatial harmonic is performed to properly account for leakage effects. The proposed approach is used to calculate the real propagation wavenumber for surface waves in their pass-band regimes, propagating at arbitrary angles on two-dimensional periodic printed structures. Complex propagation wavenumbers can be derived as well for both bound modes in their stop-band regimes and proper and improper leaky modes in their relevant physical and non-physical regions. Results for a reference uniplanar compact photonic bandgap structure are reported demonstrating how the application of this rigorous technique provides a new detailed picture of the different modal behaviours and a more accurate determination of its band-gap zones.