Modal analysis of arbitrary-shaped 2D periodic structures printed on a grounded dielectric slab: Real and complex solutions

In this paper a full-wave numerical approach devoted to modal analysis of planar 2D periodic structures printed on a grounded dielectric slab with arbitrary metallization within the unit cell is presented. The proposed technique is based on a mixed-potential integral equation, solved by the method of moments in the spatial domain. Twodimensional periodic vector and scalar Green's functions are derived in the spectral domain; this permits to properly account for leakage effects by choosing the correct spectral determination for each spatial harmonic. Real propagation constant for surface waves in their pass-band regimes and complex propagation constant both for bound modes in their stop-band regimes and for proper and improper leaky modes can be efficiently derived. Results for a uniplanar compact photonic bandgap structure, demonstrating the capabilities of this approach, are reported in this paper.