Efficient calculation of the dispersion diagram of planar electromagnetic band-gap structures by the MoM/BI-RME method

The characterization of planar electromagnetic band-gap structures requires the calculation of the dispersion diagram of the modes supported by the periodic structure and the phase of the reflection coefficient under plane-wave illumination. In this paper, we present a novel method for the calculation of the dispersion diagram. The electromagnetic analysis is based on the method of moments/boundary integral-resonant mode expansion (MoM/BI-RME) method and leads to the formulation of a homogeneous matrix problem. The solution of this problem is performed by an iterative procedure: for a given value of the propagation phase constant, the frequency range is scanned to find the frequencies where the field equation has a nontrivial solution. The search of these frequencies is based on the tracking of the eigenvalues in the complex plane, and proved more efficient than other classical methods (direct search of the determinant zeros, singular value decomposition). The reflection coefficient can be readily determined by using the MoM/BI-RME method, already developed for the analysis of the scattering from frequency selective surfaces. The method is applied to the characterization of the classical uniplanar, compact photonic-bandgap structure, and analysis results show the accuracy of the method, its efficiency, and its convergence properties.