Spurious Mode Free Broadband Green’s Function Technique for Periodic Scatterers Using The Combined Field Integral Equation Formulation

Abstract

The recently developed broadband Green’s function technique provides an effective and novel approach to characterize the bands of periodic scatterers. It converts an electric field integral equation (EFIE) or a magnetic field integral equation (MFIE) into a linear eigenvalue problem of moderate size through representing the lattice Green’s function in a hybrid form that includes an exponentially convergent spatial series and a fast convergent spectral series. The linear eigenvalue problem then yields all the bands of interest simultaneously. However, the bands derived from the linear eigenvalue problem is reported to include both physical modes and spurious modes. Thus, it takes extra efforts to reject the spurious modes through checking the extinction theorem. And numerically checking the extinction theorem requires intelligent supervision and decreases the overall efficiency of the algorithm. In this paper, a new strategy is devised to formulate an easy-to-handle linear eigenvalue problem from the combined field integral equation (CFIE) with the hybrid representation of the Green’s function. The CFIE is a linear combination of the EFIE and MFIE with judiciously chosen combination coefficients. The Nystrom method is utilized to discretize the CFIE into matrix equations to ensure high accuracy and reach agreement between EFIE and MFIE. This new linear eigenvalue problem is shown to have only physical modes as its eigenvalues on the real axis. This work represents a huge leap in making the broadband Green’s function a practical technique.