Efficient Band Characterization of 3D Periodic Scatterers Using Broadband Dyadic Green's Function of Vector Potential A

The broadband Green's function method is applied to characterize the band diagram and modal fields of 3D periodic PEC scatterers, and it converts the band characterization problem into a linear eigenvalue problem. This is the first time that the broadband Green's function method is used to deal with 3D scattering problem of periodic scatterers. Distinct from the conventional surface integral equation (SIE) formulation using electric field E and the magnetic field H, we formulate the SIE using the vector potential A and its dyadic Green's function. The periodic dyadic Green's function of vector potential A is represented in a fast convergent Floquet plane wave series and an exponentially convergent spatial series evaluated at an imaginary wavenumber. The Galerkin's method is applied to discretize the SIE into a matrix form, where RWG basis functions and rooftop basis functions are used to represent the vector and scalar unknowns on the surface, respectively. This matrix equation is then converted into a linear eigenvalue problem of a moderate size with the help of the hybrid representation of the periodic dyadic Green's function. The solution to the linear eigenvalue problem then yields all the band solutions and modal fields of the periodic scatters simultaneously.