Effects of Localized Defects / Sources in a Periodic Lattice Using Green's Function of Periodic Scatterers

A novel method is developed to efficiently analyze the effects of localized defects and excitation sources in a periodic array of scatterers such as photonic crystals and metamaterials. The Green's function of the periodic scatterers and the free space Green's function are used to formulate a set of coupled surface integral equations (SIEs) over one or multiple enclosed surfaces surrounding the localized defects and / or excitation sources. The defects can be the removal, deformation, displacement, or distortion in material properties of a scatterer in localized cells. The Green's function of the periodic scatterers represent the field response due to a point source inside the array of the periodic scatterers. The periodic scatterer Green's function is only required to be calculated once to solve any form of defects and/or sources in the localized region of interest. The Green's function of the periodic scatterers can be also represented using few band solutions of the periodic lattice by using the newly developed BroadBand Green's Function with Low wavenumber extraction (BBGFL) technique. This renders the approach applicable to efficient broadband simulations of localized defects / sources analysis and designs.