Green’s functions, including scatterers, for photonic crystals and metamaterials

Abstract

The Green’s functions are physical responses due to a single point source in a periodic lattice. The single point source can also correspond to an impurity or a defect. In this paper, the Green’s functions, including the scatterers, for periodic structures such as in photonic crystals and metamaterials are calculated. The Green’s functions are in terms of the multiband solutions of the periodic structures. The Green’s functions are broadband solutions so that the frequency or wavelength dependences of the physical responses can be calculated readily. They are obtained by integrating the periodic Green’s function including the scatterers in the Brillouin zone. Low wavenumber extraction methods are used to accelerate the convergence rate of the multiband expansions. The low wavenumber component represents the reactive near field. The band solutions of the periodic structure are obtained from a surface integral equation solution, which is effectively converted to a linear eigenvalue problem, giving multiple band solutions simultaneously. Numerical results are illustrated for the band modal fields, the periodic Green’s functions, and the single point source Green’s functions for two-dimensional (2D) perfect-electric-conductor (PEC) scatterers in a 2D lattice.