Using a discrete dipole approximation to predict complete scattering of complicated metamaterials

We develop a numerical technique for simulating metamaterial electromagnetic response based on an adaptation of the discrete dipole approximation (DDA). Our approach reduces each constituent metamaterial element within the composite to a point dipole with electric and magnetic polarizabilities, rather than assuming a homogenized effective material. We first validate the approach by computing the scattering cross-section for a collection of densely spaced isotropic dipole moments arranged within a cylindrical area, and compare with the known result from Mie theory. The discrete dipole approach has considerable advantages for the design of gradient and transformation optical media based on metamaterials, since the absence of local periodicity in other common design approaches leaves them with questionable validity. Several variants of iconic cloaking structures are investigated to illustrate the method, in which we study the impact that different configurations of dipolar elements can have on cloak performance. The modeling of a complex medium as polarizable dipoles provides a much closer connection to actual metamaterial implementations, and can address key nonlocal phenomena, such as magnetoelectric coupling, not accessible to most current numerical metamaterial approaches.