Spatial transform techniques like transformation optics and conformal mapping have arisen as the dominant techniques for designing metamaterial devices. However, these techniques only produce the electrical permittivity and permeability as a function of position. The manner in which these functions are converted into physical metamaterial lattices remains elusive, except in some simple or canonical configurations. Metamaterial lattices designed by spatial transforms are composed of elements of different sizes, orientations, and designs. The elements must be distributed and oriented in a manner that makes the final lattice smooth, continuous, have uniform density, be free of unintentional defects, and have minimal distortions to the elements. Any of these would weaken or destroy the electromagnetic properties of the lattice. This paper describes a general purpose method to generate such arbitrary metamaterial lattices. Inputs to the algorithm are the permittivity and permeability functions as well as the baseline metamaterials that can provide the necessary permittivity and permeability values. In prior research, we reported a simple finite-difference technique for calculating the permittivity and permeability functions for arbitrary shaped devices using transformation optics. The present work is illustrated by generating an electromagnetic cloak of arbitrary shape that was designed using the previously reported technique. The final metamaterial cloak is simulated using the finite-difference time-domain method and performance compared to other cloaks reported in the literature.
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