Variation of device topology for material simplification as three-dimensional transformation optics methodology

摘要

A three-dimensional (3-D) transformation optics (TO) methodology is presented using polyhedral meshing and homogeneous materials, in which, the topology of the device is varied, in order to achieve material simplification. The device is divided into a minimal number of polyhedral segments, and a linear transformation is applied to each polyhedron. The polyhedrons and transformations are tried to be chosen so that the volume is conserved through the transformation, and if possibly, some transformed materials are equivalent to free space. A few 3-D waveguide coupler and carpet cloak problems are solved to demonstrate and evaluate the proposed methodology. For instance, it is shown that a right-angle 3-D rectangular waveguide bend can be designed using only one two-dimensional (2-D) homogeneous material. Also, resize couplers are designed using only one or two 2-D homogeneous materials. A carpet cloak is demonstrated which uses only two material types, filling five polyhedral meshing segments. Similar problems would have required much larger number of meshing segments and material types, using previous methods. Therefore, using the proposed methodology, 3-D TO-based guiding and cloaking devices will be more feasible. Furthermore, a 3-D finite difference time domain (FDTD) method is developed to verify the results of some examples.